> I need to know how to calculate x^y where y is not an integer. Any > help in this matter would be appreciated. Depending on where one is in number theory, one can do one of the following. [1] If y is a rational number, write y = p/q and compute the q'th root of x^p. For example, 6^(2/3) is equal to the cube root of 6^2 = 36. Of course x^(-y) = (1/x)^y = 1/(x^y). [2] If y is not a rational number, one can use logarithms: x^y = exp(y * log(x)). This form is also useful in problems involving calculus. Note that log(x) has periodicity 2 * pi * i, if one is in the complex plane; this can lead to somewhat odd results. -- #191, ewill3@earthlink.net It's still legal to go .sigless. ==== > > I need to know how to calculate x^y where y is not an integer. Any > help in this matter would be appreciated. With x positive x = e ^ ln (x), substitute back into expression and evaluate. ==== > [ how to calculate x^y where y is not an integer?] With x positive x = e ^ ln (x), substitute back into expression and > evaluate. > An example may help. If given the chore of computing 7.5 ^ 12.34 you'd compute ln(7.5) as about 2.0149030, take that times 12.34 to get about 24.863903, and then take e^(24.863903) which is 6284286702.63, the final answer. I'm away from my trusty calculator, but in Win95 left-clicked on Start button, Programs, Accessories, Calculator, 7.5, ln button of calculator, * button, 12.34, = button, filled in the inv check-box, clicked on ln button again{which performed an e^x operation and cleared the inv checkbox.} ==== > I need to know how to calculate x^y where y is not an integer. Any > help in this matter would be appreciated. If y is rational, i.e. y = a/b, then b th root (x^a). For example, x^2/3 = cube root of (x^2). Otherwise, check out: http://mathworld.wolfram.com/Power.html Lurch ==== > I need to know how to calculate x^y where y is not an integer. Any >> help in this matter would be appreciated. If y is rational, i.e. y = a/b, then b th root (x^a). For example, x^2/3 = cube root of (x^2). Otherwise, check out: http://mathworld.wolfram.com/Power.html ??? I don't see a mathematical definition of x^y on that page, nor anything else that might be what he's looking for when he asks how to calculate it... >Lurch > ************************ David C. Ullrich ==== >> I need to know how to calculate x^y where y is not an integer. Any >> help in this matter would be appreciated. >If y is rational, i.e. y = a/b, then b th root (x^a). For example, >x^2/3 = cube root of (x^2). Otherwise, check out: >http://mathworld.wolfram.com/Power.html ??? I don't see a mathematical definition of x^y on that > page, nor anything else that might be what he's looking > for when he asks how to calculate it... >Lurch > ************************ David C. Ullrich Is that your profound contribution? Lurch ==== >>I have another more general question, if you don't mind : is there an >>intuitive meaning for a nilpotent group ? Nilpotent groups are closely connected to nilpotent lie algebras, >which is where the name actually comes from, as I understand it, and >where nilpotent actually makes some sense. >As to intuitive meaning, that will depend a lot on you, I guess. [...] >Others think of them as groups constructed through central extensions, >which is not a bad way to think about them either. Some of us just instinctively think, Product of p-groups. Realistically I just think about p-groups, period, and then mutter something about direct products at the end of the story. (And if you want an intuitive meaning of p-groups, think about layers of small vector spaces over the field of characteristic p, forming the quotients of chains of normal subgroups. I don't necessarily think only of central extensions, by the way; in fact one of the prototypes I keep in mind is a semidirect product of a Z/p acting on a p-dimensional vector space over GF(p). I'll bet most people don't think about the dihedral group of order 8 this way...) Of course, some of us carry along a related intuitive notion that group means finite group. You'll have to modify the previous paragraph if you think otherwise. dave X-Received: (from approve@localhost) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBSDc1T02534; ==== [.snip.] J. Willekens ==== > Notice that the in Noble Verse 57:25 above, Allah Almighty says clearly We > sent down iron.... and He didn't say We created iron from earth.... > Allah Almighty's claim was very accurate and precise. We sent down > iron..... clearly states that iron was created outside the earth and was > brought down by the Will of Allah Almighty for a purpose, and that is > (material for) Mighty war, as well as many benefits for mankind, that Allah > Noble Quran, 57:25) > Hypothetically, if this is proven incorrect, and the iron did not come down, would you be willing to give up on the Quran? Bill X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 02:12 PM, Mark K. Bilbo said: >There is no down in space. There is if you send a goose up. I don't know if that's enough down for a jacket. -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org ==== speak thusly: > at 02:12 PM, Mark K. Bilbo said: > >>There is no down in space. > > There is if you send a goose up. I don't know if that's enough down > for a jacket. The poor goose... -- Mark K. Bilbo X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 07:30 PM, Goran Jakupovic said: >Like somebody else already said not just iron, but all atoms starting >with helium and heavier now in solar system were products of >supernova. No. Helium is predominantly primordial, Beryllium and Lithium are almost entirely primordial. The conditions for light element nucleosynthesis are very different from the conditions for heavier elements. Stars produce Helium, but they destroy Lithium and Beryllium. There's more Helium in the Universe now than right after the big bang, but not a lot more. -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org ==== > down is relative like meaning closer to core like when you get down > from > bed. but the quran has things being created on earth but for some odd > reason > it diverges with iron. it says we sent down iron. iron was not created > on > earth according to quran. how did the quran know that iron came down? > down > meaning from elsewhere. it was not made on this earth. god caused iron > to > descend. coincidence? > > It's untrue. Iron was here when the earth was formed. It did not come > later. > And if anything, it came up from the core from volcanoes and the like. > > you are mistaken in a small way. iron not even from this solar system. it > came from other stars and had to land on earth. maybe it was primitive > molten earth but earth was here. if earth was not here what iron land on? > simple logics no offense. the miracle is that quran say many things created > on earth and if this book from man who forging gods word man just say iron > like people and animals and plants and mountains was created on earth. but > for some reason quran treats iron different and say that it is sent down to > earth. why not just say it was created on earth? because that would be > wrong. -- > saab siddiqui al mujahed > but you have to change the (a) to @ for it to work Iron is an element, copper is an element, carbon is an element, and so on. What scientific basis do you have for your belief that iron came latter than the others? What made up the earth that the iron landed on? Bill ==== thusly: > >> thusly: >> right. i did not say it came to earth after it finished with animals > plants >> and all that. i only noted that the quran has many things created on > earth >> but for some reason does not have iron created on earth. >> What about all the *other elements that weren't formed here? > > what about them? are you trying to raise an argument ex silentio? if it > turns out on usenet you never once say your mothers maiden name does that > necessarily mean you did not know your mothers maiden name? as for the > elements other than iron i will be agnostic on what the author of the quran > knew about them for now. So this is like one of those christian arguments. God failed to mention anything *useful like penicillin but seems to have mumbled something vague about iron. -- Mark K. Bilbo <245fb07.0312261913.713872dc@posting.google.com> X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 07:13 PM, raynand@netzero.net (Jefferson Rourke) said: >Atheism is simply a lack of belief in gods. No, that's Agnosticism. Atheism is the belief in the lack of a god. -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org ==== > at 07:13 PM, raynand@netzero.net (Jefferson Rourke) said: > >Atheism is simply a lack of belief in gods. > > No, that's Agnosticism. Atheism is the belief in the lack of a god. How about un-theist. Does that work for you? I think the god-concept is a nonexistant mind created reality that it is used as a tool to dupe the gullible. I think religious mysticism is a form of mental illness and madness that is unique to the human mind on this planet. This still work for you? I think the god-concept and religion have held back the development of the human race by 2000 to 3000 years. Instead of looking for the nonexistent afterlife the human race should be working to build a better life here and now. If not for religion and the god-concept it is a possible that we could be on other planets by now and have lifespans of over 500 years. The loss and waste of potential in the human race because of the god-concept is immense. Still working for you? If all of this does not fit within your definition parameters please let me know about my ill-defined thought processess. Jefferson Rourke Laissez-Faire! <245fb07.0312261913.713872dc@posting.google.com> <3fee0f44$21$fuzhry+tra$mr2ice@news.patriot.net> <245fb07.0312272002.3afa03c1@posting.google.com> X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 08:02 PM, raynand@netzero.net (Jefferson Rourke) said: >How about un-theist. Does that work for you? It's not a question of whether it works for me; it's a question of whether it works for the English language. The English terms are agnostic and atheist. What would work for me is honesty, which you are not exhibiting. >I think religious mysticism is a form of mental illness and madness >that is unique to the human mind on this planet. Then you were lying when you stated that Atheism is simply a lack of belief in gods. You have gone beyond not believing in a god to believing that there is no god. >I think the god-concept and religion have held back the development >of the human race by 2000 to 3000 years. Perhaps it did. And perhaps it had the oposite effect. Do you have evidence, or is it just a matter of faith for you? >Still working for you? Nope. But if your faith works for you, . . . >If all of this does not fit within your definition parameters please >let me know about my ill-defined thought processess. You might start with post hoc ergo propter hoc. -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org ==== > at 08:02 PM, raynand@netzero.net (Jefferson Rourke) said: > >How about un-theist. Does that work for you? > > It's not a question of whether it works for me; it's a question of > whether it works for the English language. The English terms are > agnostic and atheist. What would work for me is honesty, which you are > not exhibiting. I honestly answered the first time. Atheism is a lack of belief in gods. It works just fine for my use of the english language. >I think religious mysticism is a form of mental illness and madness >that is unique to the human mind on this planet. > > Then you were lying when you stated that Atheism is simply a lack of > belief in gods. You have gone beyond not believing in a god to > believing that there is no god. Are you really this simple? Can you read the definition you were given? A pro-individual, free market laissez-faire capitalist like myself could be an atheist or a statist, communist could be an atheist. Both lack a belief in gods but they have totally different philosophies and world views yet both are atheists. How does my thinking that the god-concept is a mind disease change my atheism (lack of belief in gods)? You are not making sense. >I think the god-concept and religion have held back the development >of the human race by 2000 to 3000 years. > > Perhaps it did. And perhaps it had the oposite effect. Do you have > evidence, or is it just a matter of faith for you? Look at the history of the Catholic church. Look at the history of Islam. Look at history period. If you would like me to cite references I can do so. How about the thousands of books and multiple libraries that were burned by the church and christians at the beginning of the Dark Ages? What was burned? Gnostic Basilides. Porphyry's 15 volume treatise condemning christianity. Emperor Theodosious had 27,000 papyrus scrolls burned because they contained the doctrinal basis for the gospels. By offering rich rewards Ptolemy Philadelphius gathered 270,000 ancient documents and burned them. It was said in jest that christians heated their baths with the ancient wisdom/knowlege of Greece and Rome. The leaders of the Crusades burned all of the books they could find including ancient Hebrew scrolls. Pope Gregory VII (1021-1085) burned the entire Apollo library to the ground. In 1233 the works of Maimondes were burned along with 12,000 volumes of the Talmud. In 1244 18,000 books of various kinds were destroyed by religious leaders. According to one eyewitness account, Cardinal Ximenes delivered to the flames in the square of Granada 80,000 Arabic manuscripts. This is the tip of the iceburg my friend. Do you think the destruction of all of this knowledge and the anti-knowledge attitudes of the authorities at this time might have had a wee bit to do with the human race entering the Dark Ages? August 24, 1572 10,000 Protestants were slaughtered by order of Pope Gregory XIII. Crusades. Witch burning. Killing of heretics etc. etc. It has been estimated that 250,000,000 human beings have been killed in the name of your nasty god-concept throughout recorded history. Do you think the destruction of all of these people and their potential may have held up the development of the human race? I could go on and on and on but time doesn't allow for it. Try looking up a little history besides that shit we were taught in the public school system. >Still working for you? > > Nope. But if your faith works for you, . . . Haven't been paying attention have you? You should have phrased it as my lack of faith in your mind created god-concept works just fine for me. >If all of this does not fit within your definition parameters please >let me know about my ill-defined thought processess. > > You might start with post hoc ergo propter hoc. Don't know what this means. But if you really wanted me to know the meaning you would have posted it in english instead of trying to make yourself look like something you aren't. Jefferson Rourke Laissez-Faire! ==== speak thusly: > at 08:02 PM, raynand@netzero.net (Jefferson Rourke) said: > >>How about un-theist. Does that work for you? > > It's not a question of whether it works for me; it's a question of > whether it works for the English language. The English terms are > agnostic and atheist. What would work for me is honesty, which you are > not exhibiting. Nope. Wrong. Some of the colloquial connotations that have accreted to the words are similar to what you're claiming but colloquial meaning shifts around all the time. Atheism is lacking belief in any gods. The word was coined to mean that. That is what atheists use the word to mean. That is the meaning. -- Mark K. Bilbo ==== thusly: >> at 07:13 PM, raynand@netzero.net (Jefferson Rourke) said: >> >>Atheism is simply a lack of belief in gods. >> >> No, that's Agnosticism. Atheism is the belief in the lack of a god. > > How about un-theist. Does that work for you? I think the god-concept > is a nonexistant mind created reality that it is used as a tool to > dupe the gullible. Actually, there's no point to trying to change terms. Theists would trash any term used. And atheism actually *is un- or maybe more accurately non- theism. Since a- means without. As in amoral means *without morals as contrasted to immoral which is *not moral. The in- prefix meaning opposite of or not. What they try to claim is atheism is, is more something you might call intheism (to coin a word). That would be opposite of theism. Atheism works fine. Fits the way we do things in the language (hence the word was brought into the language to mean without theism). Theist misunderstanding or even deliberate obfuscation notwithstanding... -- Mark K. Bilbo ==== > thusly: > >> at 07:13 PM, raynand@netzero.net (Jefferson Rourke) said: >> >>Atheism is simply a lack of belief in gods. >> >> No, that's Agnosticism. Atheism is the belief in the lack of a god. > > How about un-theist. Does that work for you? I think the god-concept > is a nonexistant mind created reality that it is used as a tool to > dupe the gullible. > > Actually, there's no point to trying to change terms. Theists would trash > any term used. > > And atheism actually *is un- or maybe more accurately non- theism. > Since a- means without. As in amoral means *without morals as > contrasted to immoral which is *not moral. The in- prefix meaning > opposite of or not. > > What they try to claim is atheism is, is more something you might call > intheism (to coin a word). That would be opposite of theism. > > Atheism works fine. Fits the way we do things in the language (hence the > word was brought into the language to mean without theism). Theist > misunderstanding or even deliberate obfuscation notwithstanding... Hey Mark: I was just trying to have a bit of fun with the guy and see what his response would be. I thought I had the definition right the first time and I was writing off of the top of my head without double checking. Hope you had a happy Winter Solstice, Jefferson Rourke ==== thusly: >> thusly: >> > at 07:13 PM, raynand@netzero.net (Jefferson Rourke) said: > >Atheism is simply a lack of belief in gods. > > No, that's Agnosticism. Atheism is the belief in the lack of a god. >> >> How about un-theist. Does that work for you? I think the god-concept >> is a nonexistant mind created reality that it is used as a tool to >> dupe the gullible. >> >> Actually, there's no point to trying to change terms. Theists would trash >> any term used. >> >> And atheism actually *is un- or maybe more accurately non- theism. >> Since a- means without. As in amoral means *without morals as >> contrasted to immoral which is *not moral. The in- prefix meaning >> opposite of or not. >> >> What they try to claim is atheism is, is more something you might call >> intheism (to coin a word). That would be opposite of theism. >> >> Atheism works fine. Fits the way we do things in the language (hence the >> word was brought into the language to mean without theism). Theist >> misunderstanding or even deliberate obfuscation notwithstanding... > > Hey Mark: > > I was just trying to have a bit of fun with the guy and see what his > response would be. I thought I had the definition right the first time > and I was writing off of the top of my head without double checking. No big thing. I was just rattling along on an interesting (to me at least) subject. I can't help it. I'm moving more and more into linguistics as (if things hold together) will be my next field. Words fascinate me to no end... -- Mark K. Bilbo ==== speak thusly: > at 07:13 PM, raynand@netzero.net (Jefferson Rourke) said: > >>Atheism is simply a lack of belief in gods. > > No, that's Agnosticism. Atheism is the belief in the lack of a god. No, atheism is lacking belief in gods. We know, we're atheists. -- Mark K. Bilbo X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 11:42 AM, Saab Siddiqui said: >im snipping mr metz points that i have no response to at this >time. Good; that is proper quoting style for Usenet. You'll see people is generally something to avoid and not to imitate. >not that star collide with earth but that matter from star like iron >collide with earth. The Earth was formed by the accretion of matter. Much of that matter was Iron. There was already a substantial amount of Iron when the Earth was very small. The material that fell later included a lot of elements besides Iron, and had no higher percentage of Iron than the initial material. Given the outgassing of lighter elements, the primordial proto-Earth probably had a higher concentration of Iron than the new material falling on it did. -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 04:56 PM, Mark K. Bilbo said: >The process is that iron forms in stars. The stars go nova and eject >material which includes iron. No. Iron forms in significant quantities only in stars that go supernova. A simple nova is not hot enough or dense enough. -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== >Not just large, but dense. A white dwarf star is about the size of >the Earth, Well, I prefer a yellow dwarf, but would rather that it remain a safe 93,000,000 miles away ;-) >I do wonder what would happen if the impacting object was a neutron star, Lethal. The details would depend on the size, but I imagine that the radiation would kill us before we had a chance to observe the rest. -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 01:51 AM, Steve Knight said: > Great. Some camel fucking, rag head, sand muncher, At least he is not a racist xenophobe like you. *PLONK* -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org ==== >How do you prove what the (imaginary) zeroes of the Fibonacci polynomials >are? http://mathworld.wolfram.com/FibonacciPolynomial.html F(1,x)=1 >F(2,x)=x >F(k,x)=xF(k-1,x)+F(k-2,x) Let G(T,x) = sum F(k,x) T^k, so that (1 - x T - T^2) G(T,x) = T, so that G(T,x) = T/(1-xT-T^2) which we can expand using partial frations: G(T,x) = a(x)/(1-r(x)T) + b(x)/(1-s(x)T) where r(x) and s(x) are the roots of the quadratic Z^2 - x Z - 1 . Then F(k,x), which is the coefficient of T^k in G, is simply a(x) r(x)^k + b(x) s(x)^k. So the roots are the values of x which make ( r(x)/s(x) )^k = -b(x)/a(x). I make it out to be that a(x) = 1/sqrt(x^2+4) and b(x) = - a(x), so -b(x)/a(x) = 1. So the roots are the values of x which make r(x) = zeta s(x) where zeta is any k-th root of unity. I further find r and s to be x/2 +- sqrt(x^2+4)/2, so this is equivalent to the equations x + sqrt(x^2+4) = zeta ( x - sqrt(x^2+4) ) [Note that zeta <> 1] (zeta + 1) sqrt(x^2+4) = (zeta - 1) x (zeta + 1)^2 (x^2+4) = (zeta - 1)^2 x^2 (4 zeta) x^2 + 4 (zeta + 1)^2 = 0 x^2 = - (zeta + 1)^2 / zeta Writing zeta = exp( 2 pi i p/k ) we can then rewrite the last line as x = ( +- i) (exp( 2 pi i p/(2k) ) + exp( - 2 pi i p/(2k) ) = ( +- i) 2 cos( pi p/k ). dave ==== >How do you prove what the (imaginary) zeroes of the Fibonacci polynomials >are? >http://mathworld.wolfram.com/FibonacciPolynomial.html >F(1,x)=1 >F(2,x)=x >F(k,x)=xF(k-1,x)+F(k-2,x) Let G(T,x) = sum F(k,x) T^k, so that (1 - x T - T^2) G(T,x) = T, so > that G(T,x) = T/(1-xT-T^2) which we can expand using partial frations: > G(T,x) = a(x)/(1-r(x)T) + b(x)/(1-s(x)T) where r(x) and s(x) are > the roots of the quadratic Z^2 - x Z - 1 . Then F(k,x), which > is the coefficient of T^k in G, is simply a(x) r(x)^k + b(x) s(x)^k. > So the roots are the values of x which make > ( r(x)/s(x) )^k = -b(x)/a(x). I make it out to be that a(x) = 1/sqrt(x^2+4) and b(x) = - a(x), > so -b(x)/a(x) = 1. So the roots are the values of x which make > r(x) = zeta s(x) > where zeta is any k-th root of unity. I further find r and s to be > x/2 +- sqrt(x^2+4)/2, so this is equivalent to the equations > x + sqrt(x^2+4) = zeta ( x - sqrt(x^2+4) ) [Note that zeta <> 1] > (zeta + 1) sqrt(x^2+4) = (zeta - 1) x > (zeta + 1)^2 (x^2+4) = (zeta - 1)^2 x^2 > (4 zeta) x^2 + 4 (zeta + 1)^2 = 0 > x^2 = - (zeta + 1)^2 / zeta > Writing zeta = exp( 2 pi i p/k ) we can then rewrite the last line as > x = ( +- i) (exp( 2 pi i p/(2k) ) + exp( - 2 pi i p/(2k) ) > = ( +- i) 2 cos( pi p/k ). > it yet. ==== > Don > > Have you looked at > > http://www.utm.edu/research/primes/mersenne/ > > 163 does not appear here either. > > Mike Yes, thanks Mike. Tom, Greetings, Re: Mersenne numbers, Mp163 .MZD03-Oct.MPTH163 The search for Mersenne primes begins by looking for small factors of (mersenne numbers) 2^prime -1. That's what I did. My letter proves a low factor for 2^163-1. Showing (on a pocket calculator) that it ISN't a Mersenne PRIME. I have photographed mersenne number plates MP163 and MP67 in my (one street away.) And Mercurial factorisation HG 7817 etc. LN 2718, PI 315, PI 180. All in Newtown. = 70^2 + 14^2 == 5200 -2*52. = 14^2 x(5^2+1.) I have also eliminated some exponents about recent world records on sci.math , groups.google.com. About 2^(13.4 million) -1. e.g. 