mm-271
===
: Re: Interpreting Standard Deviation as a
percentage by support1.mathforum.org (8.11.6/8.11.6/The Math
Forum, $Revision: 1.9 primary) id i2DDCCB25558;Yea, this guy
wants me to do some tests to prove some things thatreally
aren't true. But you know how it is; you can prove
almostanything you want to with stats. Anyways, he's going to
pay me checksome correlations and what not. I just got
confused when he startedtelling me weird things like one
standard deviation is about 5%.. Youmust be right though, 20%
of the mean would make sense. I was justreally confused by
what he was saying, I had never heard the s.d.> Let us say
you have a mean return of 15.6%. And you have astandard>
deviation of 20.4%.> Your sentence is ambiguous. It's clear
that the mean rate of> return is 15.6%, but it is ambiguous as
to whether the stddeviation> is in absolute or relative
terms.>*However*, it is standard in financial circles for the
standarddeviation to>be in absolute terms.> In other words, is
the rate of return that is one standard> deviation above the
mean 15.6% + 20.4% = 36% (this would be> taking the 20.4% as
an absolute), or is the rate of return> that is one std dev
above the mean 15.6% + 0.204*15.6% = 18.78%> (this would be
taking the 20.4% as relative)?> So, which does the person (or
the problem) mean when it> quotes a std dev of 20.4%?> How
many percent is one standard deviation, and> how do I compute
such a number?> If the 20.4% std dev quote means the std dev
is 20.4% of the> mean, then the std dev is 3.18%. If the 20.4%
std dev quote> is absolute, then the std dev is 20.4%.> In this
case it gets confusing because the thing being> measured is
itself a percentage!> Consider it this way -- the mean return
is 0.156. Now,> is the standard deviation 20.4% (of 0.156) or
is it 0.204?> I was talking to someone, and he said one
standard deviation isabout> 5%... how did he get this number,
please I need help with thisASAP.> Looks like he's thinking
relative, but he's still off.>*My* guess is that this someone
is completely ignoring the facts ofthe case>at hand, and just
blindly plowing standard facts about the stockmarket>(mean
return about 15%, variance about 25%, or std dev about 5%,
andall>varying depending on the time scale you choose to
measure -- and the>measurement techniques and even which
market you choose to measure).>Given the data, your guess is
as good as mine.>Jon Miller
===
: Is A Sphere A Type of
Manifold?What are the basic shape categories in topology?Bret
Cahill
===
: Re: Logarithms - Please help . THANKS>I have my
examinations coming up soon and need help on the following.
Would>appreciate if someone would post the solutions to my
problems. Appreciated, perhaps. Helpful, no.The way you learn
this is primarily not by looking at others' solutions but by
creating your own. If you get stuck, after a genuine effort,
or if you get a wrong answer and honestly can't figure out
why, then post (with the work you did) and you'll get useful
help.There are always people willing to post answers or even
solutions, but in my opinion as a teacher they are not really
helping you learn.-- Stan Brown, Oak Road Systems, Cortland
County, New York, USA http://OakRoadSystems.comAn expense does
not have to be required to be considered necessary. -- IRS Form
1040 line 23 instructions
===
: Re: Logarithms - Please help
. THANKSMr Teacher, to prove that I have asked genuine help
here are my solutions.The only reason I asked for explanation
is to compare with my solutions tosee where I was going wrong.
To prove it, let me copy you my solutions.Question 1.I do not
know how to approach the problem.Question 2.log(2x-1) +
log(x+4) = 1log(2x-1)(x+4) = log 10(2x-1)(x+4) = 10 22x + 8x -
x - 4 = 10 22x +7x-4 -10 = 0 22x + 7x -14 =0I tried to
factorize beyond this but could not proceed further. Can you
helpnow?log x + log (x+2) = 3 2 2log x + log x * log 2 = 3 2 2
2since we know that log 2 = 1 2log x + log x * 1 = 3 2 2log (x
* x) = 3 2 2log x = 3 2 2 3x =2x 2 = 8 _____x = /8I have
attempted the questions on my own several times only if you
could seemy working papers and when I failed to get the right
answer, I chose to putalready and I put my question on the
newsgroup only after trying severaltimes.>I have my
examinations coming up soon and need help on the
following.Would>appreciate if someone would post the solutions
to my problems.> Appreciated, perhaps. Helpful, no.> The way
you learn this is primarily not by looking at others'>
solutions but by creating your own. If you get stuck, after a>
genuine effort, or if you get a wrong answer and honestly
can't> figure out why, then post (with the work you did) and
you'll get> useful help.> There are always people willing to
post answers or even solutions,> but in my opinion as a
teacher they are not really helping you> learn.> --> Stan
Brown, Oak Road Systems, Cortland County, New York, USA>
http://OakRoadSystems.com> An expense does not have to be
required to be considered> necessary. -- IRS Form 1040 line 23
instructions
===
: Re: Logarithms - Please help .
THANKS>Question 1.>I do not know how to approach the
problem.It would have been nice to remind us what the problem
was. >1- Solve for y in terms of x> __>log y = 3 log /x + 2log
10> b b bI'm guessing you mean base-b logs here. I _think_ your
problem is this: log_b(y) = 3 log_b(sqrt(x)) + 2 log_b(10)Use
the identity n*log(x) = log(x^n): log_b(y) = log_b( sqrt(x^3)
) + log_b(10^2) log_b(y) = log_b( x^(3/2) ) + log_b(100)Use
the identity log(A) + log(B) = log(AB): log_b(y) = log_b( 100
* x^(3/2) )use the identity that log_b(A) = log_b(B) if and
only A = B: y = 100 * x^(3/2)or y = 100 * sqrt(x^3)>Question
2.>log(2x-1) + log(x+4) = 1>log(2x-1)(x+4) = log 10Correct,
but watch the notation: log((2x-1)(x+4)) orlog[(2x-1)(x+4)] or
similar. Order of operations is important.>(2x-1)(x+4) =
10Right.> 2>2x + 8x - x - 4 = 10Again, multi-line expressions
are problematic in Usenet. Many of us write exponents with ^
as on some calculators: 2x^2 + 7x - 4 = 10> 2>2x + 7x -14 =0>I
tried to factorize beyond this but could not proceed further.
Can you help>now?Good -- now I know exactly where you're
having a problem, and I can help.To factor a trinomial, you
need to find two numbers that add up to the coefficient of x
(7) and multiply to the product of the coefficient of x^2 and
the constant (2*(-14) = -28). The candidate factors of -28 are
1, -28 2, -14 4, -7 7, -4 14, -2 28, -1and none of those pairs
adds to 7. Therefore the trinomial cannot be factored in
integers, ad you must resort to the quadratic formula. (You
could also complete the square, which in fact is what the
quadratic formula does.) x = [-b +- sqrt(b^2-4ac)] / (2a) x =
[7 +- sqrt(49-4*2*(-14))] / 4 x = [7 +- sqrt(49+112)] / 4 x =
-(7/4) +- sqrt(161)/4>log x + log (x+2) = 3> 2 2I'm guessing
those are base-2 logs?>log x + log x * log 2 = 3> 2 2 2This is
not correct. It is true that (for a given base) log(x) + log(2)
= log(x*2) or log(2x)You used this identity correctly in your
preceding problem. But it is not true that log(x) * log(2) =
log(x+2) <-- FALSERemember that logarithms are exponents, so
they _reduce_ the level of an operation. In other words,
multiplying two numbers is analogous to adding their
logarithms.Correct solution: log_2(x) + log_2(x+2) = 3Use
log(A)+log(B) = log(AB): log_2(x^2+2x) = 3Use the definition
of logarithms: x^2 + 2x = 2^3 x^2 + 2x = 8 x^2 + 2x - 8 = 0
(x+4)(x-2) = 0 x = -4 or 2Checking in the original equation,
-4 does not work since log(-4) is not defined in the reals;
therefore -4 is an extraneous solution. But 2 is a solution:
log_2(2) + log_2(4) = 1 + 2 = 3>I have attempted the questions
on my own several times only if you could see>my working papers
and when I failed to get the right answer, I chose to
put>already and I put my question on the newsgroup only after
trying several>times.That's nice. Please remember that we
can't read your mind and know what you tried. I would never
have guessed, for instance, that factoring a quadratic was at
the root of your difficulty on one problem, or that applying a
sort of inverse distributive law was your trouble on
another.Also, please be aware that you should generally not
quote an entire discussion easiest to follow, quote only the
specific parts you are responding to; and put your comments
afterward, as you see most of us do here.-- Stan Brown, Oak
Road Systems, Cortland County, New York, USA
http://OakRoadSystems.comAn expense does not have to be
required to be considered necessary. -- IRS Form 1040 line 23
instructions
===
: Re: Logarithms - Please help .
THANKSContent-transfer-encoding: 8bit> Mr Teacher, to prove
that I have asked genuine help here are my solutions.> The
only reason I asked for explanation is to compare with my
solutions to> see where I was going wrong. To prove it, let me
copy you my solutions.> Question 1.> I do not know how to
approach the problem.The problem is difficult to read. I'll
rewrite it a little.You want to solve log_b(y) = 3log_b(Dx) +
2log_b(10) for y.3log_b(Dx) + 2log_b(10) =
log_b(D^3*x^3*10^2)So y = D^3*x^3*10^2If I didn't read the
problem correctly, I'm sure you can modify thesolution. >
Question 2.> log(2x-1) + log(x+4) = 1> log(2x-1)(x+4) = log
10> (2x-1)(x+4) = 10> 2> 2x + 8x - x - 4 = 10> 2> 2x +7x-4 -10
= 0> 2> 2x + 7x -14 =0> I tried to factorize beyond this but
could not proceed further. Can you help> now? The equation is
correct but it doesn't factor nicely - use thequadratic
equation to find the roots. [Question 3] > log x + log (x+2) =
3> 2 2> log x + log x * log 2 = 3> 2 2 2No, you've used the log
formula backwards. Do this like you didQuestion 2 and note x =
-4 is not an answer.[...][Bonus]For your trig problems, note,
for example, tan(x) = 1.4217 means x = arctan(1.4217) is one
answer. Your calculator will give you ananswer between -90
degrees and 90 degrees. Look at the graph of tan tofind the
other angles. For Question 6, you have cos(x) = 1/2.418.> I
have attempted the questions on my own several times only if
you could see> my working papers and when I failed to get the
right answer, I chose to put> already and I put my question on
the newsgroup only after trying several> times.[...]This
newsgroup gets a lot of questions that appear to be
studentsasking us to do their homework for them. Some evidence
of work, as inyour current post, will almost certainly get you
some help. Youroriginal post looked as if you had just copied
an assignment.-- Paul SperryColumbia, SC (USA)
===
: Re:
Logarithms - Please help . THANKS> Mr Teacher, to prove that I
have asked genuine help here are my solutions.> The only reason
I asked for explanation is to compare with my solutions to> see
where I was going wrong. To prove it, let me copy you my
solutions.> Question 1.> I do not know how to approach the
problem.> Question 2.> log(2x-1) + log(x+4) = 1>
log(2x-1)(x+4) = log 10> (2x-1)(x+4) = 10> 2> 2x + 8x - x - 4
= 10> 2> 2x +7x-4 -10 = 0> 2> 2x + 7x -14 =0> I tried to
factorize beyond this but could not proceed further. Can