'twin primes about mersenne prime exponent.' or 'factors of mersenne numbers.' ?? 80mill... divides M_13mill... search don.lotto@paradise.net.nz Gimps require one supercomputer week to prove the world's largest known prime number. After it has been selected by 200,ooo distributed personal computers.(??) Penguin dictionary of curious +interesting numbers states (1987) 29th mersenne prime = M_132049. This held me up for a while. The revised edn (David Wells 1997) gives that Mp as the 30th and inserts a more recent M_110503 as 29th. Unfortunately I missed that interesting date 11.05.03 and 25th = 21.7.01. 29th = 1.3.2049 etc. there seem to be lots. They are supposed to say (probably-possibly the 40th Mersenne prime) if not all indicies have been checked twice. Readers Guide abstracts reported M_858433 is prime?. I confirmed a FACTOR and possibly reported a typo. In fact it should be M_859433 may be prime. I advised author David Wells of a number of errors in [1987] and he acknowledged me in Revised Edn [1997.] (I claim 1/*61 and 7^*510 and 1215306625.eis) I have about 45 sequences in On-line encyclopedia of integer sequences. search google njas research eis lookup. Don.McDonald 29.12.03 23:13 > > myfile.> DON02. Calc.Factors.FermatMers.Mersenne.CARMP163.SPMP163 > subject:Mersenne numbers, Mp163 > D.Calc.Factors.FermatMers.Mersenne.CARMP163.SPMP163 > > We look at the usual long multiplication of, for > example, 123*48. ... In message you write: > Dear > nzlc teletext powerball#860 total prize pool $34million lies. > teletext pball#860 total prize pool $34mill lies. > > 10 lotto always add twice..lies. (teleph keypad) > very deceptive and misleading. > > how many ticket sells?. > $7.248 588 million powerball. > > > don.mcdonald 27.12.03 23:23 > 04/389-6820. > >>D.LOTTO.lotoadvice.clients.NZLCLotter.pball+twic > > check-- > > > (prob) -- #formula,-- value, -- FACTORS -- , (centiseconds). > --- > 2 860 # draw powerball..=860= 2^2*5*43*all 3cs > 27.12.03 > > divis 1 roll down. > winners x $ dividend. > > 3 11*1558133 div 2..=17139463= 11*19*82007*all 7cs > 4 95*714 div 3..=67830= 2*3*5*7*17*19*all 4cs > 5 725*151 divis 4..=109475= 5*5*29*151*all 4cs > 6 3328*55 divis 5..=183040= 2^8*5*11*13*all 4cs > 7 8899*28 divis 6..=249172= 2^2*7*11*809*all 4cs > > 9 p(3)+p(4)+p(5)+p(6)+..p(7).. > total dividends should be $17.7 mill > > =17748980= 2^2*5*887449*all 11cs > > 10 lotto always add twice..lies. (teleph keypad) > =568625929723389440= Accy?(2^2*3*7*167* 47s. > > 11 34748980 tot prize pool > too big by $ 17.ooo,ooo m..=34748980= 2^2*5*7*47*5281*all 7cs > > 14 210*323 primorial..=67830= 2*3*5*7*17*19*all 5cs > 15 double digit bounce..(teleph keypad > =36825334448268624= Accy?(2^2*3*19*2^2*53*761861437609prime 1mn > > 16 55331155338899..=55331155338899= 11*43*116979186763prime 39s. > > e n d. prog c241Q 24.2.03 close *spool > ==== The opposite of a profound truth is another profound truth. -- Niels Bohr What Rovelli doesn't seem to understand is that this all makes perfect sense once you give up strict equivalence and distinguish the background and physical metrics. JS: I do not understand this distinction. Please give more details what you mean. PZ: In that case you don't understand Newtonian physics either, which makes precisely this distinction: you don't understand the Newtonian distinction between real and fictitious forces. But at least you are honest enough to admit it. :-) JS: What I understand is that fictitious or inertial forces are artifacts of the non-geodesic timelike motion of the local frames of reference. I understand Coriolis, centrifugal, standing on a scale in an elevator as inertial forces. I also understand that LOCALLY there is, APPROXIMATELY, no way to distinguish the inertial force from a gravity force or G-force on a SINGLE TEST PARTICLE 1 NOT ON A TIMELIKE GEODESIC in sense of connection field for parallel transport (Experiment A), IF one MAKES NO ATTEMPT to measure the relative tidal acceleration between TWO OTHER TEST PARTICLES 2 & 3 BOTH ON TIMELIKE GEODESICS with ZERO G-FORCE (Experiment B). My OPERATIONALISM is showing, which you ignore in your too abstract formal analysis. Therefore, you end up in a false comparison comparing apples to oranges so to speak by confounding the essentially different, indeed, complementary in Bohr's sense of total experimental arrangements - even of macro relevance, Experiments A & B. Further, I do not see how you tie that to strict equivalence, which, if I understand you, you say is fundamentally wrong in some way? I do not understand how you mean background and physical above. Do you mean nondynamical and dynamical. The problem is that you introduce key terms without enough contextual background to understand what you mean. In many cases an equation would eliminate the ambiguity. Now if you mean by strict equivalence that Einstein did not include Experiment B as a matter of principle in his early formulations, then if indeed, that is historically correct, then he may have made an error that was later corrected and is completely corrected in MTW (1973), which I suppose you say EEP is a correspondance, which is always the way I viewed it to begin with. If indeed your history of the evolution of Einstein's thought on his own theory is correct, I do not know if it is, then it is a minor footnote only. I am sure similar stories exist in the evolution of all the great theories of physics from Newton on. Have you read pp. 112 - 114 that completely demolishes Hal Puthoff' s use of dr/dt = c' = c/K radial null geodesic in his Tables. PZ: It does no such thing. I would not even characterize pp 112-114 as an argument. It is simply a sketch of a model in which *everything* is quantized except the raw manifold. JS: It shows no intrinsic meaning to Puthoff's r and t as he means it in his Tables. PZ: In Rovelli's approach, almost everything is quantized and time itself has no fundamental meaning. So, OK, things are VERY different in Rovelli's theory. No argument there. He wants to dig down to the raw manifold so he can quantize the stripped-off Einsteinian chronogeometric structure of spacetime, replete with its unified metric, thinking this may be the real solution to the quantum gravity conundrum. I say he has not properly understood the status and meaning of the unified metric. He has simply skated over this. He is trying to run before he can walk. ... What does he mean by fluctuations? JS: What do you mean by kinematical g_uv and dynamic gravitational g_uv apart from Ruvwl = 0 in the former and not in the latter. PZ: I mean what it means in Newtonian physics. JS: Huh? Newton uses forces with action at a distance. He never invokes any geometrodynamical replacement of forces the way Einstein does. Newton never talks of a metric so what do you mean? Do you simply mean again the distinction between inertial and non-inertial frames of reference? There are no fictitious or inertial forces in inertial frames. Newton only had implicitly the idea of a global frame of reference not local frames of reference on a rigid Euclidean space with a rigid absolute time. Einstein in 1905 unified rigid space and rigid time into a rigid space-time in which space and time separately were no longer rigid. Special Relativity uses a NONDYNAMICAL background RIGID 4D space-time that ACTS on MATTER WITHOUT BACK-ACTION of MATTER on space-time. Einstein by 1915 corrects that approximation in General Relativity. Space-time GEOMETRY is now DYNAMICAL in TWO WAY RELATION (Bohm and (MASS-ENERGY). Similarly, nonlocal linear unitary evolving orthodox micro-quantum theory with signal locality has a NON-DYNAMICAL BIT pilot wave relative to its IT extra-variable. The BIT is of course DYNAMICAL relative to its ENVIRONMENT via boundary conditions, stochastic pumps, semi-classical couplings etc. I am only here talking SELF-REFERENTIAL DYNAMICS of a kind not even recognized in other interpretations of micro-QM where IT FROM BIT (Wheeler) BIT is complete description of micro-quantum reality. This includes all collapse models with the possible exception of Penrose's OR and all many-worlds models from Everett to Gell-Mann/Hartle to David Deutsch's multi-verse and also Cramer's transactional. Shelly Godstein takes a wrong turn IMHO in his Bohmian Quantum Gravity paper in Physics Meets Philosophy at the Planck Scale in rejecting a source for the pilot wave where it is most important on the vast scale of the Universe in the FRW limit. In contrast to micro-quantum theory, MACRO-QUANTUM THEORY is P.W. Anderson's More is different in action IMHO. MACRO-QUANTUM THEORY is local, non-unitary nonlinear with presponse (Dick Bierman) signal nonlocality in the sense of Antony Valentini's violation of sub-quantal heat death. The nonlocal linear micro-quantum Schrodinger equation in the configuration space of entangled parts of the whole is replaced by a local nonlinear MACRO-QUANTUM Landau-Ginzburg equation coupled to a residual micro-quantum Schrodinger equation in the sense of the old two-fluid model of Tiza but now generalized. This seems to go against some of Lenny Susskind's and t'Hooft's ideas and seems to support some of Hawking's older ideas on information loss in black holes. However, I am not sure of that. Lenny et-al seems to want to misapply micro-quantum theory in the MACRO-domain ignoring PW Anderson's More is different? I could be wrong. We shall see. The phase-transition from an unstable completely random white zero point noise micro-quantum vacuum to a metastable MACRO-QUANTUM VACUUM with colored zero point noise controlled by Vacuum Coherence has a lower q-entropy defined as log of the phase space needed by the vacuum. 96% of the stuff of The World, we have been forced by the weight of FACTS to expand our notion of MATTER as MASS-ENERGY to include VIRTUAL ZERO POINT ENERGY or EXOTIC VACUA. Zero Point energy has w = Pressure/Energy Density = -1. Dark energy is exotic vacuum with negative micro-quantum pressure and dark matter is the same, but with positive pressure. All lepto-quarks have dark matter vortex string cores which prevent the distributed electric charge of the IT extra-variable from exploding. This is consistent with J.P. Vigier's notion of tight atomic states and it solves the old Abraham-Becker-Lorentz self-energy of the electron problem from ~ 100 years ago. The smallness of the cosmological constant is not solved by string theory as Ed Witten admits, but it is, IMHO, solved by MACRO-QUANTUM VACUUM COHERENCE. http://qedcorp.com/APS/EmergentGravity.pdf Key prediction: No dark matter detector will click with the right dark stuff because all dark stuff is virtual not real. Dark stuff looks like w ~ 0 at a distance but up close it is w = -1 as one day interstellar space probes using dark energy weightless warp (Alcubierre) drives will confirm. What is interesting about Lenny Susskind's theory however is the connection between black holes and elementary lepto-quarks and gauge force bosons as merely a matter of the complexity or bit length of the strings in which string has dual meaning as vibrating strings of energy and strings of computer theory in the sense of algorithmic complexity and all that. This is already seen in black hole thermodynamics where Area/Lp^2 ~ number of bits and the world hologram idea. ==== > Sure, math has little to do with actual numbers. But sometimes you > need to look at literals to look for patterns. Even when you're > result is radix neutral, the elegance of hexadecimal will set your > brain in a mode of logic and intelligence. Unless you're examining > bowling scores, use hexadecimal. Re: Hexadecimal leads to insight. google 4e6 in hex (= 3d 0900.) don.mcdonald 3 dimension phone calls. 30.12.03 X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 03:36 PM, Timothy Murphy said: >Isn't that all equipment? Only if 18 is a multiple of 4. -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 05:54 AM, mensanator@aol.compost (Mensanator) said: >Which explains why DEC used octal for 16-bit registers and 20-bit >addressing? When did I ever say that everything DEC did with the PDP-11 was reasonable? For that matter, when did I ever say that anything DEC did with the PDP-11 was reasonable? More to the point, A implies B is not equivalent to B implies A. -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org ==== >Message-id: <3fee0d35$13$fuzhry+tra$mr2ice@news.patriot.net > at 05:54 AM, mensanator@aol.compost (Mensanator) said: >Which explains why DEC used octal for 16-bit registers and 20-bit >>addressing? When did I ever say that everything DEC did with the PDP-11 was >reasonable? For that matter, when did I ever say that anything DEC did >with the PDP-11 was reasonable? When did I say it was unreasonable? My point apparently went completely over your head. What you _did_ say was Headecimal is only reasonable for equipment that deals with numbers in bytes that are multiples of 4 bits. It would be unreasonable for the PDP-11 to use hex because the index register designations are three bits, thus making the machine language more easily interpreted when the dump is in octal. If the PDP-11 had 16 registers instead of 8, then it would be reasonable to use hex. Note that this has nothing to do with word size or addressing. Of course, a real programmer would understand that. More to the point, A implies B is not equivalent to B implies A. -- Mensanator Ace of Clubs X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 01:17 AM, mensanator@aol.compost (Mensanator) said: >My point apparently went completely over your head. No, your point was simply irrelevant. >What you _did_ say was >with numbers in bytes that are multiples of 4 bits. > K3wl. No read it very carefully and note what I did *NOT* write in it. >It would be unreasonable for the PDP-11 to use hex >thus making the machine language more easily >interpreted when the dump is in octal. Only for people whose ability to do mental arithmetic is impaired. >Note that this has nothing to do with word size or addressing. I note your belief to that effect. >Of course, a real programmer would understand that. ROTF,LMAO! There is a difference between understanding why somebody did something stupid and pretending that it wasn't stupid. The fact that I don't agree with the decision doesn't mean that I didn't understand it before you were born. I repeat, >>More to the point, A implies B is not equivalent to B implies A. You quoted it, but appear to have not read and understood it. -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org ==== > Making a mistake on sci.math is a good way to attract _corrections_. > You could have learned what you've learned about analytic > continuation a lot faster if you'd simply tried to avoid being > certain you were right and everyone else was wrong, _even > though_ (as you _said_) you did not understand the construction > that others were talking about. To all: please excuse my not being good at following what others have done. So, there are two approaches to the construction of a Riemann surface from a given relation f(w,z)=0: the original which goes from relation to system of branches to Riemann surface, and the modern which bypasses the introduction of branches. But one may think that branches are worth studying for there own sake, and then in context just think of Riemann surfaces as a byproduct. This is about branches. Branches cannot be studied from the given equation on its own. Auxillary entities have to be introduced, first an ordinary point z0 in the z-plane to serve as an initial value for z. This done the solutions of the equation f(w,z0)=0, say w1, w2, w3... will be initial values for branches. Now, permutations on branches produced by analytic continuation round closed circuits are already determined without the branches as yet being fully specified. A circuit from z0 passing among but not through singularities and returning to z0 sends each initial value into an initial value which may be the same or different. The permutation depends only on the homotopy class of the circuit. These classes depend in turn on the branch points which are determined by the given equation. So one gets the idea that associated with a specific branch point there may be a specific branch permutation. It turns out that this is only so when another auxillary entity, namely a set of branch boundaries, is introduced. So one arrives at a theory but one which depends on auxillary entities which are arbitrary. At this point it is useful to take a short digression into the philosophy of language. A statement may be made in different languages but must be made in some language. So it can be claimed that a statement is language-independent only in the sense that it is translatable. This is the best that can be done. By analogy what is needed in the present theory is to show that from a result for one set of auxillary entities a result for any other can be derived. This is easy and well known for an alternative initial point. The two points are joined by an arc and the arc added to the circuit. It is not quite as simple for an alternative set of boundaries but it can be done. With this, branches and permutations on branches are treated in a way which is as general as it can be. ==== [lots of stuff] I think you've got it. Good show. Lee Rudolph ==== It's just pretty depressing to > see a book tell you that you have learned next to nothing that you should know > coming into graduate school. Any comments or advice would be appreciated, > including book suggestions (the author tends to say I've heard that > such-and-such book is good though I have not seen it which is pretty odd > considering the focus of the book). You may have trouble getting into a top ranked graduate program if your background is deficient. However, what's far more important is what you do in the graduate school you do get into. Many will allow you to take a few undergraduate courses to firm up your background. Another clue to what you will eventually need to know is the book of problems from UCBerkely qualifying exams published by Springer. Don't let snobs tell you that a PhD from a less than top-ranked school is worthless. It isn't. What is important is to work with an active and productive researcher with a national (or international) reputation in his/her field of research. Such people will make sure you do a good thesis and will be able to write letters that say what prospective employers want to hear. There are such people even at lower ranked schools due to the bad job market of recent years. You may even do better than you might at a top school because as a good student you'll get a lot more attention than you would otherwise. ==== > I checked out a book called All the Mathematics You Missed [But Need to Know > for Graduate School] from the library and was surprised by its contents. The > book is divided into 16 sections that I am supposed to know before I get > into > graduate school. This is my last year and I can check off very little. > > Here are the sixteen topics that I need to know along with whether or not I > will have completed them by the end of the year: > [...] > I know that looks awful, even beyond awful, with 5/16. I don't think it's > realistic that I could learn that much material over the Summer. Which areas > do I absolutely need to know? > That kind of depends on what the grad school you go to expects. For example, some schools will expect you to have some familiarity with undergraduate complex analysis in their graduate complex analysis course, and some won't. What may be most helpful is to take a look at Lebesgue integration. At least get a rough outline of what it's about. And in particular, you can be more careful about checking details and stuff for the preliminary stuff like measures and sigma algebras. This is probably one of the harder topics in a first year grad course, and it helps to get a start on it. Another thing is to learn some point set topology before you get to grad school. It shouldn't be too hard to learn, given that you've had real analysis. This will really help in learning graduate level analysis. Even though there is such a thing as graduate point set topology, few places offer a course in it, and many assume you've learned undergrad point set topology somehow. There's nothing like walking into an analysis or algebraic topology class and learning that you're *supposed* to know what a locally compact, connected, Hausdorff space is. You might as well learn about Gaussian curvature of surfaces in R^3. It motivates a lot of very advanced material that you may very well run into in some of your classes. And it's a relatively simple topic that is fun to learn about. It should offer a nice respite from Lebesgue integration or whatnot. There's more stuff you could learn (like the generalized Stokes theorem), but probably it not essential, and you have more than enough on your hands already. > Is this book very accurate in what I SHOULD know for graduate school? Almost > everything seems to roughly fall under analysis/applied math. [...] I think so. Note your ideas about applie math are rather misguided. > > The strange thing is that, besides applied math classes, I'm taking or have > taken what they offer in terms of pure math. It's just pretty depressing to > see a book tell you that you have learned next to nothing that you should know > coming into graduate school. Cheer up; you have a jump on all your future classmates who will not have a clue that they should know these things. Sometimes it takes people a year or two in grad school before they realize they need to remedy their ignorance in some of these topics, and then it's very late and hard to fix. Besides, doesn't the author say he doesn't expect the reader to know all these things? After all, look at the title; clearly he expects you to have missed some of the topics. The emphasis should be on the phrase *should know*. I could go on all day about what you should'a, but it won't help you much. > Any comments or advice would be appreciated, > including book suggestions (the author tends to say I've heard that > such-and-such book is good though I have not seen it which is pretty odd > considering the focus of the book). > > I remember flipping through this book at Borders, and thinking the references were rather scanty in some spots. with the list of references for those topics in the book, so I can comment on whether I think they are sufficient or lacking. I remember most seemed sufficient. ==== I'll try to clear a few things up. The lowest grade I've made in a math course is a B+. Normally I just get A's. For what it's worth, my school is a Tier 2 school according to US News and World Reports. It also has a PhD program. Some of the professors that are well known do not want to teach undergraduates, so that is partly (I think) why topology is not offered. I'm interested in algebra and number theory. That is why I was surprised when the book had only 2 sections on algebra and none on number theory. I've taken the regular number theory course and an algebraic number theory one as well. Two of the Professors that are writing my recommendations were disappointed with where I wanted to apply. One of them has told me that I have research potential but I guess that can be interpreted as just being nice. ==== [...] | Two of the Professors that are writing my recommendations were disappointed | with where I wanted to apply. One of them has told me that I have research | potential but I guess that can be interpreted as just being nice. Take it seriously if they think you should try applying to some better schools. It's too bad you didn't get better opportunities as an undergraduate, but consider that water under the bridge. It's still some years from when you have to do anything, but one thing you might want to keep in mind for when you get there: If you wind up in a PhD program which is only okay, but you have reason to believe you're doing thesis work of a higher caliber (so it seems like you might be on your way to being underrated), I'd recommend trying to get letters of recommendation from bigger names in addition to your advisor. I was always crummy at self-promotion, but even I know that it does your career good to be well- connected. So as you get into a field, get acquainted with some of the people already established in it. When you get good results, see if you can get favorable letters. It was heartening when I was looking for mathematical jobs when someone from one of the schools I'd had an interview with came up to me afterward, and said something like, Hey, Professor [name] was just telling us about you, and evidently it was something good he'd told them. Not that I got the job :-( but it sure can help the odds. I remember a guy who managed to get a letter of recommendation from Deligne saying something like, this guy solved a problem we tried to solve. He did get the job! Keith Ramsay ==== > I'll try to clear a few things up. The lowest grade I've made in a math course > is a B+. Normally I just get A's. For what it's worth, my school is a > Tier 2 school according to US News and World Reports. It also has a > PhD program. Some of the professors that are well known do not want to > teach undergraduates, so that is partly (I think) why topology is not > offered. your school does not seem impressive at all. even in cases where prefessors do not like teaching undergrads, an undergrad topology course offering is a must. of course that can be resolved by offering independent studies. does your school offer such? if it does, why didn't you study undergrad topology independently? > I'm interested in algebra and number theory. That is why I was surprised > when the book had only 2 sections on algebra and none on number theory. > I've taken the regular number theory course and an algebraic number > theory one as well. in general, a gap in undergrad algebra, advanced calculus, and topology is a very serious one for anyone pursuing a graduate math degree. a gap in number theory is not. > Two of the Professors that are writing my recommendations were disappointed > with where I wanted to apply. assuming your report is accurate, your professors have good reasons to be dissapointed - graduate math degrees from unranked programmes are generally worthless in the job market. > One of them has told me that I have research potential but I guess that > can be interpreted as just being nice. true. but if his/her assessemnt is accurate, then you should endeavour to fill in the gaps in your undergrad math preparation and then shoot high for a ranked math graduate school. ==== >I'll try to clear a few things up. The lowest grade I've made in a math course >is a B+. Normally I just get A's. For what it's worth, my school is a Tier >2 school according to US News and World Reports. It also has a PhD program. >Some of the professors that are well known do not want to teach undergraduates, >so that is partly (I think) why topology is not offered. I'm interested in algebra and number theory. That is why I was surprised when >the book had only 2 sections on algebra and none on number theory. I've taken >the regular number theory course and an algebraic number theory one as well. Two of the Professors that are writing my recommendations were disappointed >with where I wanted to apply. One of them has told me that I have research >potential That's different. You didn't mention those letters in your original post. You should apply to a few good schools. Those professors have a better idea than you do about your ability compared to the students those places usually admit. The worst that could happen is they turn you down... >but I guess that can be interpreted as just being nice. No. Math professors are not nice. It's a condition of employment. ************************ David C. Ullrich ==== > I'll try to clear a few things up. The lowest grade I've made in a math > course > is a B+. Normally I just get A's. For what it's worth, my school is a Tier > 2 school according to US News and World Reports. It also has a PhD program. > Some of the professors that are well known do not want to teach > undergraduates, > so that is partly (I think) why topology is not offered. > > I'm interested in algebra and number theory. That is why I was surprised when > the book had only 2 sections on algebra and none on number theory. I've taken > the regular number theory course and an algebraic number theory one as well. > > Two of the Professors that are writing my recommendations were disappointed > with where I wanted to apply. One of them has told me that I have research > potential but I guess that can be interpreted as just being nice. > Hmm...this is interesting. It sounds like to me that they think you could do better. Perhaps you are being overly pessimistic. Granted, the discussion on sci.math thus far has not been encouraging, but it has mostly centered around getting into really hard schools. Your professors probably have a better idea than you of where you can get in. If they think you can get in somewhere better, then follow their advice! Your professors may also have a better reputation than you think. Even if they're not hotshots (that don't teach, as you mention above), you shouldn't dismiss them; if they have decent reputations, and/or have connections, you could do very well with their recommendations. Am I right in thinking that you've decided to apply to some masters programs, instead of some doctoral programs? I urge you to read my other posts in this discussion. Basically, you may very well be shooting yourself in the foot if you decide to go the masters route. ==== > Am I right in thinking that you've decided to apply to some masters > programs, instead of some doctoral programs? I urge you to read my > other posts in this discussion. Basically, you may very well be > shooting yourself in the foot if you decide to go the masters route. I should say that I agree with Chan-Ho Suh here. (Surprise!) I think that the best reason to go to a masters program, for someone who someday hopes to get a doctorate, is that they have failed to get into the sort of doctoral programs they think they need in order to succeed. I think this is true for all disciplines, actually. Some of the comments here suggest that a masters may be a positive detriment to some math PhD programs; but if you could have gotten a decent doctorate anyway, then in any discipline, math or not, the masters is really only a waste of a couple years. Note that this is the hidden message of the Philosophical Gourmet excerpt I quoted. The only reason to get a masters is if without it, you would not be able to get into a decent doctoral program. Perhaps it doesn't help in math as much as it might in some fields, but regardless, if you can get into a decent doctoral program, then you shouldn't get a separate masters first. And the only way to know if you can get into a decent doctoral program is to apply. Thomas ==== > Two of the Professors that are writing my recommendations were > disappointed with where I wanted to apply. One of them has told me > that I have research potential but I guess that can be interpreted > as just being nice. You mean, in the sense that they thought you should apply to better schools? Take that advice! I think one should aim high, while being prudent, in this as everything. I think it's always a good idea to apply to several places that you think are beyond your reach. ==== >Message-id: [...] >If you are aiming for a ph.d, then I would suggest getting into the best M.S >program you can, and then apply to a great ph.d program when you get your >M.S.. This is essentially what I am doing, for I am in the same situation. >Good luck! Lurch This is basically what I plan on doing. Is it bad to get a masters at a school with a PhD program and then transfer to another school afterwards, even if you get good recommendations? I'm applying to a few pretty low-ranked PhD programs and one masters program. I just don't know of any really GREAT masters programs but I'm sure they are out there. Do you know of any? ==== I think there are several mathematics programs for people with weak backgrounds at interesting schools ,e.g. , Mathematics Opportunity Committee at Berkeley , and perhaps Princeton or Harvard have something similar . Best of Luck. > I checked out a book called All the Mathematics You Missed [But Need to Know > for Graduate School] from the library and was surprised by its contents. The > book is divided into 16 sections that I am supposed to know before I get into > graduate school. This is my last year and I can check off very little. Here are the sixteen topics that I need to know along with whether or not I > will have completed them by the end of the year: 1. Linear Algebra - Yes > 2. Real Analysis - Yes > 3. Differentiating Vector Valued Functions (jacobians, inverse function > theorem) - No (nothing like this taught at my school) > 4. Point Set Topolgy - No (not offered here) > 5. Classical Stokes Theorems - Yes > 6. Differential Forms and Stokes Theorem - No (nothing like that here) > 7. Curvature for Curves and Surfaces (differential geometry) - No (not offered) > 8. Geometry - No (only course offered is one for future high school teachers > and was advised not to take it) > 9. Complex Analysis - No (schedule conflicts last year and this year) > 10. Countability and the Axiom of Choice - No (not offered but I have looked > into it a bit) > 11. Algebra - Yes > 12. Lebesgue Integration - No (not undergrad here) > 13. Fourier Analysis - No (I thought this was for engineers) > 14. Differential Equations - Yes > 15. Combinatorics and Probability - No (combinatorics not offered; probability > only after calc-based statistics is taken) > 16. Algorithms - No (the closest thing to what is described here is a mid-level > computer science course). I know that looks awful, even beyond awful, with 5/16. I don't think it's > realistic that I could learn that much material over the Summer. Which areas > do I absolutely need to know? Is this book very accurate in what I SHOULD know for graduate school? Almost > everything seems to roughly fall under analysis/applied math. The math > department has no one that does any research whatsoever in geometry (for those > areas listed here). Only 2 sections are devoted to algebra and there is > nothing about number theory. The strange thing is that, besides applied math classes, I'm taking or have > taken what they offer in terms of pure math. It's just pretty depressing to > see a book tell you that you have learned next to nothing that you should know > coming into graduate school. Any comments or advice would be appreciated, > including book suggestions (the author tends to say I've heard that > such-and-such book is good though I have not seen it which is pretty odd > considering the focus of the book). ==== > I checked out a book called All the Mathematics You Missed [But Need to > Know for Graduate School] from the library and was surprised by its > contents. The book is divided into 16 sections that I am supposed to > know before I get into graduate school. This is my last year and I > can check off very little. > > Here are the sixteen topics that I need to know along with whether or > not I will have completed them by the end of the year: > > 1. Linear Algebra - Yes > 2. Real Analysis - Yes > 3. Differentiating Vector Valued Functions (jacobians, inverse > function theorem) - No (nothing like this taught at my school) > 4. Point Set Topolgy - No (not offered here) > 5. Classical Stokes Theorems - Yes > 6. Differential Forms and Stokes Theorem - No (nothing like that here) > 7. Curvature for Curves and Surfaces (differential geometry) - No > (not offered) > 8. Geometry - No (only course offered is one for future high school > teachers and was advised not to take it) > 9. Complex Analysis - No (schedule conflicts last year and this year) > 10. Countability and the Axiom of Choice - No (not offered but I have > looked into it a bit) > 11. Algebra - Yes > 12. Lebesgue Integration - No (not undergrad here) > 13. Fourier Analysis - No (I thought this was for engineers) > 14. Differential Equations - Yes > 15. Combinatorics and Probability - No (combinatorics not offered; > probability only after calc-based statistics is taken) > 16. Algorithms - No (the closest thing to what is described here is a > mid-level computer science course). > > I know that looks awful, even beyond awful, with 5/16. I don't think > it's realistic that I could learn that much material over the Summer. > Which areas do I absolutely need to know? strong background in in areas 1-11. at least moderate working knowledge in areas 11-15. > Is this book very accurate in what I SHOULD know for graduate school? Almost > everything seems to roughly fall under analysis/applied math. The math > department has no one that does any research whatsoever in geometry (for those > areas listed here). Only 2 sections are devoted to algebra and there is > nothing about number theory. > > The strange thing is that, besides applied math classes, I'm taking or have > taken what they offer in terms of pure math. It's just pretty depressing to > see a book tell you that you have learned next to nothing that you should know > coming into graduate school. Any comments or advice would be appreciated, > including book suggestions (the author tends to say I've heard that > such-and-such book is good though I have not seen it which is pretty odd > considering the focus of the book). it seems clear that you wasted your undergrad years in a bad math school (typical.) that alone is good reason for you to quit while you are not so far behind, assuming that a major reason for you to pursue math is a job, including academic math jobs beyond k-12. now, if the main reason for you to pursue math is for it's own sake (extremely unlikely,) then you will need to patch the huge gaps your undergrad institution left behind, and then engage in graduate math studies, preferably in a highly ranked programme. ==== >>What you need to know before starting grad school varies considerably >>from place to place - you probably don't have any chance at all of >>getting into one of the best graduate programs in the country, but >>there are plenty of graduate math departments around where most >>of the incoming students will have a background more or less like >>yours (and plenty of places where the majority of incoming grad >>students will be entering with what the department considers an >>inadequate background, because they can't get the students they >>want - it happens a lot that incoming students at medium-level >>grad programs start by taking a lot of undergraduate classes >>that didn't exist where the student came from.) >>One bit of advice would be next time, if you intend to go to >>grad school, do your undergrad work at a place with a slightly >>stronger program. Maybe a little late for that now... I realized that I had no shot at any top program about a year ago when I looked >at the course offerings at the Ivy League schools and MIT. This is my senior >year so it's too late to go to a stronger program. I know that my department >is bad but now it's just could have and should have. How realistic is it >to get a masters degree and transfer to a better school? Hard to say. I don't know of any examples (in math) of someone with a BS from a mediocre place who got a master's from some place better and then a PhD from a top school. The fact that I don't know of any examples doesn't prove there are none - Bushnell has stated that he knows of plenty of such examples (otoh he's failed to name any, after being asked twice...) But it really doesn't follow that you're screwed. You should be able to get into a PhD program _somewhere_ if that's what you want. Then later when you're applying for jobs the fact that the place you got your degree was not a top school will not be in your favor, but if you've written a really fabulous thesis people will overlook that - if you settle the Riemann hypothesis people will be interested regardless of where you got your degree. >Are you just screwed >if you did not go to the right school and take the right courses with the right >professors? When we're talking about undergraduate work probably right courses is the main thing. And the right grades in those courses. (You could arrange to flunk philosophy or something, so you get to stick around another year and fill in a few gaps...) >>As far as what you should really know, probably the most >>important thing is that you have a good idea what a _proof_ >>is, and you have some facility writing correct proofs of relatively >>easy facts (by this I mean most of the exercises in a beginning >>abstract algebra course, say. The algebra you say you've >>taken was about groups and rings and things, not like >>a high-school algebra course, right?) Of course. >By the way, many of the topics you're thinking of as >>applied math are _also_ very important in pure math - >>it may not look that way from the course offerings where >>you went to school. (In particular, although there is >>certainly such a thing as a _course_ in Fourier analysis >>that's meant for engineers, Fourier analysis itself is >>incredibly important in many fields of math. Same for >>complex.) The applied math courses here are almost exclusively for engineering or physics >majors. There is a class that covers Fourier Analysis >and Partial Differential Equations but I (mistakenly?) thought that it was for >the engineering and physics people. >************************ >>David C. Ullrich > ************************ David C. Ullrich ==== > Hard to say. I don't know of any examples (in math) of someone with > a BS from a mediocre place who got a master's from some place > better and then a PhD from a top school. The fact that I don't > know of any examples doesn't prove there are none - Bushnell > has stated that he knows of plenty of such examples (otoh he's > failed to name any, after being asked twice...) We can also look at catalogues from schools that list all the degrees of their faculty. Of course, that is often somewhat dated, but it's at least published information so I don't need to be reticent about names. UMass/Amherst's math department includes one Nathaniel Whitaker, who is BA, Hampton Institute, 1974; MS, Cincinatti, 1981; PhD, California, 1987. I assume that California means UC Berkeley. I looked through the list of current grad students at Cornell. I found one Liang Chen, who has a BS from Peking University and a MS from the University of Wisconsin at Madison, and is now at Cornell. And Jose Trujillo Ferreras, who has a Licenciado from the Universidad Autonoma de Madrid, and an MA from Duke and is now at Cornell. Jennifer Fawcett is BA from Rice, MA from UC Davis, and now at Cornell. Lee Gibson, BS from the University of Kentucky, MS from the University of Louisville, now at Cornell. Farkhod Eshmatov, BS from Tashkent State University, MA from SUNY Binghamton, now at Cornell. That's six, in about ten minutes of web looking. Thomas ==== > Hard to say. I don't know of any examples (in math) of someone with >> a BS from a mediocre place who got a master's from some place >> better and then a PhD from a top school. The fact that I don't >> know of any examples doesn't prove there are none - Bushnell >> has stated that he knows of plenty of such examples (otoh he's >> failed to name any, after being asked twice...) We