youhelp> now?> log x + log (x+2) = 3> 2 2> log x + log x * log
2 = 3> 2 2 2> since we know that log 2 = 1> 2> log x + log x *
1 = 3> 2 2> log (x * x) = 3> 2> 2> log x = 3> 2> 2 3> x =2> x
2 = 8> _____> x = /8> I have attempted the questions on my own
several times only if you couldsee> my working papers and when
I failed to get the right answer, I chose toput> already and I
put my question on the newsgroup only after trying several>
times.>I have my examinations coming up soon and need help on
the following.> Would>appreciate if someone would post the
solutions to my problems.> Appreciated, perhaps. Helpful, no.>
The way you learn this is primarily not by looking at others'>
solutions but by creating your own. If you get stuck, after a>
genuine effort, or if you get a wrong answer and honestly
can't> figure out why, then post (with the work you did) and
you'll get> useful help.> There are always people willing to
post answers or even solutions,> but in my opinion as a
teacher they are not really helping you> learn.> --> Stan
Brown, Oak Road Systems, Cortland County, New York, USA>
http://OakRoadSystems.com> An expense does not have to be
required to be considered> necessary. -- IRS Form 1040 line 23
instructionsNot all quadratics, in fact, very few factor. For
these, you need to useeither the quadratic formula or complete
the square. Personally, I'd say usethe technique of completing
the square because you will need this skill inanalytic
geometry and integral calculus.David Moran
===
: Re:
Logarithms - Please help . THANKSwant the group to do your
homework eh?? well i can give you a few clues.for the first
one then use the laws of handling logarithms on the right
handside of the equation so as you are left with a 'single'
logarithm statement.then the arguments of the logarrithms each
side of the equation are thesame, this then yielding the
desired relationship.Same for the second one,except you are
applying the logarithm manipulationlaws to the left hand side,
and you should get a quadratic here.again a similar story for
3. just look over the manipulation laws oflogarithms and apply
them to the question and then a nice easy equationshould drop
out.question 4. you could solve by drawing the tangent
function.question 5. well what do you know about inverse trig
functions?question6 again use your calculator and draw a
graph.> I have my examinations coming up soon and need help on
the following.Would> much appreciated.> 1- Solve for y in terms
of x> __> log y = 3 log /x + 2log 10> b b b> 2- Solve log (2x -
1) + log ( x+4) = 1> 3- Solve log x + log (x +2) = 3> 2 2>
4-Find all angles less than 360.bc that satisfy the following
: tan =1.4217> 5- Find all angles less than 360.bc that
satisfy the following inverse> trignometric function.> Arccos
(.8660)> 6- Find all values for in degrees ( to the nearest
0.01.bc) for 0.bc < = <> 360.bc if sec = 2.418
===
: Re: A
NEW MATH CHAT ROOM by support1.mathforum.org
(8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id
i2DM5G311385;>Hi thought I would ask for your room and tell
you about one
at>http://
www.universalscience.comthanks.
===
: Re: Hypocritical
Fortune Tellers (What are the odds?)I'm not about to get into
this, but the creator of the threadmentioned something
interesting - the 29x29th chapter has 29 verses?For one, the
distinction of verses in the Bible was determined afterthe
bible was written, and was utilized to help transcription
(muchlike numbered lines is used in programming).Further, in a
large source of text, such as the Bible, you can find aLOT of
potentially rare occurrences of letter and number
combinations.Doesn't mean that they are spiritually
important.Reminds me a little of probability theory I read in
high school. Theodds of 2 individuals in a classroom of 20
having the same birthday isa little less than 5% chance,
whereas with 14 classrooms of 20 each,the chances of a
classroom having 2 people with the same birthday isover 50%.
An exceptionally unlikely event can occur with enough data.The
Bible, being a large source of data, contains several
unlikelycombinations.
===
: Re: Hypocritical Fortune Tellers
(What are the odds?)> I'm not about to get into this, but the
creator of the thread> mentioned something interesting - the
29x29th chapter has 29 verses?> For one, the distinction of
verses in the Bible was determined after> the bible was
written, and was utilized to help transcription (much> like
numbered lines is used in programming).> Further, in a large
source of text, such as the Bible, you can find a> LOT of
potentially rare occurrences of letter and number
combinations.> Doesn't mean that they are spiritually
important.> Reminds me a little of probability theory I read
in high school. The> odds of 2 individuals in a classroom of
20 having the same birthday is> a little less than 5% chance,
whereas with 14 classrooms of 20 each,> the chances of a
classroom having 2 people with the same birthday is> over 50%.
An exceptionally unlikely event can occur with enough data.>
The Bible, being a large source of data, contains several
unlikely> combinations.Daniel is the 6th in a sequential set
of Books that together contain 4973verses (the 666th prime),
pretty as Daniel is in part about 666:22 Song 11723 Isaiah
129224 Jeremiah 136425 Lamentations 15426 Ezekiel 127327
Daniel 357 <-the 6th in the set28 Hosea 19729 Joel 7330 Amos
146 ---- 4973 <- the 666th prime
===
: Re: Hypocritical
Fortune Tellers (What are the odds?)> hey daryl, i'm waiting
for a response.> You called me psychotic and then you come>
pressuring me for a response to your verbal> abusiveness, just
who the hell are you?!!!> You're just another abusive
anonymous> vulgar dog spewing out garbage and> unwilling to
back it up with your own> real name. -Daryl Shawn Kabatoff uhhhh, where did i call you psychotic? i'm just questioning
your> mathematics. you're the one getting all defensive. i
asked you toprovide> links to the other forums that you
supposedly post at. i got nothing.> www.christianity.com is
one of the biggest christian forums on the> internet.> if God
told you to post on religious forums, then you would think
that> this> site would be one of your first stops.> my name is
Colin Dickson - October 27th, 1974. you can even do one of>
your> little readings on me if you want to. i didnt use my
real namebecause> when it asked for a user name for the
newsgroups, i put in the username> that> i use on all the
other forums that i post at. happy now?> I haven't head any
instruction from God directing me to> publish web sites on the
internet, nor to contribute to other> people's web sites. I
post on some religious forums on the> usenet, not on the
internet. Some people use the internet> as a portal to access
my usenet postings.Humm, interesting, you say that you
contribute toreligious forums on the usenet and not on the
internet.I bet you do that because this way your material
isarchived. Am I right?> You stated can you not see how
psychotic your theory about> satan and his dark angels is
about a cointoss? And by stating> that my beliefs are
psychotic is little different than calling me> psychotic. God
desires that I get off my butt and go for a walk,> and try to
make some one to one human contact, and show the> indivual
evidence that his or her name is a gift from God. I> want the
individuals middle name and also the names and> birthdays of
the individual's family members. When you provide> me with
your common name and birthday, it's not unlike> showing me a
portion of a petal from a flower, rather than the> entire
flower. If you want to be used as an example to others,> get
me the missing stats, mail me photocopies of family ID,> and
send me some cash. I work full time on this, it's unfair> that
you would request that I work for you and then rather> than
offer me payment, you throw abuse at me.> -Daryl S.
Kabatoff
===
: Re: Hypocritical Fortune Tellers (What are
the odds?)> hey daryl, i'm waiting for a response.> You
called me psychotic and then you come> pressuring me for a
response to your verbal> abusiveness, just who the hell are
you?!!!> You're just another abusive anonymous> vulgar dog
spewing out garbage and> unwilling to back it up with your
own> real name. -Daryl Shawn Kabatoff> uhhhh, where did i
call you psychotic? i'm just questioning your> mathematics.
you're the one getting all defensive. i asked you to> provide>
links to the other forums that you supposedly post at. i got
nothing.> www.christianity.com is one of the biggest christian
forums on the> internet.> if God told you to post on religious
forums, then you would think that> this> site would be one of
your first stops.> my name is Colin Dickson - October 27th,
1974. you can even do one of> your> little readings on me if
you want to. i didnt use my real name> because> when it asked
for a user name for the newsgroups, i put in theusername>
that> i use on all the other forums that i post at. happy
now?> I haven't head any instruction from God directing me
to> publish web sites on the internet, nor to contribute to
other> people's web sites. I post on some religious forums on
the> usenet, not on the internet. Some people use the
internet> as a portal to access my usenet postings.> Humm,
interesting, you say that you contribute to> religious forums
on the usenet and not on the internet.> I bet you do that
because this way your material is> archived. Am I right?Yes
indeed, this is the case. Thank you for clarifyingthis matter.
-Daryl> You stated can you not see how psychotic your theory
about> satan and his dark angels is about a cointoss? And by
stating> that my beliefs are psychotic is little different
than calling me> psychotic. God desires that I get off my butt
and go for a walk,> and try to make some one to one human
contact, and show the> indivual evidence that his or her name
is a gift from God. I> want the individuals middle name and
also the names and> birthdays of the individual's family
members. When you provide> me with your common name and
birthday, it's not unlike> showing me a portion of a petal
from a flower, rather than the> entire flower. If you want to
be used as an example to others,> get me the missing stats,
mail me photocopies of family ID,> and send me some cash. I
work full time on this, it's unfair> that you would request
that I work for you and then rather> than offer me payment,
you throw abuse at me.> -Daryl S. Kabatoff
===
: Re:
Hypocritical Fortune Tellers (What are the odds?)> hey
daryl, i'm waiting for a response.> You called me psychotic
and then you come> pressuring me for a response to your
verbal> abusiveness, just who the hell are you?!!!> You're
just another abusive anonymous> vulgar dog spewing out garbage
and> unwilling to back it up with your own> real name. -Daryl
Shawn Kabatoff> uhhhh, where did i call you psychotic? i'm
just questioning your> mathematics. you're the one getting all
defensive. i asked you to> provide> links to the other forums
that you supposedly post at. i gotnothing.>
www.christianity.com is one of the biggest christian forums on
the> internet.> if God told you to post on religious forums,
then you would thinkthat> this> site would be one of your
first stops.> my name is Colin Dickson - October 27th, 1974.
you can even do oneof> your> little readings on me if you want
to. i didnt use my real name> because> when it asked for a user
name for the newsgroups, i put in the> username> that> i use on
all the other forums that i post at. happy now?> I haven't
head any instruction from God directing me to> publish web
sites on the internet, nor to contribute to other> people's
web sites. I post on some religious forums on the> usenet, not
on the internet. Some people use the internet> as a portal to
access my usenet postings.> Humm, interesting, you say that
you contribute to> religious forums on the usenet and not on
the internet.> I bet you do that because this way your
material is> archived. Am I right?> Yes indeed, this is the
case. Thank you for clarifying> this matter. -DarylNo problem,
we'll continue this later, God willing. -Shawn> You stated
can you not see how psychotic your theory about> satan and his
dark angels is about a cointoss? And by stating> that my
beliefs are psychotic is little different than calling me>
psychotic. God desires that I get off my butt and go for a
walk,> and try to make some one to one human contact, and show
the> indivual evidence that his or her name is a gift from God.
I> want the individuals middle name and also the names and>
birthdays of the individual's family members. When you
provide> me with your common name and birthday, it's not
unlike> showing me a portion of a petal from a flower, rather
than the> entire flower. If you want to be used as an example
to others,> get me the missing stats, mail me photocopies of
family ID,> and send me some cash. I work full time on this,
it's unfair> that you would request that I work for you and
then rather> than offer me payment, you throw abuse at me.>
-Daryl S. Kabatoff>
===
: Re: Hypocritical Fortune
Tellers (What are the odds?)