can also look at catalogues from schools that list all the degrees >of their faculty. Of course, that is often somewhat dated, but it's >at least published information so I don't need to be reticent about >names. UMass/Amherst's math department includes one Nathaniel Whitaker, who >is BA, Hampton Institute, 1974; MS, Cincinatti, 1981; PhD, California, >1987. I assume that California means UC Berkeley. That's _one_ example that seems valid, at least if California does mean Berkeley. My reaction to most of the examples below is the same as the people who've already replied - the majority of the places that you seem to be regarding as mediocre seem like pretty good schools to me. This is certainly true of most of the places you say people got their master's degrees. Take the person with the BA from Rice. You think that here undergraduate transcript looks anything like the transcript of the OP's? >I looked through the list of current grad students at Cornell. I >found one Liang Chen, who has a BS from Peking University and a MS >from the University of Wisconsin at Madison, and is now at Cornell. >And Jose Trujillo Ferreras, who has a Licenciado from the Universidad >Autonoma de Madrid, and an MA from Duke and is now at Cornell. >Jennifer Fawcett is BA from Rice, MA from UC Davis, and now at >Cornell. Lee Gibson, BS from the University of Kentucky, MS from the >University of Louisville, now at Cornell. Farkhod Eshmatov, BS from >Tashkent State University, MA from SUNY Binghamton, now at Cornell. That's six, in about ten minutes of web looking. Thomas ************************ David C. Ullrich ==== > Take the person with the BA from Rice. You think that here > undergraduate transcript looks anything like the transcript of > the OP's? Who knows? It's possible to have bad grades from a good school, and good grades from a bad school. I'm speaking only about the latter. Thomas ==== > Take the person with the BA from Rice. You think that here >> undergraduate transcript looks anything like the transcript of >> the OP's? Who knows? It's easy to find out with a little web searching. At we read that an undergad degree at Rice requires 8 courses at 300 level or above. To get an idea what that means we look at the course offerings in three recent semesters (details below). And we conclude that the transcript of someone with a degree from Rice looks _nothing_ like the OP's transcript - it's possible that he hasn't taken even _one_ course that's anything like a 300+ course at Rice, much less 8. (He says he's taken algebra - it's hard to know how the content of that course compares with the content of a similarly-named course at Rice. But it's easy to guess what the typical admissions committee is going to guess about the comparison between the similarly named courses at the two schools...) Citing a person with a BA from Rice as an example of someone with a mediocre BA who nonetheless got into a good PhD program by getting a master's from a good place turns out to be as ridiculous as it seemed to me yesterday, before I looked up the details. Details: http://math.rice.edu/Courses/webpages.html Math 401: Differential Geometry Math 423: Partial Differential Equations Math 444: Geometric Topology Math 468: Potpourri (Dynamical Systems) Math 499/699:Math. Sciences VIGRE Seminar: Computational Algebraic Geometry Math 590: Current Mathematics Seminar Math 591: Graduate Teaching Seminar MATH 356 ABSTRACT ALGEBRA Credits 3.00 Spring 03 * DISTRIBUTION COURSE: GROUP III Groups: normal subgroups, factor groups, Abelian groups. Rings: ideals, Euclidean rings, and unique factorization. Fields: algebraic extensions, finite fields. Students may not take this course and Math 463. 001 HB 227 - MWF 02:00PM - 02:50PM Hyeon, Donghoon David Enr: 12 Max: 0 MATH 366 GEOMETRY Credits 3.00 Spring 03 * DISTRIBUTION COURSE: GROUP III Topics chosen from Euclidean, spherical, hyperbolic, and projective geometry, with emphasis on the similarities and differences found in various geometries. Isometries and other transformations are studied and used throughout. The history of the development of geometric ideas is discussed. This course is strongly recommended for prospective high school teachers. 001 HB 227 - MWF 03:00PM - 03:50PM Hassett, Brendan Enr: 32 Max: 0 MATH 382 COMPLEX ANALYSIS Credits 3.00 Spring 03 * DISTRIBUTION COURSE: GROUP III Study of the Cauchy integral theorem, Taylor series, residues, as well as the evaluation of integrals by means of residues, conformal mapping, and application to two-dimensional fluid flow. May not receive credit for this course and Math 427. 001 HB 227 - MWF 01:00PM - 01:50PM Song, Joung Min Jaime Enr: 26 Max: 0 MATH 390 UNDERGRADUATE COLLOQUIUM Credits 1.00 Spring 03 * DISTRIBUTION COURSE: GROUP III Lectures by undergraduate students on mathematical topics not usually covered in other courses. Each student is required to give one lecture and to attend all sessions. 001 HB 423 - MF 12:05PM - 12:50PM Jones, Frank Enr: 7 Max: NA MATH 402 DIFFERENTIAL GEOMETRY Credits 3.00 Spring 03 to year. Prereq- Math 401 and either Math 443 or permission of the instructor. 001 HB 423 - TTH 09:25AM - 10:40AM Wolf, Michael Enr: 3 Max: 0 MATH 424 PARTIAL DIFFERENTIAL EQUATIONS Credits 3.00 Spring 03 See Math 423. 001 HB 423 - MWF 02:00PM - 02:50PM Jones, Frank Enr: 8 Max: 0 MATH 426 TOPICS IN REAL ANALYSIS Credits 3.00 Spring 03 harmonic analysis, probabilty theory, advanced topics in measure theory, ergodic theory, and elliptic integrals. 001 HB 423 - TTH 01:00PM - 02:20PM Veech, William A. Enr: 2 Max: 0 MATH 427 COMPLEX ANALYSIS Credits 3.00 Spring 03 Study of the Cauchy-Riemann equation, power series, Cauchy's integral formula, residue calculus, and conformal mappings. 001 HB 427 - MWF 10:00AM - 10:50AM Boshernitzan, Michael Enr: 9 Max: 0 MATH 443 GENERAL TOPOLOGY Credits 3.00 Spring 03 Study of basic point set topology. Includes a treatment of cardinality and well ordering, as well as metrization. Prereq: MATH 321 or permission of instructor recommended. 001 HB 427 - MWF 02:00PM - 02:50PM Clark, Gregory Enr: 8 Max: 0 MATH 445 ALGEBRAIC TOPOLOGY Credits 3.00 Spring 03 Introduction to the theory of homology. Includes simplicial complexes, cell complexes and cellular homology and cohomology, as well as manifolds, and Poincare Duality. Prereq- Math 444 and either Math 356 or Math 463 or permission of instructor. 001 HB 427 - MWF 01:00PM - 01:50PM Cochran, Tim D. Enr: 10 Max: 0 MATH 464 ALGEBRA II Credits 3.00 Spring 03 See Math 463. 001 HB 423 - MWF 11:00AM - 11:50AM Boshernitzan, Michael Enr: 8 Max: 0 MATH 465 TOPICS IN ALGEBRA Credits 3.00 Spring 03 Pre-req- Math 356 or Math 463 or permission of the instructor. 001 HB 427 - MWF 09:00AM - 09:50AM Hassett, Brendan Enr: 5 Max: 0 MATH 468 POTPOURRI Credits 3.00 Spring 03 This course will consider power series, real analytic functions, and some related matters. Prereq- Math 321 and either Math 382 or Math 427 (which may be taken concurrently), or permission of the instructor. 001 TBA - TTH 01:00PM - 02:20PM Semmes, Stephen Enr: 3 Max: NA MATH 490 SUPERVISED READING Credits Spring 03 No description. 001 TBA - TBA Staff Enr: 6 Max: NA 002 TBA - TBA Staff Enr: 1 Max: NA 003 TBA - TBA Staff Enr: 0 Max: NA MATH 502 TOPICS IN DIFFERENTIAL GEOMETRY Credits 3.00 Spring 03 The Atiyah-Singer theorem, secondary invariants, and related topics. 001 HB 427 - TTH 10:50AM - 12:05PM Forman, Robin Enr: 20 Max: 0 MATH 522 TOPICS IN REAL ANALYSIS Credits 3.00 Spring 03 Geometric Measure Theory treats measure-theoretic properties of geometrically defined sets of various dimensions. Some of the critical notions are Hausdorff measure, rectifiable sets, and rectifiable currents. The k dimensional Hausdorff (outer) measure H k(A) gives, for every nonnegative number k , a precise notion of the k dimensional size of A . Rectifiable sets and currents arise as limits of k dimensional manifolds. these occur in the solution of the Plateau Problem of finding a k dimensional surface of least k dimensional area having a given boundary. Graduate student standing or permission of instructor. 001 TBA - MWF 12:00PM - 12:50PM Staff Enr: 7 Max: NA MATH 590 CURRENT MATHEMATICS SEMINAR Credits 1.00 Spring 03 Lectures on topics of recent research in mathematics delivered by mathematics graduate students and faculty. Prereq: graduate student standing or permission of the department. 001 HB 227 - TTH 02:30PM - 03:45PM Staff Enr: 25 Max: NA MATH 591 GRADUATE TEACHING SEMINAR Credits 1.00 Spring 03 Discussion on teaching issues and practice lectures by participants as preparation for classroom teaching of mathematics. Graduate student status or permission of department. 001 HB 427 - T 02:30PM - 03:30PM Staff Enr: 15 Max: NA MATH 800 THESIS AND RESEARCH Credits Spring 03 http://www.rice.edu/projects/courses/2002fall/MATH.html MATH 321 INTRODUCTION TO ANALYSIS I Credits 3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III A thorough treatment of basic methods of analysis such as metric spaces, compactness, sequences and series of functions. Also further topics in Liouville theory. Prereq- Math 222 or permission of department. 001 HB 427 - MWF 03:00PM - 03:50PM Semmes, Stephen Enr: 21 Max: NA MATH 355 LINEAR ALGEBRA Credits 3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Linear transformations and matrices, solution of linear equations, eigenvalues and eigenvectors, quadratic forms, rational canonical form, Jordan canonical form. 001 HZ 210 - MWF 02:00PM - 02:50PM Clark, Gregory Enr: 108 Max: NA MATH 368 TOPICS IN COMBINATORICS Credits 3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Study of combinatorics and discrete mathematics. Topics that may be covered include graph theory, Ramsey theory, finite geometries, combinatorial enumeration, combinatorial games. Prereq- Math 211. 001 HB 227 - MWF 03:00PM - 03:50PM Stong, Richard A. Enr: 26 Max: NA MATH 381 INTRODUCTION TO PARTIAL DIFFERENTIAL EQU Credits 3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Laplace transform: inverse transform, applications to constant coefficient differential equations. Boundary value problems: Fourier series, Bessel functions, Legendre polynomials. 001 HZ AMP - MWF 01:00PM - 01:50PM Evans, Richard Enr: 73 Max: NA MATH 390 UNDERGRADUATE COLLOQUIUM Credits 1.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Lectures by undergraduate students on mathematical topics not usually covered in other courses. Each student is required to give one lecture and to attend all sessions. 001 HB 227 - MF 12:05PM - 12:55PM Jones, Frank Enr: 6 Max: 0 MATH 401 DIFFERENTIAL GEOMETRY Credits 3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Study of the differential geometry of curves and surfaces in R3. Includes an introduction to the concept of curvature and thorough treatment of the Gauss-Bonnet theorem. 001 HB 427 - TTH 09:25AM - 10:40AM Wolf, Michael Enr: 12 Max: NA MATH 423 PARTIAL DIFFERENTIAL EQUATIONS Credits 3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Theory of distributions. Wave equation, Laplace's equation, heat equation. Fundamental solutions. Other topics include first order hyperbolic systems, Cauchy-Kowalewski theorem, potential theory, Dirichlet and Neumann problems, integral equations, elliptic equations. 001 HB 427 - MWF 02:00PM - 02:50PM Jones, Frank Enr: 9 Max: NA MATH 425 REAL ANALYSIS Credits 3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Lebesgue theory of measure and integration. 001 HB 423 - TTH 01:00PM - 02:20PM Wiandt, Tamas Enr: 13 Max: NA MATH 428 TOPICS IN COMPLEX ANALYSIS Credits 3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Special topics include Riemann mapping theorem, Runge's Theorem, elliptic function theory, prime number theorem, Riemann surfaces. 001 HB 453 - MWF 10:00AM - 10:50AM Hassett, Brendan Enr: 4 Max: NA MATH 444 GEOMETRIC TOPOLOGY Credits 3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Introduction to algebraic methods in topology and differential topology. Elementary homotopy theory. Covering spaces. 001 HB 427 - MWF 09:00AM - 09:50AM Hempel, John P. Enr: 10 Max: NA MATH 463 ALGEBRA I Credits 3.00 Fall 02 * DISTRIBUTION COURSE: GROUP III Groups, rings, fields, vector spaces. Matrices, determinants, eigenvalues, canonical forms, multilinear algebra. Structure theorem for finitely generated abelian groups. Galois theory. 001 HB 453 - MWF 11:00AM - 11:50AM Hempel, John P. Enr: 12 Max: NA MATH 490 SUPERVISED READING Credits Fall 02 No description. 001 TBA - TBA Staff Enr: 3 Max: 0 002 TBA - TBA Staff Enr: 2 Max: NA 003 TBA - TBA Staff Enr: 0 Max: NA MATH 521 ADVANCED TOPICS IN REAL ANALYSIS Credits 3.00 Fall 02 Topic TBA. 001 GRB 212W - MWF 03:00PM - 03:50PM Hardt, Robert M. Enr: 7 Max: NA MATH 527 ERGODIC THEORY AND TOPOLOGICAL DYNAMICS Credits 3.00 Fall 02 No description 001 HB 427 - TTH 10:50AM - 12:05PM Veech, William A. Enr: 3 Max: NA MATH 541 TOPICS IN TOPOLOGY Credits 3.00 Fall 02 No description. 001 HB 423 - MWF 01:00PM - 01:50PM Cochran, Tim D. Enr: 9 Max: NA MATH 590 CURRENT MATHEMATICS SEMINAR Credits 1.00 Fall 02 Lectures on topics of recent research in mathematics delivered by mathematics graduate students and faculty. Prereq: graduate student standing or permission of the department. 001 HB 427 - T 02:30PM - 03:50PM Song, Joung Min Jaime Enr: 25 Max: 0 MATH 591 GRADUATE TEACHING SEMINAR Credits 1.00 Fall 02 Discussion on teaching issues and practice lectures by participants as preparation for classroom teaching of mathematics. Graduate student status or permission of department. 001 HB 453 - TH 02:30PM - 03:50PM Masters, Joseph Enr: 14 Max: 0 MATH 800 THESIS AND RESEARCH Credits Fall 02 >It's possible to have bad grades from a good school, and >good grades from a bad school. I'm speaking only about the latter. Thomas ************************ David C. Ullrich ==== >> Take the person with the BA from Rice. You think that here >> undergraduate transcript looks anything like the transcript of >> the OP's? >Who knows? > > It's easy to find out with a little web searching. When I said who knows I meant not which classes did she take but did she do well in them. Thomas ==== > Take the person with the BA from Rice. You think that here >> undergraduate transcript looks anything like the transcript of >> the OP's? Who knows? It's possible to have bad grades from a good school, and >good grades from a bad school. I'm speaking only about the latter. I think it has been mentioned in this thread that grades (and also GRE scores) are maybe not too important; the list of courses taken might matter much more (assuming the grades average at least a B or so) and the extra-curricular indicators may be even more telling (someone else mentioned things like undergrad publications). In all these ways the weak student at the strong school has more opportunities than the strong student at the weak school, IMHO. It would be very interesting to find data about pipeline issues like this. Assume for a moment the (actually quite bogus) premise that every high-school math-lover dreams of a full professorship. Assume as well that institutions can be broken into equivalence classes which can be linearly ordered (maybe not too bad an assumption). Fix a cohort of people (say, US citizens born in one year) and assume that they operate in a closed system of opportunities and feeder stages. (Not really accurate, since so many students cross borders, but we could assume the number of positions to be held by members of the cohort will stay fixed for a while.) Then one can track a cohort of people through various stages: admission to university graduation with bachelor's degree in math admission to grad school attainment of PhD postdoc tenure-track job tenured professorship At each stage, one could take a census of how many from the cohort are in Harvard-class schools; how many at a Rice-class school; how many at Big State U; how many at Local Community College, etc. This would provide a statistical answer to the OP's questions (which may or may not be applicable to that one person, of course). My hunch is that the genius comments made elsewhere are pretty accurate, which is to say that the main job of schools is to stand out of the way and let the bright students flower and identify themselves. That would be reflected in the data if we found that each institution tends to be fed only be institutions of comparable or superior rank: the passages from stage to stage are simply filters which let the best progress. Actual data are hard to come by but for example the AMS regularly publishes data about where the Group-I PhDs get their first jobs, the Group-IIs, etc. These data tend on the whole to support the hunch I just made. Also available are the column totals. A typical age cohort in the US is nowadays about 4 million. About 2-3 million will enter college (including community college), 1-2 million will complete college, of whom about 1% will be math majors. In some years almost every one of them who wants it can find a spot in a grad school, but that's not true when the economy is bad, and it's harder to do when the number of mathematically-strong foreign students is high. At the output end there, we know there are only something like 1000-1200 new PhD's per year in the US, only half of whom are originally from the US. Officially-named post-doc positions must number in the low hundreds (counted as openings per year, not total inhabitants). Regular academic positions advertised per year number in the high hundreds, but the bulk of those are at the lower-ranked schools. (You can peruse the annual compendium of job openings to quantify this if you wish.) Finally, the number of tenure cases decided positively per year has to be in the mid-hundreds, again far more at the lower schools (where turnover is higher) than at Ivy level. In short: only a tiny fraction of youngsters who are good at math will make it all the way to the end. One can always be optimistic and hope for some upward migration, but at almost every level this seems unlikely. For example, there may be hundred openings every year for postdocs at Ivy-class schools. Where do you think the successful applicants will come from? Some will come from, say, Kansas or Wyoming, but the great majority are surely from Ivy-class grad schools. Those same schools produced several times that number of PhDs the previous year, so where will the rest of their students go? They will be grabbing the tenure-track openings at Kansas and Wyoming, forcing _their_ students to look for jobs at schools with no graduate program at all, etc. Seems to me this would make for a dandy study by a budding economist! dave ==== > > Hard to say. I don't know of any examples (in math) of someone with > a BS from a mediocre place who got a master's from some place > better and then a PhD from a top school. The fact that I don't > know of any examples doesn't prove there are none - Bushnell > has stated that he knows of plenty of such examples (otoh he's > failed to name any, after being asked twice...) > > We can also look at catalogues from schools that list all the degrees > of their faculty. Of course, that is often somewhat dated, but it's > at least published information so I don't need to be reticent about > names. > > UMass/Amherst's math department includes one Nathaniel Whitaker, who > is BA, Hampton Institute, 1974; MS, Cincinatti, 1981; PhD, California, > 1987. I assume that California means UC Berkeley. > > I looked through the list of current grad students at Cornell. I > found one Liang Chen, who has a BS from Peking University and a MS > from the University of Wisconsin at Madison, and is now at Cornell. And Peking University is mediocre?? Not to mention, Wisconsin is comparable to Cornell, so it doesn't really prove anything. Cornell is more selective, but reputation-wise it's very similar. > And Jose Trujillo Ferreras, who has a Licenciado from the Universidad > Autonoma de Madrid, and an MA from Duke and is now at Cornell. Sigh...as someone else has mentioned, do you regard any place from outside the U.S. as mediocre? > Jennifer Fawcett is BA from Rice, MA from UC Davis, and now at > Cornell. Rice is a pretty good place for an undergraduate math degree, especially if you're planning to specialize in low-dimensional topology. Getting a recommendation from Hempel is a good thing; and she did in fact do that. As for Jennifer (nickname - Sunny), she is not a good example for the point you are making because she transferred over with Thurston when he moved from Davis. Also, let me add that Sunny was good enough to get into Berkeley when she applied to grad schools. So this is really a not very good example, is it? > Lee Gibson, BS from the University of Kentucky, MS from the > University of Louisville, now at Cornell. Farkhod Eshmatov, BS from > Tashkent State University, MA from SUNY Binghamton, now at Cornell. > > That's six, in about ten minutes of web looking. > I think I've spent enough time on this also. ==== > And Jose Trujillo Ferreras, who has a Licenciado from the Universidad > Autonoma de Madrid, and an MA from Duke and is now at Cornell. > > Sigh...as someone else has mentioned, do you regard any place from > outside the U.S. as mediocre? Not at all. I am simply giving people who earned an intermediate masters from a third institution. Thomas ==== > > And Jose Trujillo Ferreras, who has a Licenciado from the Universidad > Autonoma de Madrid, and an MA from Duke and is now at Cornell. > > Sigh...as someone else has mentioned, do you regard any place from > outside the U.S. as mediocre? > > Not at all. I am simply giving people who earned an intermediate > masters from a third institution. > > Thomas Why? David Ullrich specifically said he didn't know any example of people getting a degree from a *mediocre* undergrad, then an M.S. at a better school, and then a Ph.D. at a *top* school. He then mentioned you had not given any examples of such. To which you responded by listing examples, one of which is quoted above. If you are indeed simply giving examples of those who earned an intermediate masters from a third institution, that's irrelevant. ==== > Why? David Ullrich specifically said he didn't know any example of > people getting a degree from a *mediocre* undergrad, then an M.S. at a > better school, and then a Ph.D. at a *top* school. He then mentioned > you had not given any examples of such. To which you responded by > listing examples, one of which is quoted above. What I *said*, originally, was that for someone who went to a nothing-special school, it was not crazy to get a good masters if you can't get into topnotch PhD programs. I made a fair prima facie case for why this is so, including examples from other fields. I was asked do you know anyone who did that and I said yes (more than