Looks like you really enjoy
talking to yourself.J
===
: Re: Hypocritical Fortune Tellers
(What are the odds?)> Zaphod Beeblebrox the 1st i presume.....
oh wait... his name is in hisemail> address colin
dickson...... anyway....OMG!!!! you REALLY got me there.> step
off christianity.com... it isnt that good... crosswalk.com has
more> content....alright, fine, www.crosswalk.com ... i dont
care. as long as its someplacewhere a lot of real intelligent
and ready-to-debate chrsitians there.. frommy experience at
www.christianity.com those guys would never let a fraudlike
this daryl kabatoff guy get away with using Bible to support
hisnumerology.> everyone who belives in the Lord Jesus Christ
will be saved and theres no> use fighting over petty little
crap.... if you accept Jesus in your life> and heard and are
in his word to better understand him he will workthrough>
you... and hes called _everyone_ to do something acording to
his talent....> hes not gonna make a hammer and tell it to
wipe noses...... zaphod i think> you should leave the poor guy
alone... daryl you should stop doing thingsin> the name of the
lord and demanding payment...if you believe in him he is> your
suffency.... remember the money changers in ther temple?....its
jusnot> kosher :)> stev-oleave the guy alone?? i've got him
saying that God told him that this ishis path in life in one
post and then contradicting this very statement inthe other. i
just want to get an explanation on that.
===
: Turing
Machines + space complexity/boundsJust wondering if anyone can
help me out with this as its comming up to exam season here in
the UK.Basically, there are questions set for us that go
something along the lines of:Given an integer k, the set of
TM-computable functions f,and inputs x of f, Does TMf need at
most k tape cells on x?and also:For the set of TM-computable
functions f and inputs x of f, is there an integer k such that
TMf needs at most k tape cells on x?Can anyone give me an idea
of how I should go about answering these sort of questions? I
dont want a solution (although if you have some examples, that
would be nice), I'd just like some help to push me in the right
direction so I can do them on my own :-) If you have some
useful web sites that deal with these sorts of things, then
that would also be great.Matt
===
: matrices of revolutioni
was trying to figure the standard matrix for rotating a
vectoraround another vector some number of radians in 3-D and
i cant findany where in my linear algebra a way to do it. ive
found a fewdifferent little 'hints' on how to do it i think.
like if u find e1 e2and e3 (basically i j and k) and find what
they become after therotation then the standard matrix will be
[a1 a2 a3] where a1 a2 anda3 are the new transformed vectors.
but i have no idea how to find a1a2 and a3. also, ive found
how to do it around an axis. but im stillvery confused on how
to do it around any random vector.any help would be
nice
===
: Re: matrices of
revolutionContent-transfer-encoding: 8bit> i was trying to
figure the standard matrix for rotating a vector> around
another vector some number of radians in 3-D and i cant find>
any where in my linear algebra a way to do it. ive found a
few> different little 'hints' on how to do it i think. like if
u find e1 e2> and e3 (basically i j and k) and find what they
become after the> rotation then the standard matrix will be
[a1 a2 a3] where a1 a2 and> a3 are the new transformed
vectors. but i have no idea how to find a1> a2 and a3. also,
ive found how to do it around an axis. but im still> very
confused on how to do it around any random vector.> any help
would be niceI think you may have some difficulty getting an
answer to this -certainly one from me. Can you say _precisely_
what you mean byrotating a vector around another vector?-- Paul
SperryColumbia, SC (USA)
===
: a simple Probability problem
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision: 1.9 primary) id i2E2aNH04860;Can anybody answer
this question: Function f(x) return 0 with probability p,
(0Can anybody answer this question: >Function f(x)
return 0 with probability p, (0probability
1-p; function g(x) return 0 with probability 1-p, return0>with
probability p. Assume we don't know the value of p. My
question>is what's the probability when f(x)=g(x)?>Thank you
very much!>Kevin
===
: Re: a simple Probability
problemalt.math.undergrad:> Can anybody answer this question:
> Function f(x) return 0 with probability p, (0 probability 1-p; function g(x) return 0 with probability
1-p, return 0> with probability p. I'm assuming that this last
bit should read 'return 1 withprobability p'; if it's the first
condition that's in error,and g(x) returns 1 with probability 1
- p and 0 withprobability p, the answer is different.> Assume
we don't know the value of p. My question> is what's the
probability when f(x)=g(x)?Indeterminate: there isn't enough
information. It would beconsistent with the information given
that g(x) = 1 - f(x),in which case Pr(f(x) = g(x)) = 0. If f
and g areindependent, Pr(f(x) = g(x) = 0) = Pr(f(x) = 0 & g(x)
= 1) =p*(1-p) = Pr(f(x) = g(x) = 1), so Pr(f(x) = g(x))
=2*p*(1-p). The maximum possible value of Pr(f(x) = g(x))
is2*min{p, 1-p}.Brian
===
: Re: tensorsWhenever you dont
understand a term, you could try something
likewww.wikipedia.com :-)You could also try planetmath.org,
etc.http://en.wikipedia.org/wiki/TensorAnyway, you can think
of a tensor this way:you've got scalars (numbers)you've got
vectors (arrays of numbers) - tensors of rank 1you've got
matrices (arrays of arrays of numbers) - tensors of rank 2so
tensors of rank 3 would be cubes of numbers requiring 3
indicestensors of rank n are data structures requiring n
indices.In fact tensors are transformations/functions in a
way, but they aremultidimensional.There is also significance
as to whether the indices are superscriptor subscript,
corresponding to covariant and contravariantvectors. Keep in
mind that there is a physics way to define tensorsand a
mathematical way. In mathematics for example, the set
ofcovariant tensors is isomorphic to the set of one-forms.
Tensor theorygoes beyond mere notation, of
course.-Greg
===
: Proving a(b - c) = ab - ac with the field
axiomsIf I have the field axioms:(Ax1) x+y = y+x(Ax2) x+(y+z) =
(x+y)+z, x(yz) = (xy)z(Ax3) x(y+z) = xy + xz(Ax4) x + 0 = x, x
* 1 = x(Ax5) if x != 0 then there is a y such that xy = 1And
the following theorems at my disposal:T1 if a+b = a+c, then b
= cT2 given a and b, there exists exactly one x such that a+x
= bT3 b - a = b + (-a)T4 -(-a) = aAnd I'm asked to prove: a(b
- c) = ab - acHow would I go about it?So far i've done thisa(b
- c)a(b + (-c)) (T3)ab + a(-c) (Ax3)I'm not sure how to prove
a(-c) = -acI'm not sure what to do. In particular there
doesn't seem to be muchavailable to me describing the results
of multiplication by positive andnegative numbers. Perhaps
I've gone about it all wrong.
===
: Re: Proving a(b - c) =
ab - ac with the field axioms Complete solution sent to the
e-mail address you had the decency toprovide.>If I have the
field axioms:>(Ax1) x+y = y+x>(Ax2) x+(y+z) = (x+y)+z, x(yz) =
(xy)z>(Ax3) x(y+z) = xy + xz>(Ax4) x + 0 = x, x * 1 = x>(Ax5)
if x != 0 then there is a y such that xy = 1>And the following
theorems at my disposal:>T1 if a+b = a+c, then b = c>T2 given a
and b, there exists exactly one x such that a+x = b>T3 b - a =
b + (-a)>T4 -(-a) = a>And I'm asked to prove: a(b - c) = ab -
ac>How would I go about it?>So far i've done this>a(b - c)>a(b
+ (-c)) (T3)>ab + a(-c) (Ax3)>I'm not sure how to prove a(-c) =
-ac>I'm not sure what to do. In particular there doesn't seem
to be much>available to me describing the results of
multiplication by positive and>negative numbers. Perhaps I've
gone about it all wrong.
===
: Re: Proving a(b - c) = ab -
ac with the field axioms> If I have the field axioms:> (Ax1)
x+y = y+x> (Ax2) x+(y+z) = (x+y)+z, x(yz) = (xy)z> (Ax3)
x(y+z) = xy + xz> (Ax4) x + 0 = x, x * 1 = x> (Ax5) if x != 0
then there is a y such that xy = 1That's not all the axioms
for a field.> And the following theorems at my disposal:> T1
if a+b = a+c, then b = c> T2 given a and b, there exists
exactly one x such that a+x = b> T3 b - a = b + (-a)> T4 -(-a)
= a> And I'm asked to prove: a(b - c) = ab - ac> How would I go
about it?> So far i've done this> a(b - c)> a(b + (-c)) (T3)>
ab + a(-c) (Ax3)> I'm not sure how to prove a(-c) = -acyou
need x - x = 0 and x0 = 00 = ac - ac = ac + -(ac)0 = a0 = a(c
- c) = a(c + -c) = ac + a(-c)-ac = a(-c) thm 1
===
: Re:
Proving a(b - c) = ab - ac with the field axioms> If I have
the field axioms:> (Ax1) x+y = y+x> (Ax2) x+(y+z) = (x+y)+z,
x(yz) = (xy)z> (Ax3) x(y+z) = xy + xz> (Ax4) x + 0 = x, x * 1
= x> (Ax5) if x != 0 then there is a y such that xy = 1>
That's not all the axioms for a field.You're right, my
mistake. I missed this one:(Ax4b) For every real number x
there is a real number y such that x + y = 0.> And the
following theorems at my disposal:> T1 if a+b = a+c, then b =
c> T2 given a and b, there exists exactly one x such that a+x
= b> T3 b - a = b + (-a)> T4 -(-a) = a> And I'm asked to
prove: a(b - c) = ab - ac> How would I go about it?> So far
i've done this> a(b - c)> a(b + (-c)) (T3)> ab + a(-c) (Ax3)>
I'm not sure how to prove a(-c) = -ac> you need x - x = 0 and
x0 = 0The interesting thing about this is that the very next
theorem I'm supposedto prove is:0 * a = a * 0 = 0So for me to
assume it at this point would be cheating I think.> 0 = ac -
ac = ac + -(ac)> 0 = a0 = a(c - c) = a(c + -c) = ac + a(-c)>
-ac = a(-c) thm 1
===
: Re: Significant 2 factor ANOVA
result with a non-sig post hoc mult t-test?er, am I missing
something here? doesn't 'significant at the 5% level'equate to
p < 0.05, which, means all of your 'before 16' t values.
However,what post-hoc multiple comparison test did you use?
Newman-Keuls?> I wondered if anyone could help me at all.> I'm
an undergraduate psychology student and am having difficulty
with> understanding> whether a significant 2 factor ANOVA
result can have a non-significantpost> hoc multiple t-test? I
will try to elaborate.> The two factors are: 1) Emotion (which
had three levels: negative, neutral> and positive) and 2) Life
period (which had two levels: under 16 years of> age and over
16 years of age).> What I'm interested in is seeing if there
is any difference between the> levels within the first
factor.> The results from my 2 factor ANOVA test are as
follows> F = 11.303, df = 2, p = 0.000> Which given a
significance level of 5% is significant.> However, using a
post-hoc t-test on all possible combinations of factor 1> and
factor 2 (6 combinations) adjusting the significance level to
0.00833> (to keep the same level of probability of a type I
error occuring). Those> tests give the following results. None
of them are significant to the 5%> level.> Before 16> Negative
and neutral> t = -3.166, df = 11, p = 0.009> Neutral and
positive> t = 2.313, df = 11, p = 0.041> Negative and
positive> t = -2.701, df = 11, p=0.021> After 16> Negative and
neutral> t = -2.909, df = 13, p = 0.12> Neutral and positive> t
= 1.437, df = 13, p = 0.174> Negative and positive> t = -1.266,
df = 13, p=0.228> What assumptions can I make about differences
between factor 1 given the> differences in significance levels?