one) at MIT. I certainly don't claim I have given conclusive examples. On the other hand, people claiming the contrary have given no examples of any kind, nor have they given any reasons to the contrary. At some point, you folks need to provide *some* kind of reason beyond your common agreement. Thomas ==== > > Why? David Ullrich specifically said he didn't know any example of > people getting a degree from a *mediocre* undergrad, then an M.S. at a > better school, and then a Ph.D. at a *top* school. He then mentioned > you had not given any examples of such. To which you responded by > listing examples, one of which is quoted above. > > What I *said*, originally, was that for someone who went to a > nothing-special school, it was not crazy to get a good masters if you > can't get into topnotch PhD programs. > > I made a fair prima facie case for why this is so, including examples > from other fields. I was asked do you know anyone who did that and > I said yes (more than one) at MIT. > > I certainly don't claim I have given conclusive examples. On the > other hand, people claiming the contrary have given no examples of any > kind, nor have they given any reasons to the contrary. > > At some point, you folks need to provide *some* kind of reason beyond > your common agreement. Well, as someone who stepped into this thread rather late in the game, I know my impressions of what is going on may be very different from people actively engaged in the thread; however, it appears to me there are several related, but different, discussions going on. There is one, started by Lee Rudolph, in which the topic of 'bootstrapping' oneself up the prestige ladder, through a masters, is raised. Your response, with examples (*not* the one about MIT), was issued directly to David Ullrich's response in this discussion. That's why I, and I think several others, interpreted your issuing of examples as being related to this idea of 'bootstrapping'. So my comment above was in that context. i believe what said Lee off in the first place was your comment that: Then with a respected masters under your belt, you are an excellent competitor with the people who are coming straight out of the best undergrad programs. As I've explained in another post (regarding genius), this doesn't appear to be so. But your point is taken, obviously, one has to do what one can to improve one's chances of getting into a better Ph.D. program than one would initially, in light of a mediocre (or worse) undergrad. In any case, I think this subthread is dying out, since it's rather clear now that nobody is really arguing about anything. I'll post a response to your response to my genius post, since I think that still has some life in it. ==== > Hard to say. I don't know of any examples (in math) of someone with > a BS from a mediocre place who got a master's from some place > better and then a PhD from a top school. The fact that I don't > know of any examples doesn't prove there are none - Bushnell > has stated that he knows of plenty of such examples (otoh he's > failed to name any, after being asked twice...) We can also look at catalogues from schools that list all the degrees > of their faculty. Of course, that is often somewhat dated, but it's > at least published information so I don't need to be reticent about > names. UMass/Amherst's math department includes one Nathaniel Whitaker, who > is BA, Hampton Institute, 1974; MS, Cincinatti, 1981; PhD, California, > 1987. I assume that California means UC Berkeley. I looked through the list of current grad students at Cornell. I > found one Liang Chen, who has a BS from Peking University and a MS > from the University of Wisconsin at Madison, and is now at Cornell. > And Jose Trujillo Ferreras, who has a Licenciado from the Universidad > Autonoma de Madrid, and an MA from Duke and is now at Cornell. > Jennifer Fawcett is BA from Rice, MA from UC Davis, and now at > Cornell. Lee Gibson, BS from the University of Kentucky, MS from the > University of Louisville, now at Cornell. Farkhod Eshmatov, BS from > Tashkent State University, MA from SUNY Binghamton, now at Cornell. That's six, in about ten minutes of web looking. > Do you want tp say that any university outside US (Madrid, Beijing in your examples) are mediocre places? > Thomas ==== > I realized that I had no shot at any top program about a year ago >> when I looked at the course offerings at the Ivy League schools and >> MIT. This is my senior year so it's too late to go to a stronger >> program. I know that my department is bad but now it's just could >> have and should have. How realistic is it to get a masters >> degree and transfer to a better school? Are you just screwed if you >> did not go to the right school and take the right courses with the >> right professors? No. The typical advice in your place is to apply to a good masters >program. This generally means a school that offers only the masters >and not the doctorate in your field. Find the best ones, and if you >did well as an undergrad and have decent GREs, you should be able to >get in without a problem. Then with a respected masters under your >belt, you are an excellent competitor with the people who are coming >straight out of the best undergrad programs. Hey, just call me a starry-eyed old cynic, but I find it really, *really* hard to believe that from the point of view of the Ivy League schools and MIT, or any top program, there even *exist* any respected masters degrees. Do you know of a single example of someone who got a (respected or otherwise) masters degree in mathematics at a school that offers only the masters and not the doctorate in mathematics, and was then accepted to any top program, specifically, one of the Ivy League schools and MIT? Lee Rudolph ==== I asked tb+usenet@becket.net (Thomas Bushnell, BSG) >Do you know of a single >example of someone who got a (respected or otherwise) masters >degree in mathematics at a school that offers only the masters >and not the doctorate in mathematics, and was then accepted >to any top program, specifically, one of the Ivy League >schools and MIT? He produced (not in direct response to that question) the following. (1) A faculty member at UMass--Amherst with an MS from Cincinatti (1981) and a Ph. D. from Berkeley (1987). Since Cincinatti is not a school that offers only the masters and not the doctorate in mathematics, this is not an example. (2) A grad student at Cornell with an MS from the University of Wisconsin at Madison. Since UWM is not a school that offers only the masters and not the doctorate, this is not an example. (3) A grad student at Cornell with an MA from Duke. Since Duke is not a school that offers only the masters and not the doctorate in mathematics, this is not an example. (4) A grad student at Cornell with an MA from UC Davis. Since UC Davis is not a school that offers only the masters and not the doctorate in mathematics, this is not an example. (5) A grad student at Cornell with a master's from the University of Louisville. Finally, an example! for, indeed, the University of Louisville does not offer a doctorate in mathematics. (However, his BA was from the University of Kentucky, which *does*.) (6) A grad student at Cornell with a master's from SUNY Binghampton. Since SUNY Binghampton is not a school that offers only the masters and not the doctorate in mathematics, this is not an example. Well, I only *asked* for a single example, so I can't say I didn't get what I asked for. The tare/wheat ratio was a bit high, though. >That's six, in about ten minutes of web looking. Only for very small values of six. Lee Rudolph ==== > Well, I only *asked* for a single example, so I can't say > I didn't get what I asked for. The tare/wheat ratio was a bit > high, though. I gave examples of people with intermediate masters from third institutions, which is what I thought you said you wanted. Still, as I said, I have made a prima facie case, and so far, you haven't given *any* reasons to think I'm wrong. I really am interested, but just blank assertion isn't worth much, is it? *Some* kind of explanation would be appropriate, don't you think? rightly or wrongly, is expected by admissions committees in math--and not so much in other subjects. This is an excellent point, but the same correspondent mixed up people with mediocre records and people with excellent records from second-class schools. The latter do not necessarily look like non-hotshots who are making up for their earlier failures. Thomas ==== >Message-id: > I realized that I had no shot at any top program about a year ago > when I looked at the course offerings at the Ivy League schools and > MIT. This is my senior year so it's too late to go to a stronger > program. I know that my department is bad but now it's just could > have and should have. How realistic is it to get a masters > degree and transfer to a better school? Are you just screwed if you > did not go to the right school and take the right courses with the > right professors? >>No. The typical advice in your place is to apply to a good masters >>program. This generally means a school that offers only the masters >>and not the doctorate in your field. Find the best ones, and if you >>did well as an undergrad and have decent GREs, you should be able to >>get in without a problem. Then with a respected masters under your >>belt, you are an excellent competitor with the people who are coming >>straight out of the best undergrad programs. Hey, just call me a starry-eyed old cynic, but I find it really, >*really* hard to believe that from the point of view of the >Ivy League schools and MIT, or any top program, there even >*exist* any respected masters degrees. Do you know of a single >example of someone who got a (respected or otherwise) masters >degree in mathematics at a school that offers only the masters >and not the doctorate in mathematics, and was then accepted >to any top program, specifically, one of the Ivy League >schools and MIT? Lee Rudolph Just to clear this up, I meant that I knew that I had no shot at any top program without going to one of the best schools. It seems like my program would roughly put me around the junior level at one of the best schools when I graduate. Furthermore, I'm sure there are more math majors at the very best schools than there are spots in PhD programs at those schools, so I assumed that they could even filter down to some of the 'great' schools that aren't quite the best, making it even harder to get into those. Basically, I want to be able to get into a very good state school. ==== > Hey, just call me a starry-eyed old cynic, but I find it really, > *really* hard to believe that from the point of view of the > Ivy League schools and MIT, or any top program, there even > *exist* any respected masters degrees. Do you know of a single > example of someone who got a (respected or otherwise) masters > degree in mathematics at a school that offers only the masters > and not the doctorate in mathematics, and was then accepted > to any top program, specifically, one of the Ivy League > schools and MIT? Yes, in math, physics, and in philosophy. A master's degree from a doctoral program generally means we let him go because he couldn't hack it. But a good master's degree (say in philosophy from Tufts) means a lot. It means this person has done well in an advanced program, carries no implied failure, and indicates to most people reviewing applications that they can do graduate work well. This is exactly what is not clear when an applicant comes from a second-rate undergrad school. All your annoying scare quotes serve only to obscure the point: There are three different kinds of masters degrees out there in strictly academic subjects (subjects like math, physics, or philosophy): * There are the ones which are kind exit for someone washing out of a doctoral program; * There are the ones that smaller schools can offer to try and boost their profile; * There are ones that are taught by top-notch faculty, well respected in their field, and which carry weight. The latter two generally exist only in departments that do not offer a doctorate. Both the latter two have very similar promotional materials, and it's important to figure out the difference. Those who receive the last sort are generally better off in their application than if they had not gone, most especially when their undergraduate degree is from a less stellar school. I quote, for example, from the Philosophical Gourmet Report: Who should consider an M.A. program in philosophy? Three categories of students who ultimately want to get a Ph.D. and pursue an academic career might benefit from such programs: (i) students whose undergraduate major was not philosophy; (ii) students who majored in philosophy at universities with philosophy departments outside the mainstream of the profession; and (iii) students who majored in philosophy, have a solid grounding in the various areas of philosophy, but who studied philosophy at smaller colleges and universities, or at institutions with weak academic reputations....Students in each category may be both qualified and able to get into the Ph.D. programs of their choice; but students who fit into one of these categories may be more likely to have trouble getting into Ph.D. programs and may be good candidates to benefit from M.A. programs. A good M.A. program will provide many benefits: it will allow a student to get a basic grounding in philosophy or expand the breadth of her existing knowledge; to develop increased familiarity with current debates in philosophy; to prepare and polish written work in philosophy that will be useful in the applications process for Ph.D. programs; and to get to know some established philosophers who can then provide meaningful letters of recommendation for Ph.D. programs. This advice applies pretty much to any strictly academic subject, for which there isn't an industry demand for master's degrees. In computer science, for example, a master's degree is a real job boost all by itself, and the schools have adjusted to suit, and so the advice doesn't carry over so easily. But for a strictly academic subject, where the job qualification is really a doctorate, this is what a terminal master's program is good for. And to repeat, yes, I know people in a variety of fields who were admitted to top-notch graduate programs upon receiving a master's at such a school. Thomas ==== > Hey, just call me a starry-eyed old cynic, but I find it really, >> *really* hard to believe that from the point of view of the >> Ivy League schools and MIT, or any top program, there even >> *exist* any respected masters degrees. Do you know of a single >> example of someone who got a (respected or otherwise) masters >> degree in mathematics at a school that offers only the masters >> and not the doctorate in mathematics, and was then accepted >> to any top program, specifically, one of the Ivy League >> schools and MIT? Yes, in math, physics, and in philosophy. A master's degree from a doctoral program generally means we let him >go because he couldn't hack it. But a good master's degree (say in >philosophy from Tufts) means a lot. It means this person has done >well in an advanced program, carries no implied failure, and >indicates to most people reviewing applications that they can do >graduate work well. Well, I'll have to say I'm amazed to hear about the math example. But I believe you. (Would it be within the limits of your discretion to say which doctoral program *in math*, in particular, took this person? Was it one of the Ivy League schools and MIT?) What, by the way, is the nature of the evidence on which you would base a statement (which you didn't make, explicitly) that a master's degree *in mathematics* indicates to most people reviewing applications that the person with the degree can do graduate work *towards a doctorate in mathematics* well? I freely admit that I have never reviewed applications for a graduate program in mathematics. Have you? I know a lot of people who have, and have sometimes talked to them about the process. Have you? >This is exactly what is not clear when an applicant comes from a >second-rate undergrad school. All your annoying scare quotes serve only to obscure the point: They aren't scare quotes, they are quotation marks that mark direct quotations. I regret that you find them annoying (but I'm not sorry I put them in; quite the contrary, I'm glad I put them in, and I hope you will learn to find them, not annoying, but a positive joy, once you have perceived their function and appreciated that it is very useful). >There are three different kinds of masters degrees out there in >strictly academic subjects (subjects like math, physics, or >philosophy): * There are the ones which are kind exit for someone washing out of a > doctoral program; Right. >* There are the ones that smaller schools can offer to try and boost > their profile; * There are ones that are taught by top-notch faculty, well respected > in their field, and which carry weight. The latter two generally exist only in departments that do not offer a >doctorate. Both the latter two have very similar promotional >materials, and it's important to figure out the difference. So that I can compare my ideas of quality with yours, could you give examples--not in physics or philsophy, but in math--of a few master's programs of the latter two types (in departments that do not offer a doctorate)? Would, for example, Boston College's master's program in mathematics count (in the second of the latter two types)? They certainly have some top-notch faculty, well-respected in their field teaching master's students, but I have not heard that the graduates of their master's program are getting in to top schools (because, indeed, I have not heard that they have any ambitions beyond the master's degree, with its concomitant payoff if you're a school teacher in Massachusetts)-- I don't hear everything, naturally. If not BC, perhaps some other school in the Boston area? >Those who receive the last sort are generally better off in their >application than if they had not gone, most especially when their >undergraduate degree is from a less stellar school. I quote, for example, from the Philosophical Gourmet Report: [deleted] Philosophy is a different kettle of fish entirely from mathematics, and the material I deleted seems to me quite irrelevant to a discussion of master's degrees in mathematics. >This advice applies pretty much to any strictly academic subject, So you assert. I have my doubts. You haven't yet given me much reason (by my standards) to lose my doubts. >for >which there isn't an industry demand for master's degrees. In >computer science, for example, a master's degree is a real job boost >all by itself, and the schools have adjusted to suit, and so the >advice doesn't carry over so easily. But for a strictly academic subject, where the job qualification is >really a doctorate, this is what a terminal master's program is good >for. And to repeat, yes, I know people in a variety of fields Including, you say, mathematics--the only one I'm interested in talking about. Let's stick to that one in the sequel, if you don't mind. >who were >admitted to top-notch graduate programs upon receiving a master's at >such a school. How'd they do? Lee Rudolph ==== > Well, I'll have to say I'm amazed to hear about the math example. > But I believe you. (Would it be within the limits of your discretion > to say which doctoral program *in math*, in particular, took this > person? Was it one of the Ivy League schools and MIT?) MIT. > What, by the way, is the nature of the evidence on which you > would base a statement (which you didn't make, explicitly) > that a master's degree *in mathematics* indicates to most > people reviewing applications that the person with the degree > can do graduate work *towards a doctorate in mathematics* well? Can you explain why you think that mathematics should be different than other disciplines? Your continual protestations that you think it amazing and unheard of suggests to me simply that you can't think of anything you could say other than your open mouthed amazement. So far, all you can say is I can't believe it! In response to which, unless you can say why, is simply repeat what I have said. Or, if you have a criticism of what I've said, then to make it, rather than allude vaguely to it. > Philosophy is a different kettle of fish entirely from mathematics, > and the material I deleted seems to me quite irrelevant to a > discussion of master's degrees in mathematics. Can you say what the differences are? >This advice applies pretty much to any strictly academic subject, > > So you assert. I have my doubts. You haven't yet given me > much reason (by my standards) to lose my doubts. Well, so far you haven't even explained the doubt, other than said it's there. I'm afraid I don't give much credence to doubts of that degree. In other words, if you want the conversation to continue, you gotta do more than just say you still haven't proven it to me. I've made a fair prima facie case, and if you have an objection to register to it, do so. Perhaps you have misunderstood what I'm saying. I'm saying that a bachelors from Podunk U, plus a masters from Really-Cool-U, is worth as much as a bachelors from Really-Cool-U. Thomas ==== > Well, I'll have to say I'm amazed to hear about the math example. >> But I believe you. (Would it be within the limits of your discretion >> to say which doctoral program *in math*, in particular, took this >> person? Was it one of the Ivy League schools and MIT?) MIT. > What, by the way, is the nature of the evidence on which you >> would base a statement (which you didn't make, explicitly) >> that a master's degree *in mathematics* indicates to most >> people reviewing applications that the person with the degree >> can do graduate work *towards a doctorate in mathematics* well? Can you explain why you think that mathematics should be different >than other disciplines? Your continual protestations that you think it amazing and unheard of >suggests to me simply that you can't think of anything you could say >other than your open mouthed amazement. So far, all you can say is I can't believe it! In response to >which, unless you can say why, is simply repeat what I have said. Or, >if you have a criticism of what I've said, then to make it, rather >than allude vaguely to it. > Philosophy is a different kettle of fish entirely from mathematics, >> and the material I deleted seems to me quite irrelevant to a >> discussion of master's degrees in mathematics. Can you say what the differences are? >This advice applies pretty much to any strictly academic subject, >> >> So you assert. I have my doubts. You