Is it possible to have one test saying> there is a significant
difference and a post-hoc t-test suggesting thereare> no
significant differences between any of the factors?> ...> My
Raw data is below to see if there are any obvious mistakes I
have made> above, although can be ignored...> Mean Reaction
Times (ms) before 16:> P Negative Neutral Positive> 1 3034.30
3048.30 3953.60> 2 5045.60 7315.00 6462.60> 3 7165.30 7112.40
6667.70> 4 5243.40 6674.90 5998.00> 5 3913.70 4466.40 4968.20>
6 3634.30 7144.40 4265.00> 7 4717.50 5871.90 4789.60> 8 6331.80
4686.80 5325.50> 9 3144.10 4987.70 3938.90> 10 3649.20 6039.70
4196.30> 11 5347.40 6831.40 6331.70> 12 7340.30 9434.20
8128.90> Mean Reaction Times (ms) after 16:> P Negative
Neutral Positive> 1 2210.30 2508.70 2587.80> 2 1596.40 2869.80
2738.00> 3 4769.80 6976.90 6479.30> 4 3194.60 5409.60 4182.00>
5 4834.20 5766.20 5256.00> 6 4276.10 5256.50 4735.60> 7
5909.60 5303.80 6427.30> 8 3194.60 5409.60 4182.00> 9 2851.40
2440.30 3546.10> 10 4732.80 6014.70 3277.80> 11 6978.00
8316.00 7374.70> 12 3036.40 2610.80 3971.60> 13 3194.60
5409.60 1482.00> 14 7455.70 6442.50 6659.50
===
: Re: matrix
notation by support1.mathforum.org (8.11.6/8.11.6/The Math
Forum, $Revision: 1.9 primary) id i2EDOQ701689;>In my diff eqs
course, we are studying matrix exponentials, forexample>dY/dt =
AY, where Y is an n-dimensional vector, and A is an
n*ncoefficient>matrix. Our text using bold face for both the
matrix and the vector.When>writing by hand, what is the
accepted notation? I usually put thesingle>Rich Huhn Use
capital letters for matrices.
===
: need help 4 testing by
support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision: 1.9 primary) id i2EDxGm04850;call for shinpeter do
you here me?
===
: Math Help! *Testing* by
support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision: 1.9 primary) id i2EDxHu04880;What is 2+2?Call 4
Hobbit * Testing 1-2-3 *
===
: Re: A NEW MATH CHAT ROOM by
support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision: 1.9 primary) id
i2EDxGZ04846;y=x+b///////or///////y=x-b
===
: Re: Intergrals
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision: 1.9 primary) id i2EDxGk04864;Hi yogi..my lecture
notes didnt teach us wat trig substitutions to sub.. so
imquite blur but using trig to sub.. hee hee.. so im learning
all i canin this forum.i've another 2 qns here.. (probably
involving trig sub as well)Int x/(1+9x^4) dxInt
(2x^2+11)/(x^2+4) dx
===
: Copyright Issue: Dik Winter
publishing my workUnfortunately Dik Winter seems intent on
continuing to use my writingon his webpages without my
permission.My guess is that he feels that there's little I can
do about it fromhere as he's in the Netherlands.I need advice
on handling this person.How do you get someone to obey basic
laws when they're hiding out inanother country?Here's one of
his
webpages:http://homepages.cwi.nl/~dik/english/mathematics/
jsh.htmlAnd no matter how much you hate me, I hope that you
understand thatthere's a reason why people aren't allowed to
just copy someone else'swriting and publish it at their
whim.And part of it is common decency.What can I do about Dik
Winter?James Harris
===
: Re: Copyright Issue: Dik Winter
publishing my work> Unfortunately Dik Winter seems intent on
continuing to use my writing> on his webpages without my
permission.> My guess is that he feels that there's little I
can do about it from> here as he's in the Netherlands.> I need
advice on handling this person.> How do you get someone to obey
basic laws when they're hiding out in> another country?What
makes you believe he is violating the law? You already
released the material onto the internet. I suppose you could
request that he make a link to your method if you posted it to
a newsgroup, but as he admits, the website you had your method
on no longer exists.He is using your work to illustrate some
mistakes that are easy to make. I would think this is covered
under the fair use clause. Regardless, since the Netherlands
probably have similar copyright laws to those in the US, I
would start by contacting a copyright lawyer and finding out
if there is actually a problem with what he is doing from a
legal standpoint.> Here's one of his webpages:>
http://homepages.cwi.nl/~dik/english/mathematics/jsh.html> And
no matter how much you hate me, I hope that you understand
that> there's a reason why people aren't allowed to just copy
someone else's> writing and publish it at their whim.Sometimes
they are. At a whim, no. But there are circumstances when it is
perfectly legal to copy someone else's writing.> And part of it
is common decency.> What can I do about Dik Winter?Option 1:
contact a lawyer.Option 2: contact Dik Winter.Option 3: stop
worrying about it.The first option may result in you being
instructed to follow the third.-- Will Twentymanemail:
wtwentyman at copper dot net
===
: Re: Copyright Issue: Dik
Winter publishing my work>Unfortunately Dik Winter seems
intent on continuing to use my writing>on his webpages without
my permission.>My guess is that he feels that there's little I
can do about it from>here as he's in the Netherlands.>I need
advice on handling this person.Ok, here's some advice: Read
the replies you got the lasttime you made a post with utterly
stupid complaints aboutpeople violating your copyright on
things that you _posted_in public.>How do you get someone to
obey basic laws when they're hiding out in>another
country?>Here's one of his
webpages:>http://homepages.cwi.nl/~dik/english/mathematics/
jsh.html>And no matter how much you hate me, I hope that you
understand that>there's a reason why people aren't allowed to
just copy someone else's>writing and publish it at their
whim.If he's actually violating the law you should be talking
to a lawyer,not asking for advice on sci.math. (If he's not
violating any laws,as seems clear to all us non-lawyers,
you're just making a foolof yourself. No surprise there.)>And
part of it is common decency.Guffaw. Why would _you_ expect
people on sci.math to treatyou with common decency?>What can I
do about Dik Winter?I know, try treating him with some common
decency.Like you could try the same sort of common decency
youuse with the rest of us, for exampleYou stupid head!!! What
the is wrong with you Ullrich?No matter how many ing times I
tell you to off, you keepreplying to me!!!What the is your
problem you head?You Ullrich are a stupid piece of dumb who
refuses to get themessage when someone does NOT want to talk
to you, you stupid ingty asshole.You are an ASSHOLE Ullrich!!!