haven't yet given me >> much reason (by my standards) to lose my doubts. Well, so far you haven't even explained the doubt, other than said >it's there. I'm afraid I don't give much credence to doubts of that >degree. In other words, if you want the conversation to continue, you gotta do >more than just say you still haven't proven it to me. I've made a >fair prima facie case, and if you have an objection to register to it, >do so. Perhaps you have misunderstood what I'm saying. I'm saying that a bachelors from Podunk U, plus a masters from Really-Cool-U, >is worth as much as a bachelors from Really-Cool-U. It doesn't look to you like he's misunderstood your claim, it looks like he simply doesn't believe it's so. Neither do I. You've _stated_ that you know of plenty of examples _in math_. He's asked you to _give_ such examples. He's asked this _twice_ by my count. So far you haven't given any examples. (Speaking of if you want the conversation to continue... you don't give much credence to his doubts? He hasn't even asserted he's _right_, he's just expressed _doubts_ about what you're asserting. You're the one who's making actual assertions and then refusing to back them up with examples that you say you know of. Me, I don't give much credence to people who say they have examples of something but fail to produce them when asked.) >Thomas > ************************ David C. Ullrich ==== > You've _stated_ that you know of plenty of examples _in math_. > He's asked you to _give_ such examples. He's asked this > _twice_ by my count. So far you haven't given any examples. Huh? No, I did mention I knew first hand examples at MIT. You are free to doubt, the original poster asked am I screwed because I didn't go to a first rate school. Your doubts are nothing but doubts if you have nothing to do but say I doubt it. I *am* interested in *why* you doubt it, something neither of you have deigned to say. Thomas ==== > > You've _stated_ that you know of plenty of examples _in math_. > He's asked you to _give_ such examples. He's asked this > _twice_ by my count. So far you haven't given any examples. > > Huh? No, I did mention I knew first hand examples at MIT. > > You are free to doubt, the original poster asked am I screwed because > I didn't go to a first rate school. > > Your doubts are nothing but doubts if you have nothing to do but say > I doubt it. > > I *am* interested in *why* you doubt it, something neither of you have > deigned to say. > > Thomas > > Can you explain why you think that mathematics should be different than other disciplines? Your continual protestations that you think it amazing and unheard of suggests to me simply that you can't think of anything you could say other than your open mouthed amazement. So far, all you can say is I can't believe it! In response to which, unless you can say why, is simply repeat what I have said. Or, if you have a criticism of what I've said, then to make it, rather than allude vaguely to it. -------------- Well, I really didn't think I was going to entangle myself in this thread, but I've already put a foot in (my other post), and then I got sucked into reading the whole thread. However, I think I can offer some words of explanation of why I think Lee and David both seem reluctant to accept your conclusions. This is only my own idea of what I think they are thinking/feeling, and is based on my much more limited experience. Clearly, Lee and David have much more experience in these matters and have interacted significantly more with the people in charge of making these kinds of admissions decisions. Yet I think the fact that in my handful of years in the mathematical community I've picked up on the kinds of things (that I believe) are influencing Lee and David, show how pervasive these elements can be. Basically, in the mathematics world, there is a culture of genius that is not in the subjects you've mentioned, like philosophy. Now, I need to explain what I mean by genius, because after all, we don't normally regard geniuses as being limited to mathematics. In mathematics, it is clear what genius is and who has it. If someone is a genius, there is no doubt. This is different from philosophy, where you might say, I think he's got some good ideas, but I disagree... In mathematics, you can't solve some problem, and someone else can. And if he was the only one who could, and could do it near instantaneously, there is no more arguing or discussion if this person has genius. This unambiguity (or near-unambiguity) of the quality of genius pervades the whole institution of mathematics. Especially when it comes to recommendation letters. Even if two people had a similar performance (in terms of being able to do the work, etc.) in a class, one may, in the professor's eyes, have exhibited a genius-like quality in his/her performance. Consequently, this person will get a significantly better recommendation. The other person may be seen as a good worker, but obviously not a genius. Even if they could solve the same problems, etc., the prof might think one was just better somehow. More of a genius. What does this have to do with grad school admissions? Well, think about it: if you're a mathematician, who are you going to admit? Applicant A who has done similar work (but at a much slower rate, a big indication of non-genius ability), as applicant B, who graduated college at age 16? I don't think I'm wrong as saying that even getting a masters (in the U.S.) is seen as a sign of weakness. At the least, it shows you didn't feel ready to plunge into a Ph.D. program straightaway or you weren't strong enough. Either identifies you as a non-genius. A note about the masters: I know at least one top ten school (in the U.S.) that offers a masters that will *never*, as official policy, admit someone who graduates from their own masters program into the Ph.D. program. The masters students there are also treated much worse than the doctoral students in some very obvious ways. I believe this is reflective of the disdain many top graduate programs have toward the masters. A masters from some other country, I think, is given more respect than one from the U.S. The point you are missing is that admissions committees are NOT looking at an applicant's record to see if he/she has done well. Rather they are looking for indications of genius. A transcript, etc. can help, but if they have one recommendation that is from a highly eminent mathematician saying, this person is a genius, that's *all* they need. I think you are operating under the assumption that the committees are looking at prior performance as an indicator of future performance. That's not really so. They want to see if the applicant has any genius or near-genius qualities. Now of course, there aren't that many genius-like applicants. So the best schools will follow the above pattern of behavior closest. Lesser schools will be more willing to compromise and select people, partly based on what they believe future performance will be. Will they be able to graduate with a decent thesis? Will they do well enough to reflect back favorably on the school? And so on. But even these schools (especially the schools that are top 25 -- whatever that means) will be influenced by the cult, er I mean culture, of genius. This is why you are facing such amazement from Lee and David. They are more than familiar with the culture of genius. And they know that the very best schools, which include MIT and some of the Ivy Leagues, want geniuses more than anything else. They prefer them to the hard-workers. Because the latter are unlikely to be Fields Medalists, Wolf Prize winners, etc. ==== > This is why you are facing such amazement from Lee and David. They are > more than familiar with the culture of genius. And they know that > the very best schools, which include MIT and some of the Ivy Leagues, > want geniuses more than anything else. They prefer them to the > hard-workers. Because the latter are unlikely to be Fields > Medalists, Wolf Prize winners, etc. I am inclined to agree Chan-ho, but check this out: It is important to keep in mind that no technique has been or ever will be discovered for teaching students to have ideas. All that the faculty can do is to provide an ambience in which one's nascent abilities and insights can blossom. Moreover, Ph.D. theses vary enormously in quality, from hard exercises to highly original advances. Finally, many very good research mathematicians begin very slowly, and their theses and first few papers could be of minor interest. On the whole, we feel that the ideal attitude is: (1) a love of the subject for its own sake, accompanied by inquisitiveness about things which aren't known; and (2) a somewhat fatalistic attitude concerning creative ability, and recognition that hard work is, in the end, much more important. Taken directly from http://www.math.harvard.edu/graduate/index.html#admission So, it may also be that math people from Podunk U are looking to ride the coat-tails of Geniuses. What ever happened to studying math for math's sake? I say if someone is willing to go into debt for the majority of their adult life, devote their life to the study and progress of a subject, then let them do it. This university b.s. is so ridiculous! Lurch ==== Basically, in the mathematics world, there is a culture of genius that is not in the subjects you've mentioned, like philosophy. Maybe, maybe not... > You've _stated_ that you know of plenty of examples _in math_. > He's asked you to _give_ such examples. He's asked this > _twice_ by my count. So far you haven't given any examples. > Huh? No, I did mention I knew first hand examples at MIT. > You are free to doubt, the original poster asked am I screwed because > I didn't go to a first rate school. > Your doubts are nothing but doubts if you have nothing to do but say > I doubt it. > I *am* interested in *why* you doubt it, something neither of you have > deigned to say. > Thomas > Can you explain why you think that mathematics should be different > than other disciplines? Your continual protestations that you think it amazing and unheard of > suggests to me simply that you can't think of anything you could say > other than your open mouthed amazement. So far, all you can say is I can't believe it! In response to > which, unless you can say why, is simply repeat what I have said. Or, > if you have a criticism of what I've said, then to make it, rather > than allude vaguely to it. -------------- Well, I really didn't think I was going to entangle myself in this > thread, but I've already put a foot in (my other post), and then I got > sucked into reading the whole thread. However, I think I can offer some words of explanation of why I think > Lee and David both seem reluctant to accept your conclusions. This is > only my own idea of what I think they are thinking/feeling, and is > based on my much more limited experience. Clearly, Lee and David have > much more experience in these matters and have interacted significantly > more with the people in charge of making these kinds of admissions > decisions. Yet I think the fact that in my handful of years in the > mathematical community I've picked up on the kinds of things (that I > believe) are influencing Lee and David, show how pervasive these > elements can be. Basically, in the mathematics world, there is a culture of genius > that is not in the subjects you've mentioned, like philosophy. Now, I > need to explain what I mean by genius, because after all, we don't > normally regard geniuses as being limited to mathematics. In mathematics, it is clear what genius is and who has it. If > someone is a genius, there is no doubt. This is different from > philosophy, where you might say, I think he's got some good ideas, but > I disagree... In mathematics, you can't solve some problem, and > someone else can. And if he was the only one who could, and could do > it near instantaneously, there is no more arguing or discussion if this > person has genius. This unambiguity (or near-unambiguity) of the quality of genius > pervades the whole institution of mathematics. Especially when it > comes to recommendation letters. Even if two people had a similar > performance (in terms of being able to do the work, etc.) in a class, > one may, in the professor's eyes, have exhibited a genius-like > quality in his/her performance. Consequently, this person will get a > significantly better recommendation. The other person may be seen as a > good worker, but obviously not a genius. Even if they could solve > the same problems, etc., the prof might think one was just better > somehow. More of a genius. What does this have to do with grad school admissions? Well, think > about it: if you're a mathematician, who are you going to admit? > Applicant A who has done similar work (but at a much slower rate, a big > indication of non-genius ability), as applicant B, who graduated > college at age 16? I don't think I'm wrong as saying that even getting > a masters (in the U.S.) is seen as a sign of weakness. At the least, > it shows you didn't feel ready to plunge into a Ph.D. program > straightaway or you weren't strong enough. Either identifies you as a > non-genius. A note about the masters: I know at least one top ten school (in the > U.S.) that offers a masters that will *never*, as official policy, > admit someone who graduates from their own masters program into the > Ph.D. program. The masters students there are also treated much worse > than the doctoral students in some very obvious ways. I believe this > is reflective of the disdain many top graduate programs have toward the > masters. A masters from some other country, I think, is given more > respect than one from the U.S. The point you are missing is that admissions committees are NOT looking > at an applicant's record to see if he/she has done well. Rather they > are looking for indications of genius. A transcript, etc. can help, > but if they have one recommendation that is from a highly eminent > mathematician saying, this person is a genius, that's *all* they > need. I think you are operating under the assumption that the committees are > looking at prior performance as an indicator of future performance. > That's not really so. They want to see if the applicant has any genius > or near-genius qualities. Now of course, there aren't that many genius-like applicants. So the > best schools will follow the above pattern of behavior closest. Lesser > schools will be more willing to compromise and select people, partly > based on what they believe future performance will be. Will they be > able to graduate with a decent thesis? Will they do well enough to > reflect back favorably on the school? And so on. But even these > schools (especially the schools that are top 25 -- whatever that > means) will be influenced by the cult, er I mean culture, of genius. > This is why you are facing such amazement from Lee and David. They are > more than familiar with the culture of genius. And they know that > the very best schools, which include MIT and some of the Ivy Leagues, > want geniuses more than anything else. They prefer them to the > hard-workers. Because the latter are unlikely to be Fields > Medalists, Wolf Prize winners, etc. ==== > Basically, in the mathematics world, there is a culture of genius > that is not in the subjects you've mentioned, like philosophy. Now, I > need to explain what I mean by genius, because after all, we don't > normally regard geniuses as being limited to mathematics. I think I understand clearly what you mean here, and it's is nearly a good answer. The question is: what about the genius who goes to the fair-to-middlin undergrad school? Does the culture recognize that such people really exist? Someone who does a mediocre job and then gets a stunning masters will not trigger the genius reaction, and I agree completely that the stunning masters has not helped at all. So if you are faced with a student who says I'm not that hot, but if I go get a masters, will I get a leg up? the answer is probably no. And this is a difference between math and many other fields, precisely because of the genious factor. But if you are faced with a student who *is* that hot, but is going to a fair-to-middlin undergrad school, my claim is that *they* can certainly benefit by going to a good masters program. For example, at that good masters program, for the first time, they have the chance to get a genius recommendation from a recognized name in the field. > I think you are operating under the assumption that the committees are > looking at prior performance as an indicator of future performance. > That's not really so. They want to see if the applicant has any genius > or near-genius qualities. I think this as a very important point, and I don't disagree. It's a big difference between the math culture and many other fields. (I don't mean to imply that the math culture is wrong; I assume that it works fine for math.) My point is that there is a set of people who *do* have genius or near-genius qualities, who are at less-regarded undergrad schools, and that there are people who know this. Thomas ==== > The question is: what about the genius who goes to the fair-to-middlin > undergrad school? Does the culture recognize that such people really > exist? When I was applying to grad school around 30 years ago the answer was definitely yes; I'd bet it hasn't changed. My undergrad degree is from a land-grant university far better known for football than for academics, with a math department that sent certainly less than a half-dozen graduates on to grad school in an average year (and granted about the same number of Ph.D.s) -- but I made A's in the introductory graduate courses in algebra, analysis, and (point-set) topology, had recommendations from the people who taught them, and got a decent though not stellar result on the Putnam exam one year. I got offers from two top-25 schools but dropped out for a couple of years ... and subsequently went to a different top-25 school. ==== > > Basically, in the mathematics world, there is a culture of genius > that is not in the subjects you've mentioned, like philosophy. Now, I > need to explain what I mean by genius, because after all, we don't > normally regard geniuses as being limited to mathematics. > > I think I understand clearly what you mean here, and it's is nearly a > good answer. > > The question is: what about the genius who goes to the fair-to-middlin > undergrad school? Does the culture recognize that such people really > exist? > In my experience, yes. I know of such people and know some personally. I'm pretty confident in saying every mathematician knows of at least one such case. The caveat is that these people are recognized to exist because they are so damn brilliant. It's hard to hide that kind of brilliance. So to give advice based on the fact that there are such people is rather misleading and useless. The people to whom such advice applies don't need it! I suppose if one goes to an incredibly bad undergrad, then even if one is a genius, the profs' recs won't be given much weight, if they are not held in any esteem by the letter readers. But I would say there are enough independent channels, like the Putnam, or other contests, or the possibility of publishing in undergrad journals, or collaborating with some mathematician who will be held in some esteem, that it seems unlikely a genius-type will slip through the cracks. Of course, there are very capable people who will not appear to be geniuses or near-geniuses, and I think it's fair to say going to a bad undergrad is a big handicap. > Someone who does a mediocre job and then gets a stunning masters will > not trigger the genius reaction, and I agree completely that the > stunning masters has not helped at all. > So if you are faced with a student who says I'm not that hot, but if > I go get a masters, will I get a leg up? the answer is probably no. > And this is a difference between math and many other fields, precisely > because of the genious factor. > I think this is the point that others are trying to make. > But if you are faced with a student who *is* that hot, but is going to > a fair-to-middlin undergrad school, my claim is that *they* can > certainly benefit by going to a good masters program. For example, at > that good masters program, for the first time, they have the chance to > get a genius recommendation from a recognized name in the field. > Well, the thing is that even a fair, middle-level undergrad school will often have some very good mathematicians. Especially state schools. Just because the undergrad education sucks, doesn't mean the department as a whole does! The whole trickle-down effect caused by there not being enough slots for very good mathematicians means that if you're a genius, someone will recognize you as one, and that someone or someone else that s/he knows will have a good reputation. I fear your point, while correct, is more academic than practical. If there is a very brilliant, genius-like, student that somehow got hoodwinked into going to a mediocre undergrad, and somehow s/he is not recognized as such, even through all the independent channels I mentioned above, then sure, go to a respectable state school (or wherever they will have some well-known mathematicians) and make your genius known. In fact, if the student is *that* good, after just one semester, s/he should be able to transfer to some fine academic institution. But I think in practice, this is a rare situation, and in terms of giving advice, etc., one can't expect this to be the case. > I think you are operating under the assumption that the committees are > looking at prior performance as an indicator of future performance. > That's not really so. They want to see if the applicant has any genius > or near-genius qualities. > > I think this as a very important point, and I don't disagree. It's a > big difference between the math culture and many other fields. (I > don't mean to imply that the math culture is wrong; I assume that it > works fine for math.) > I assume so too. I have doubts occasionally, but that's for another thread, I guess ;-) > My point is that there is a set of people who *do* have genius or > near-genius qualities, who are at less-regarded undergrad schools, and > that there are people who know this. > ==== > You've _stated_ that you know of plenty of examples _in math_. >> He's asked you to _give_ such examples. He's asked this >> _twice_ by my count. So far you haven't given any examples. Huh? No, I did mention I knew first hand examples at MIT. I guess you did, sorry. >You are free to doubt, the original poster asked am I screwed because >I didn't go to a first rate school. Your doubts are nothing but doubts if you have nothing to do but say >I doubt it. I *am* interested in *why* you doubt it, something neither of you have >deigned to say. The reason I doubt he's going to get into a first-rate doctoral program was not specifically because of where he did his undergraduate work, it was because of what he said about what courses he'd taken and not taken. >Thomas > ************************ David C. Ullrich X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Pose: george_cox@btinternet.com X-Punge: Micro$oft ==== at 08:17 AM, porker899@aol.com (Porker899) said: >I checked out a book called All the Mathematics You Missed [But Need >to Know for Graduate School] from the library and was surprised by >its contents. The book is divided into 16 sections that I am >supposed to know before I get into graduate school. This is my >last year and I can check off very little. Check the catalogs of the specific schools thqt you want to apply to. That sort of general checklist is at best a guide. >3. Differentiating Vector Valued Functions There wasn't a course called something like Advanced Calculus? >4. Point Set Topolgy - No (not offered here) >6. Differential Forms and Stokes Theorem - No (nothing like that >here) Ouch! >8. Geometry - No (only course offered is one for future high school >teachers and was advised not to take it) The advice was sound. The lack of a real Geometry course was unfortunate. >11. Algebra - Yes I hope that you mean Abstract Algebra; it's essential. >Which areas do I absolutely need to know? That depends on the school. But I would expect at least basic knowledge of Set theory Groups, rings and fields Topology, including the Topolgy of the Real Line Real and Complex Analysis Along with classes that you've already taken. It might turn out that some of your course work was too shallow. -- Shmuel (Seymour J.) Metz, SysProg and JOAT not reply to spamtrap@library.lspace.org ==== >Message-id: <3fee0f34$20$fuzhry+tra$mr2ice@news.patriot.net> [...] >>3. Differentiating Vector Valued Functions There wasn't a course called something like Advanced Calculus? Yes, I'm currently taking it. We are not using a book and I don't have a syllabus for the next semester yet. I guess I will have that covered. My mistake. [...] >>11. Algebra - Yes I hope that you mean Abstract Algebra; it's essential. Yes. >>Which areas do I absolutely need to know? That depends on the school. But I would expect at least basic >knowledge of Set theory Groups, rings and fields Topology, including the Topolgy of the Real Line Real and Complex Analysis Along with classes that you've already taken. It might turn out that >some of your course work was too shallow. -- > Shmuel (Seymour J.) Metz, SysProg and JOAT ==== > The problem is that the length functional, length, is not continuous > on this function space and so does not commute with limits. I often wondered if there is a 2D analogy to the 1D limit concept whereby in the 1D case, a point approaches a point, and in the 2D case a curve approaches a curve. Naturally this limit concept can be expanded (no pun intended) to include higher dimensions, ie a volume approaching a volume... etc. ==== > The problem is that the length functional, length, is not continuous > on this function space and so does not commute with limits. > > I often wondered if there is a 2D analogy to the 1D limit concept > whereby in the 1D case, a point approaches a point, and in the 2D case > a curve approaches a curve. Naturally this limit concept can be > expanded (no pun intended) to include higher dimensions, ie a volume > approaching a volume... etc. One can define the concept of limits in a very general setting in terms of any of the following frameworks: - general topological spaces, which are defined via collections of sets - metric spaces, which are defined via a distance function, e.g. see my posting in this thread concerning the sup|f-g| metric for an example - Banach spaces, which require that a norm be defined, e.g. see Rob Johnson's posting in this thread is a Banach space, every Banach space is a metric space and every metric space is a topological space. Any of these will allow you to define convergence in n-dimensions and even in infinite dimensions, i.e. even in function spaces. The nifty thing is that the most general of these frameworks, topological spaces, has an amazingly simple definition of limits which strips them down to their essentials and really enlightens what they are. Check out a book on real analysis for more info -- be sure its one that covers all the above spaces in progression. ==== |Isn't this the same problem as needing 2 pi rho ds as the integrand for |surface area rather than 2 pi rho dx? Not really, but I'd agree that the mistake which leads people sometimes to think that they need dx rather than ds is of a similar flavor. Archimedes solved some problems which today we would solve by doing an integral. One rigorous method was known as the method of exhaustion. There were other, less rigorous methods termed mechanical, which sometimes looked a bit like considering the solid to be sliced into infinitesimal slices. The ancients knew then that this kind of method required care, and they're still right. Keith Ramsay ==== > The problem is that the length functional, length, > is not continuous on this function space and so > does not commute with limits. Hmmm... the length-function is such a nice function, that we better look for a limit-definition such that length *is* continuous. This has been emphasized by others in this thread already and it goes into the heart of the matter, as I think and as the OP seems to feel by now, too. Rainer Rosenthal r.rosenthal@web.de ==== > > The problem is that the length functional, length, > is not continuous on this function space and so > does not commute with limits. > > Hmmm... the length-function is such a nice function, > that we better look for a limit-definition such that > length *is* continuous. > > This has been emphasized by others in this thread already > and it goes into the heart of the matter, as I think and > as the OP seems to feel by now, too. But the length function being nice is the problem. The intuition that length is continuous is wrong and your request to change the topology so that it becomes continuous can't work since if it did then length and lim would commute in which case the two lengths are the same. You are going to have to change your defintion of length but if you do that, the essential Euclidean nature of the problem is changed. I think the best we can do is to notice that lim length(f_n) = 2 > length(lim f_n) = sqrt(2) suggests that even if length is not continuous it may be lower semicontinuous and, in fact, that is the case. (A function g on a metric space is continuous iff g and -g are lower semicontinuous so being lower semicontinuous gets you part way to continuity.) This can all be made precise in the metric space of bounded real functions on [0,1] with the metric: d(g,h) = sup|g(x)-h(x)| and sup is over x in [0,1]. In this setting, define, length(g), the length of a bounded real function g as: sup sum sqrt( [x_i - x_(i-1)]^2 + [g(x_i) - g(x_(i-1))]^2 ) where - sup is over all partitions 0 = x_0 < x_1 < ... < x_n = 1 of [0,1] for all n - sum is over i=1,...,n ==== > The intuition that length is continuous is wrong and > your request to change the topology so that it becomes > continuous can't work ... This is clearly wrong: Let's take the discrete topology and then every function is continuous. Well, this is just the extreme of what I had in mind: Looking for a definition of convergence of function sequences, which excludes such zappel candidates. There *must* be some definition of convergence, which is in accordance with intuition. I did enough topology once so as to succeed in finding out how to do that ... But it would be nice to get a hint by some learned people around here (Dave? Robert? Rob? ...) > since if it did then length and lim would commute > in which case the two lengths are the same. No. This is correct for the discrete topology (see above) but in a richer topology this is a non sequitur. BTW why did you write twe two lengths? You have to compare length(line) to length(n-th convergent), so you have two lengths in every step n, but infinitely many lengths in all. > You are going to have to change your defintion of length No. I don't have to. On the contrary I want to hold on to the original lovely and well known length. And it's my Don Quixote's aim to kill these ugly wood-be-convergences. This can all be made precise in the metric space of > bounded real functions on [0,1] with the metric: d(g,h) = sup|g(x)-h(x)| and sup is over x in [0,1]. > Well, if we restrict our function space to piecewise differentiable function, then the line and the stepfunctions fall into that space. And if we include some epsilon-demands like d_better(g,h) := max( sup|g(x)-h(x)|, sup|g'(x)-h'(x)| ) then we should get a more decent definition of convergence. Rainer Rosenthal r.rosenthal@web.de ==== > > The intuition that length is continuous is wrong and > your request to change the topology so that it becomes > continuous can't work ... > > This is clearly wrong: Let's take the discrete topology > and then every function is continuous. Firstly, you have deleted part of my response making it seem wrong. I didn't say no topology could make it continuous. I said that you are not going to be able to make it work without changing the essential nature of the problem. Secondly, in the discrete topology, lim f_n does not equal f so the essential nature of the original problem is not preserved. Thirdly, I think it needs to be placed in a reasonably elementary common framework to stay within the spirit of the original problem and bounded functions on [0,1] with the sup|f-g| metric seems to satisfy that pretty well. ==== > The intuition that length is continuous is wrong and > your request to change the topology so that it becomes > continuous can't work ... > This is clearly wrong: Let's take the discrete topology > and then every function is continuous. > Firstly, you have deleted part of my response ... in order to get hold of the relevant part. I have the idea of a natural topology for function sequences, where the length is a continuous function. > ... you are not going to be able to make it work without > changing the essential nature of the problem. I disagree again. The essential nature of the problem is IMO the proper definition of convergence. The OP was perplexed, since the lengths of seemingly convergent functions did not converge to the length of the limit function. > Secondly, in the discrete topology, lim f_n does not equal > f so the essential nature of the original problem is not > preserved. The essential nature is well preserved, since this radical change of topology sheds light on the role of topology itself. And the essential nature is wonderfully exhibited insofar as lim f_n does not equal f in any topology, where length shall be a meaningful term. The discrete topology is just an extreme example. The topology, which I pointed to by the metric generating formula (skipped by you): d_better(g,h) := max( sup|g(x)-h(x)|, sup|g'(x)-h'(x)| ) is quite natural and not as pathological as the discrete topology. And here we have again: lim f_n <> f. > Thirdly, I think it needs to be placed in a reasonably > elementary common framework to stay within the spirit of > the original problem and bounded functions on [0,1] with > the sup|f-g| metric seems to satisfy that pretty well. Not really. The sup|f-g| metric is too rich, too far into the direction of the trivial topology, where each sequence converges against each function. How about the enhancement (d_better from above)? The spirit of the original problem is preserved, as I think. The OP could be happy. Rainer Rosenthal r.rosenthal@web.de ==== Perhaps we are just arguing over what we regard as the essential nature of the problem. To me the problem can be stated as: If f_n converges to f then why does length(f_n) not converge to length(f)? (*) Although its slightly less obvious in the poster's original formulation, when stated this way it becomes clear that the answer is that our intuitive notion of length being continuous is wrong. To me, the if part of (*) is the essential nature of the problem -- maybe not to you (since this if part is false in all your examples). I'll give you the benefit of the doubt and interpret your response as saying that the source of the problem is that the intuitive notion that f_n converges to f is wrong and a topology so defined can make it possible for length to be continuous. ==== > Perhaps we are just arguing over what we regard as > the essential nature of the problem. Well, in a way. Yes, indeed. True, true. > To me the problem can be stated as: If f_n > converges to f then why does length(f_n) not > converge to length(f)? (*) I agree. And I am completeley happy with Rob Johnson's answer, which says: 1. Our staircase f_n functions are converging to f in the C^0 norm. And one has to live with the fact that length is not continuous. 2. Our staircase f_n functions do not converge to f in the C^1 norm (my d_better() *proud*) and so there is no need for the lengths |f_n| to converge to |f|. 3. If a sequence f_n converges to f in the C^1 norm, then |f_n| are converging against |f|. Best wishes for the New Year Rainer Rainer Rosenthal r.rosenthal@web.de ==== >> The intuition that length is continuous is wrong and >> your request to change the topology so that it becomes >> continuous can't work ... > This is clearly wrong: Let's take the discrete topology >> and then every function is continuous. >> Firstly, you have deleted part of my response ... in order to get hold of the relevant part. I have the >idea of a natural topology for function sequences, where >the length is a continuous function. Define the C^0(I->R^n) and C^1(I->R^n) norms to be ||f|| = sup|f| 0 I ||f|| = sup|f| + sup|f'| 1 I I See . Suppose a sequence of curves {f_n} converges to {f} under the C^1 norm: |L(f ) - L(f)| n | | | = | | |f'(t)| - |f'(t)| dt | | | I n | | <= | |f'(t) - f'(t)| dt | I n <= ||f - f|| n 1 Thus, if a sequence of curves converges under the C^1 norm, then the lengths of the sequence will also converge to the length of the limit. Thus, length is continuous under the C^1 norm. There is no way to control length using only the C^0 norm. Even though the staircase curves converge under the C^0 norm to the diagonal, they don't converge under the C^1 norm. >> ... you are not going to be able to make it work without >> changing the essential nature of the problem. I disagree again. The essential nature of the problem is IMO >the proper definition of convergence. The OP was perplexed, >since the lengths of seemingly convergent functions did not >converge to the length of the limit function. > Secondly, in the discrete topology, lim f_n does not equal >> f so the essential nature of the original problem is not >> preserved. The essential nature is well preserved, since this radical >change of topology sheds light on the role of topology itself. >And the essential nature is wonderfully exhibited insofar as >lim f_n does not equal f in any topology, where length shall >be a meaningful term. The discrete topology is just an extreme >example. The topology, which I pointed to by the metric generating >formula (skipped by you): d_better(g,h) := max( sup|g(x)-h(x)|, sup|g'(x)-h'(x)| ) is quite natural and not as pathological as the discrete topology. >And here we have again: lim f_n <> f. > Thirdly, I think it needs to be placed in a reasonably >> elementary common framework to stay within the spirit of >> the original problem and bounded functions on [0,1] with >> the sup|f-g| metric seems to satisfy that pretty well. Not really. The sup|f-g| metric is too rich, too far into the >direction of the trivial topology, where each sequence converges >against each function. >How about the enhancement (d_better from above)? The spirit of the >original problem is preserved, as I think. The OP could be happy. Your d_better is the C^1 norm. This norm makes length a continuous function on curves. Rob Johnson take out the trash before replying ==== > Your d_better is the C^1 norm. This norm makes length > a continuous function on curves. So finally my exclamation worked Dave? Robert? Rob? ...) :-) Best wishes for 2004 Rainer Rainer Rosenthal r.rosenthal@web.de ==== > > Your d_better is the C^1 norm. This norm makes length > a continuous function on curves. > > So finally my exclamation worked Dave? Robert? Rob? ...) :-) No one was arguing that one could not define a topology that makes length continuous or that different notions of convergence exist. The problem is that none of these different notions of convergence can result in length being continuous without violating the assumptions of the problem. Thus to make length continuous you either have to give up on f_n converging to f or change the definition of length, etc. ==== >> The problem is that the length functional, length, >> is not continuous on this function space and so >> does not commute with limits. > Hmmm... the length-function is such a nice function, > that we better look for a limit-definition such that > length *is* continuous. In theory, same as we might have in theory that the speed of light is not limiting. ==== >If we have the analytic (about x = 0) real -> real function >f(x) = sum{k=0 to oo} a(k) x^k /k!, >we might, for whatever reason, >want to define g(x) as >sum{k=0 to oo} b(k) x^k /k!, > >where {b(k)} is a permutation of {a(k)}. > >I am wondering if taking the permutations of terms of exponential >generating functions, or of ordinary generating functions, has been >studied (or has any applications). > > Applications? Does it matter? Not really. :) I was wondering more specifically if there were any applications among other branches of *pure* mathematics, or in combinatorics anyway. > > Studied? The closest thing that comes to mind is Cameron's concept of > oligomorphic permutations (google that and journal of integer sequences) > > It depends on what kinds of permutations you're thinking of: e.g. a simple > involution > b(2k) = a(2k+1) > b(2k+1) = a(2k) > > it is easy to compute gfs: > > f(x) + f(-x) f(x) - f(-x) > g(x) = x ------------ + ------------ > 2 2x > > (which can be easily generalized for more similar constant bounded > distance permutations) > > But what about the gf for the Gray code permutation? EIS A003188 (take the > basic binary reflected Gray code, convert back to integers: > <0,1,3,2,6,7,5,4,..>) you get a permutation of the integers where the > distance is unbounded. and the gf for it is ..er... not nice (IMHO) (which > makes it interesting). > > Mitch Harris thanks, Leroy Quet ==== > I think what I need to do now is to take a 10 cm long, 10 gram > weighing elastic wooden stick. I will put this stick on rather > frictionless tiles of my room. I would like to bend this stick using > thumb and middle finger of my right hand. I would like to make sure > that elastic potential energy stored in this curved stick is maximum. > Now I will tie a thread to a small stone weighing about 15 gram and > other end of loose thread to center point of curved stick. I will > place this stone near center point of bended, curved stick making sure > that when I release both ends of stick, center point of stick strikes > to center of gravity of stone. Now I will release both ends of stick > to allow center point of bended stick to strike to center of gravity > of stone. Now I will see stone propelled on rather frictionless tiles > of my room. If the propelled stone pulls the stick through tied thread > in direction of motion of stone, then I have propelled the stick, > thread and stone in only one direction without having to expel > reaction mass or using propellant. You hope to use this in space, don't you? You have a problem: what happens if you use your device twice? This problem will arise in any situation in which friction forces are the same in all directions. In particular, this includes space. Think about the following experiment: you are in a little boat, on a lake. You have big, heavy stones on board. You stay in the back of the boat: you throw a stone backwards. What happens? Your boat goes forward! And quite fast. But there is a problem, you have lost your stone. You think a little and say: why not attach a rope to the stone? So that I can take it back on board! Methinks I'm a genus! We are to enter into an age of stones&ropes! And what happens if you try? When you'll use the rope to take back the stone the boat will go backward... In the end you will have not moved. You are trying to do exactly the same thing. You don't have a chance. There is a case in which you can do something, but this is no miracle (and no apocalypse, btw). This is when friction forces are big in one way and small in the other one. Say you are in the following configuration: _________________________________________________ / / / / / / / / / ,/ / / / / / / / | +---------+ | | | device | | | +---------+ | ' ------------------------------------------------- The rails on both side are here to represent (or to implement) the oriented friction forces. You can easily move the device to the left (with some click-click), but you cannot go in the other way. In such a case, you could have bow and arrow in your device, a thread to attach the arrow to the device, some motor to bring the arrow back into the device. And now, if the friction forces are small enough compared to the weight of your arrow, and the strenght of your bow, you'll have a chance. But be sure of one thing: it won't be significantly more efficient that anything else. And probably less. Try to understand this last experiment, this is probably where you are in trouble. Your intuition tells you it _has_ to work. In some particular cases, yes. But not in general, and not when it would be great. To come back to the experiment you proposed: holding the bow, you play the role of the rail. The bow cannot go backward: you hold it. But it can go forward: you allow it to go this way. I hope this has helped you to understand your mistake, I wish you a Merry Christmas, and a happy New Year. /er. ==== Let q(r,m) = --- 1 / --- --- k^r k|m k>= sqrt(m) which is, in linear-mode, sum{k|m, k>=sqrt(m)} 1/k^r, where the sum is over the divisors of m which are >= the squareroot of m. If we again sum over the divisors, but now over every positive divisor of n, so that we have: Q(r,n) = --- / q(r,m) -- m|n = sum{m|n} q(r,m), then the average of all the Q(r,n)'s, taken over the n's, approaches a limit. ie. limit{q-> oo} q 1 --- --- q / Q(r,n) = A(r) --- n=1 = limit{q -> oo} (1/q) sum{n=1 to q} Q(r,n) And A(r) is, if I am right, ... oo --- (1+1/2+1/3+...