Now why don't you take your dumb assstupid self somewhere to
GET A ING CLUE and QUIT ING REPLYINGTO ME AS IF I EVER WANT TO
TALK TO YOU!!!!!!!!!!!!! OFF!!!!Can't you get it through your
stupid head? OFF!!!!!!!!!!!!!!!!!I'm certain if you just
explained the problem clearly like thathe'd be happy to comply
with your wishes.>James Harris
===
: Re: Copyright Issue: Dik
Winter publishing my work> Unfortunately Dik Winter seems
intent on continuing to use my writing> on his webpages
without my permission.> My guess is that he feels that there's
little I can do about it from> here as he's in the
Netherlands.> I need advice on handling this person.> How do
you get someone to obey basic laws when they're hiding out in>
another country?> Here's one of his webpages:>
http://homepages.cwi.nl/~dik/english/mathematics/jsh.html> And
no matter how much you hate me, I hope that you understand
that> there's a reason why people aren't allowed to just copy
someone else's> writing and publish it at their whim.> And
part of it is common decency.> What can I do about Dik
Winter?You could try the following.Ask him very, very, almost
disgustingly politely to removethe stuff from his site, and in
turn, declare that you alwayshave been wrong about everything;
then very, very, almostpathetically apologize for all the
disgusting things you havewritten about all these brilliant
mathematicians, and finallysolemnly promise to never show up
on any mathematicsrelated public forum again.It's worth a try,
don't you think?Dirk Vdm
===
: Re: Copyright Issue: Dik
Winter publishing my workblocked sender list,> What can I do
about Dik Winter?> You could try the following.> Ask him very,
very, almost disgustingly politely to remove> the stuff from
his site, and in turn, declare that you always> have been
wrong about everything; then very, very, almost> pathetically
apologize for all the disgusting things you have> written
about all these brilliant mathematicians, and finally>
solemnly promise to never show up on any mathematics> related
public forum again.> It's worth a try, don't you think?This
was my LOL of the day. That's definitely worth a
try.http://www.crank.net/harris.html
===
: Copyrights, fair
use, and Internet realitiesSome of you may think it's ok for
Dik Winter to copy from a post Imade to Usenet and put that on
a webpage without my permission andkeep it up despite my
protests.But it can happen to you.Now then, what if you accept
that *anyone* out there can cruisethrough Usenet, pick various
posts of yours, and put up a webpageusing your writings,
against your permission, as long as they do a fewtricks to
cover themselves?1. Claim they are doing it for educational
purposes2. Claim that their work is a critical review3. Make
sure there's no advertising on their webpage to claim
it'snon-commercial.Now then, let's say that Andrew Wiles, for
instance, decided to helpout some poster on Usenet just for
the fun of it.Later...not surprisingly...he finds that half a
dozen people have nowcopied what he posted to webpages, and
when challenged they claim it'sfair use.But you see, neither
Andrew Wiles, nor Ribet, nor *any* mathematicianwho believes
they will ever be worthy of note will deal with such
athing.They will not post on Usenet because of the issue, and
the reality ofpeople like Dik Winter.A person like Dik Winter
needs to copy my work because he can't put upsomething of his
own to draw attention, or even if he can, he STILLfeels a need
to try and draw attention to himself using me.That's the issue,
using another person's work for your own personalgain, and here
it's about drawing attention.I noticed Winter's pages by doing
a Google search on *my* name andmath.Now then, a LOT of you
clearly hate me. I know that from a lot ofposts where people
express that hatred. But here you're shootingyourselves in the
foot by thinking you gain some points by cheeringDik Winter on,
as if as long as it's being done to me it's ok withyou.Sure I'm
no Andrew Wiles or a Ribet, but they can learn lessons fromthis
issue anyway, and see how the reality of the Internet today
meansthat they can't come out on a forum like this one, unless
they'vealready decided that whatever they post is fair game for
*anyone* inthe world to toss up on a webpage.But I guess, they
and you knew that already, as people like Dik Winterare out
there.James Harris
===
: Re: Looking for a good book on
proofs...You might like:Proofs from the Book Third
EditionMartin Aigner, Gunter M. ZeiglerThe above book is full
of satisfyingly short brilliant proofs thatPaul Erdos would
consider to be in The Book.The Book in which God maintains the
perfect proofs for mathematicaltheorems, following the dictum
of G. H. Hardy that there is no placefor ugly
mathematics.Reading, Writing, ProvingA Closer Look at
MathematicsUlrich Daepp, Pamela GorkinThe above book, which is
based on Polya's method of problem solving,aids students in
their transition from calculus (or precalculus) tohigher-level
mathematics.Casey