+1/k) ------------------- / k^(r+1) --- k=1 = sum{k=1 to inf} (1+1/2+1/3+...+1/k)/ k^(1+r), which is an Euler sum. [ http://mathworld.wolfram.com/EulerSum.html ] (For example, A(1) = 2*zeta(3).) (Right?) So, since q(r,m) = sum{k|m,k<=sqrt(m)} k^r /m^r (note inequality's direction here, as opposed to in q()'s definition), I wonder naively if there is some kind of zeta-function-like reflection formula for the Euler-sum analytical continuation which relates E(r) and E(2-r), where E(r) is sum{k=1 to inf} (1+1/2+1/3+...+1/k)/ k^r. (I know of no study regarding analytical continuating Euler sums at all, nor anything beyond the consideration of such at r = integers >= 2.) thanks, Leroy Quet ==== My son bought us a couple of Pepsi drinks today, which feature a Caps for caps promotion. You buy the bottle and look inside the cap for an imprint; save the caps and you can win a team hat (cap) bearing the logo of an NFL (American football) team. The imprint inside the bottle cap is usually the name of one of these teams. I don't follow sports, but the rules inside specify the names of 32 teams (which I believe is the complete set of teams in the league). When you have collected two copies of one team name, you may claim a free hat as your prize (and no, it doesn't have to bear the imprint of the team whose name you found twice). Alternatively, some of the caps carry a Buy-one-get-one-free message (according to the rules sheet). The label of the bottle states the odds of this happening to be one in six. (Shouldn't that be _odds_ of five to one? But I digress...) I believe every cap carries exactly one imprint, although it isn't clear from the rules that there are no Sorry, try again imprints. Here is my question: The rules state, Once you have your first bottle cap [with a team logo], odds of matching such cap are 1 in 36. I would like to know how they derive this number. It appears that 1/6 of the caps win a free drink, and I am guessing that the other 5/6 of the caps are equally distributed with the imprints of the 32 teams, i.e. 5/192 of the caps say Bears, 5/192 say Bengals, etc. So once you have a cap showing Bears, isn't your probability of getting a match next time 5/192 ? That's about 1/38, not 1/36. What am I missing? I considered the possibility that they meant that the odds of matching a cap you already own, _given that_ the next cap is not a free-drink cap, were 1/36. But that's obviously wrong; it's 1/32. I considered the possibility that the 1/6 was just rounded off. Repeating the calculation with 1/(5.5) of the imprints offering a free drink, the chances that the second cap is a match to a team you already have would be (1 - 1/5.5)/32, about 1/39; with only 1/(6.5) of the caps winning a free drink, a cap matches your team's (1 - 1/6.5)/32 of the time -- about 1/37.8 . So a rounding error is not ennough. Then I considered the possibility that the team names were not printed equally often. (That sounds pretty impolitic to me, but then, I'm not in marketing!) This sort of thing is common; for example, McDonalds restaurants used to have a promotion in which customers were given a free game ticket bearing the name of an ingredient in the Big Mac sandwich; collect them all (seven, IIRC) and you get a free sandwich. The company printed far fewer tickets showing Special Sauce so the odds of getting a free sandwich were lower than 1/7 even if you were given a bundle of the other six ingredients by someone else. So assume that the fraction of the caps imprinted with the name of team i is p_i = 5/192 + x_i. Then we know sum p_i = 5/6, which is to say sum x_i = 0. Also evidently the claim is that among those people with a non-free-drink cap first, 1/36 of those people will have two identical caps; I make this out to say that sum (p_i)^2 = (5/6) (1/36), which is equivalent to sum x_i^2 = (5/6) (1/36) - 32 (5/192)^2 = 5/3456. Well, that's only 2 equations in 32 unknowns. We can find some of the solutions by looking for a 2-variable problem to solve which specializes the general case. For example, suppose there are k teams with a different probability from the other 32-k teams (k=0, 1, 2, ...) Then there are just two different probabilities to compute. I find that the equations allow for the greater and smaller probabilities to be one of many different combinations: k p1 p2 1, .06347892127, .02483401328 2, .05208333333, .02430555555 3, .04694721281, .02387902397 4, .04383151175, .02350026023 5, .04166666667, .02314814815 6, .04003864192, .02281159545 [...] 12, .03472222222, .02083333333 [...] 16, .03276559609, .01931773725 [...] 27, .02893518519, .01041666663 28, .02858307311, .00825182154 29, .02820430937, .00513612055 30, .02777777778, 0 The last case corresponds to using 30 team names each 1/36 of the time and not using the other two teams at all. The cases k=12 and k=16 show the most equitable distributions of this type, minimizing respectively the ratio and the difference between the high and the low probabilities. I don't know whether we can improve these measures by allowing the p_i to assume more than just two values. So I don't know whether I'm missing a possible alternative model, but it rather looks to me that either they or I have made an arithmetic error, or else there is a gross disparity in the distribution of the team names! Mathematically, this situation is obviously the birthday paradox. Suppose again that the 32 team names are printed equally often. Once you have 33 team imprints, you must have a match; the probability p that you have at least one match once you have k imprints is shown in the table below. Also shown is the probability q that you have at least one match after k draws (about 1/6 of which should garner a free drink); q_k is sum (5/6)^i (1/6)^(k-i) binomial(k,i) p_i. k, p q 1, 0 0 2, .0312500000 .0217013889 3, .0917968750 .0639738860 4, .1769409180 .1243626630 5, .2798233032 .1993244322 6, .3923509121 .2845765171 7, .5062851161 .3755105100 8, .6142852469 .4676137835 9, .7107139352 .5568439157 ... 27, .9999999497 .9997708172 28, .9999999921 .9998813336 29, .9999999990 .9999400091 30, .9999999999 .9999703784 31, 1.0000000000 .9999857090 32, 1.0000000000 .9999932605 33, 1 .9999968919 (So if you really, really want a free team hat, probably 8 or 9 bottles of Pepsi will get you one.) But these probabilities are affected by an unequal distribution of the team names. For example, if as above we really only use 30 of the team names (equally often), then the chances of an early match go up. I didn't work out the probabilities in other cases, but it seems clear that any choice of the p_i which makes the chance of a win with two caps equal to 1/36 rather than 5/192 will increase all the other numbers in the table too, that is, the chance of having a match when you possess 3 caps should be greater than 0.091796875 no matter what solution { p_i } is chosen for the pair of equations. I didn't see how to prove this. Such is the curse of being a mathematician: even the insignificant event can lead to quite a bit of pondering! dave ==== >My son bought us a couple of Pepsi drinks today, event can lead to quite a bit of pondering! dave Pepsi has caffeine, doesn't it? -- Mensanator Ace of Clubs ==== Given Two lines whose quations are 3x+y-8=0 and -2x+by+9=0, determine the value of b such that the two lines are perpendiclar. Ok so i know that they have to be negative reciprocals and i get stuck at y=-3x+8 y=2x-9/b What exactly do i do here? TIA for helping out guys, really appreciate it! ---= 19 East/West-Coast Specialized Servers - Total Privacy via Encryption =--- ==== > Given Two lines whose quations are 3x+y-8=0 and -2x+by+9=0, determine the > value of b such that the two lines are perpendiclar. Ok so i know that they have to be negative reciprocals and i get stuck at > y=-3x+8 > y=2x-9/b What exactly do i do here? TIA for helping out guys, really appreciate it! News==---- > http://www.newsfeed.com The #1 Newsgroup Service in the World! >100,000 > ---= 19 East/West-Coast Specialized Servers - Total Privacy via Encryption =--- So you know that the slope of the second line has to be 1/3 So we can say 2/b=1/3; which means b=6. -- David Moran Chief Meteorologist Oklahoma Storm Team ==== > y=2x-9/b You've made a mistake here.... This should be y= 2x/b - 9/b > > What exactly do i do here? TIA for helping out guys, really appreciate it! > > > News==---- http://www.newsfeed.com The #1 Newsgroup Service in the World! > Privacy via Encryption =--- ==== Can you please help me, and show the steps?? ==== >Can you please help me, and show the steps?? Translated into plain text, the inequality in the subject line might be written as |x| >= |x-3| You call this a problem; I'm guessing you want to know the values of x for which this statement is true. Here's a useful hint: when a and b are real numbers, | a - b | is the distance from a to b on the number line. So your question may be phrased, Which are the numbers x which are further (or equidistant) from 0 than they are from 3? In that form there's really nothing to write down except a picture! A glance at the real number line shows that the answer is every real number to the right of (or equal to) the midpoint between 0 and 3. You can write this is symbols if you like: suggestions are { x ; x >= 3/2 } or simply [ 3/2, oo ) Before you complain that I didn't show you the steps, let me respond that you're a lot better off in mathematics if you get used to thinking about what mathematical statements _mean_ (in English, say), instead of how to manipulate the symbols. Once you understand a meaning, you can develop your own steps and tricks. dave ==== > Can you please help me, and show the steps?? Could you actually post it as ascii text instead of the crypto you used? ==== Sniper > Can you please help me, and show the steps?? |x|≥|x-3| seems to be html for |x| >= |x-3|. But this is not true for all x. It is true only for x >= 3/2. LH ==== A = event that keys are contained in box B B = event that contestant chooses box B C = event that Monty Hall opens box A Then P(keys in box B | contestant selects B and Monty opens A) = P(A | BC) = P(ABC)/P(BC) = P(C | AB)P(AB)/P(C | B)P(B) = P(C | AB)P(B | A)P(A)/P(C | B)P(B) = (1/2)(1/3)(1/3)(1/2)(1/3) 1/3 -- Mensanator Ace of Clubs ==== Because no one bothers to write their own computer simulation. knowing the value from X and not knowing the value of X, in software its just X. Herc ==== www.SymbMath.com ==== > Hey, thanks for pointing this out. I'm certain I speak for everyone > when I say I never noticed this... Well, you know you better than I do, so you must speak for me when you say you never noticed this. Jon Miller ==== IV In Rovelli's approach, almost everything is quantized and time itself has no fundamental meaning. So, OK, things are VERY different in Rovelli's theory. No argument there. He wants to dig down to the raw manifold so he can quantize the stripped-off Einsteinian chronogeometric structure of spacetime, replete with its unified metric, thinking this may be the real solution to the quantum gravity conundrum. I say he has not properly understood the status and meaning of the unified metric. He has simply skated over this. He is trying to run before he can walk. PZ: He wants to throw away time in order to keep a unified g_uv. Read Goldstein on time in QMGR. ... JS: What do you mean by kinematical g_uv and dynamic gravitational g_uv apart from Ruvwl = 0 in the former and not in the latter. I mean what it means in Newtonian physics. We can always write a metric tensor expression for the invariant interval in Newtonian mechanics. We can then covariantly describe the fictitious inertial forces of Newtonian theory (and Jack, please don't say here that you don't know what I mean) in terms of the space-time connection field. The metric gradients then determine the strength of the apparent forces that are observed in accelerated frames. They can be viewed as the metric potentials (Tolman, Bergmann) of the fictitious force field. Of course, the space-space connections are not here associated with any forces, fictitious or otherwise. JS: Are you sure of that? Everything contributes. E.g. for a charge on a timelike non-geodesic in an external EM field Fvw d^2x^u/ds^2 + {^u|vw}(dx^v/ds)(dx^w/ds) + (e/m)e(^u^v^w l)Fvwdx^l/ds = 0 {^u|vw} is the connection field e(^u^v^w l) is the 4-antisymmetric symbol. I think that's correct off-hand? (v/c)^2]^-1/2 off the time-like geodesic it is on when Fvw = 0. On the other hand the quantum BIT field is feeling Au in its phase accumulation even when Fvw = 0 at its location. So I think you have made another error using only words and not checking the relevant math. PZ: Jack, are you able to distinguish between the Lorentzian and Einsteinian interpretations of the Lorentz contraction and time dilation? John Bell a whole essay on this in Speakable and Unspeakable. Have you read it? JS: Yes, but it makes no difference to the formal structure or to the physical predictions. It is only in the informal language. It is moot. Only until that degeneracy is lifted will there be physics there. Einstein was very interested in the constructive view that was like kinetic theory to his thermodynamics. PZ: The situation here is precisely analogous: it is the difference between viewing gravitational distortions of measurements as inseparable from the nature of spacetime and the definition of its fundamental structure, on the one hand, and viewing it as a physical effect, similar to universal thermal contraction and expansion of measuring sticks (Feynman), which is regarded as *separable* from the fundamental chronogeometric structure of spacetime. JS: Again this is not really interesting physics until a significant experimentally testable difference can be found - at least in principle if not in fact. PZ: If you are really having problems with these distinctions, I suggest you re-read Feynman's Lectures on Gravitation, where he pays considerable attention to precisely this kind of issue (in the context of developing a spin-2 quantum field theory of gravitation). Feynman was a wonderful teacher. JS: Yes I know. PZ: And I find it difficult to believe that Feynman would describe his own ideas, and his own perceptive critique of Einsteinian physics, as philosofauzy. JS: I think he was objective enough to do so if the situation warranted. PZ: That is the great Einsteinian insight -- which is. unfortunately, based on strict Einstein equivalence, which is fictitious. JS: Again I really do not understand what you mean by this sentence. PZ: Then I suggest you read just about anything Einstein published on this -- at least up to 1921. It certainly seemed to make sense to him, at least at the time. JS: He changed his mind? Early ideas mature. already given you a veritable cornucopia of direct Einstein quotes on this concept! The fact is that the reason we have a unified gravitational-inertial metric in orthodox GR is because Einstein supposed that the gravitational and inertial fields were *one and the same*. JS: They essentially are. In fact the idea of a uniform gravity field without tidal curvature is rare if not impossible to come by. PZ: You and Rovelli seem to be content to have the g_uv grin without the cat. I, on the other hand, am trying to paste this same grin on a very different cat. ... Can you explain what Rovelli means by active diff invariance with respect to a raw manifold of indistinguishable points? And how his Cartesian relationism is at all relevant to existing gravitational physics and to Einsteinian relativity? JS: Good question to which at the moment I do not have a good short answer. ... JS: Yes on just another field. But NO that it's like PV and Yilmaz. Not true at all because, at least in PV, Hal uses an absolute non-dynamical background global Minkowski space PZ: That is what Rovelli *should* be doing, but he doesn't even consider this possibility. He seems to think you can treat unified g_uv as a physical field. JS: Why do you think you cannot? PZ: Because then you arrive at the absurdity of diff invariance with respect to raw spacetime manifold as some kind of physically relevant notion of relativity -- which reduces the whole thing to absurdity. JS: You lost me. What is absurd about diff invariance? Do you also think local gauge invariance is absurd? Diff invariance is to the base space of the set of physical fiber bundles as local gauge invariance is to the several fiber spaces for lepto-quark fermion sources and gauge boson forces and self-sources with the added supersymmetry mixing the two. Diff invariance is simply locally gauging the translational subgroup of the Poincare group of the base space. Doing so converts a globally flat base space to a variably curved one without torsion. Locally gauging the Lorentz sub-group seems to introduce torsion. The compensating gauge fields restore the symmetry broken by the initial local gauging. In the case of gravity, as curvature without torsion and without residual micro-quantum zero point stress-energy density tensor i.e. tuv(exotic vacuum) = [(Fine Structure Coefficient)]^-1(Witten String Tension)]/zpfguv --> 0 /zpf = Lp^-2[Lp^3|Vacuum Coherence|^2 - 1] guv = Minkowski(uv) + d(u.v) du = Lp^2(Arg Vacuum Coherence),u Restoring the translational symmetry is found in the consequence of the Bianchi identities Guv(Einstein)^;v = 0 Which is only true when there is no torsion and no exotic vacuum. With zero torsion but exotic vacuum and insignificant Tuv(Matter) Guv(Einstein)^;v + /zpf^,vguv = 0 Assuming also metricity i.e. guv^;v = 0. One of the basic equations for practical metric engineering of weightless Alcubierre warp drive and star gate time travel is Guv(Einstein)^;v + /zpf^,vguv = 0 IMHO. PZ: You cannot paste the grin of the unified metric on the cat of Cartesian relationism, in Rovelli's definition of the term. It won't stick. PZ: I can't imagine anything more wrong-headed. And you say Rovelli is a big shot? That is why I say Rovelli's position is incoherent. JS: Is coherence in the mind of the beholder? PZ: As of the above sentence it is you who is now the beholder. :-) JS: Narcissus Principle i.e. Universe as a self-excited circuit. (Wheeler) PZ: So, what's the answer? JS: The Question is: What is The Question? (Wheeler) PZ: Yes, I know I'm sticking my neck out, but this is how Rovelli's position strikes me. You yourself admit that you haven't yet been able to make sense out of his relationism. So, OK, you have faith. JS: There is no consistent ontology for quantum gravity based on any non-Bohmian interpretation of quantum theory. The exception is Shelly Goldstein's paper in the book Physics Meets Philosophy at the Planck Scale, even he makes a mistake IMHO in not sticking to NO ACTION WITHOUT DIRECT REACTION by proposing that the BIT wave function of the universe has no sources from its IT extra variable, i.e. the 3-geometry (or something deeper like spin networks maybe or perhaps a set of D-branes with strings as 1 branes). The BIT MACRO-QUANTUM WAVE OF THE UNIVERSE is IMHO Hawking's Mind of God ONLY when it has sources! That makes Fred Hoyle's Intelligent Universe conscious IMHO. ==== ----------------------------- <^> <(áÀá)> <^> ----------------------------- > [...] > Jim, I'm going on a break, the discussion is over. You are > sitting at a comfy computer and you are free to do what you > want. I am at my computer because I am fighting for my life > while I am being tortured by a spy satellite for 2 years > continuously. it is the most hideous torture in all history, > I wish you would believe me, even give me a few hours benefit > of doubt because that is all it would take to confirm my > admitedly odd story. Don't watch your TV, its a lie. Sure, discussion is over. Maybe it wasn't such a good idea of > mine to press for resolution of these questions right now. > I'm sorry if it made things harder for you than they would > otherwise be. One last word: consider finding someone YOU trust, and > using them as a sounding board, running some of your more > unusual ideas past them, before you actually put them into > action. Internets my only medium. My life's progress out of poverty and abuse because I can't defend myself from a noisy satellite depends on the kindness of strangers. Of 5,000 replies on usenet not one has been courteous, not to even spend 1 minute on my paranormal proof. The satellite picks up your thoughts and plays them out to everyone. Sounds like Sci Fi, I am in a constant forced telelpathic dialog with a team of purist sickos passing themselves off as pyschs. Anyone nearby can hear my thoughts, most people verbally abuse me to force a nasty reply. I'm the kindest man on Earth, but that's because I'm used to conceiling anything condescending. I watched my brother and sister out my window leave yesterday, pretending I wasn't home. The alternative is half dozen people sitting around me trying to tame my thoughts. Its fucking painful, they started with chinese water torutre under a 24 hour lamp in the watchhouse 2 years ago, it didn't stop, it got much much worse. Herc 100,000 witnesses to the mind broadcasting satellite that tracks you everywhere This whole block of flats can hear this post as I type, when I go out tomorrow people will question me about Jim and sci.skeptic, degrade me and wait for me to mentally retaliate and listen in, then back on usenet no one will believe it. 2 years of this. ==== In sci.math, Virgil Hancher > >> [...] >> Jim, I'm going on a break, the discussion is over. You are >> sitting at a comfy computer and you are free to do what you >> want. I am at my computer because I am fighting for my life >> while I am being tortured by a spy satellite for 2 years >> continuously. it is the most hideous torture in all history, >> I wish you would believe me, even give me a few hours benefit >> of doubt because that is all it would take to confirm my >> admitedly odd story. Don't watch your TV, its a lie. > > You can get relief by wearing a hat of aluminium foil, or by blowing > your brains out. The first is probably easier on the brains... http://zapatopi.net/afdb.html :-) -- #191, ewill3@earthlink.net It's still legal to go .sigless. ==== > It plots and analyses any x-y data for peak location, peak height, > peak > width, semi-derivative, derivative, integral, semi-integral, > convolution, > deconvolution, curve fitting, and separating overlapped > peaks > and > background. > www.chemSoftware.com ==== This is a follow up of the previous posting. Given a, b, c, d are non-square integers such that (a, b) = 1 and (c, d) = 1. Assertion: The following equality (1) is not possible. sqrt(a^5) + sqrt(b^5) = (sqrt(c) + sqrt(d))^5 (1) Any comment upon the correctness of the assertion will be appreciated. ====