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2d
comment How can I learn Real Analysis in 10 days?
oh, and if your school library has copies of old exams, use those to focus your efforts. For standard courses, the exams probably don't change much from year to year.
2d
comment How can I learn Real Analysis in 10 days?
go to your school library right now and take out a couple texts that look like they have the right contents.
2d
comment How can I learn Real Analysis in 10 days?
Stop reading math.stackexchange.com and start reading the appropriate sections in the text. Read the theory, and the statements of the worked examples, then try to solve the worked examples yourself. Drink much coffee. Make sure you get a decent night's sleep before the exam.
Jan
17
comment What are some good books about martingales?
Williams: Probability with Martingales
Feb
13
comment Can the matrices $A$ and $I+A$ have the same determinant?
do you know about eigenvalues & trace?
Jan
23
comment Division of two random variables of uniform distributions
Just to try out Mathematica's probability framework: D[Probability[ x/y <= z, {x [Distributed] UniformDistribution[{0, 1}], y [Distributed] UniformDistribution[{1, 3}]}], z] yields (for the pdf) 2 if z<1/3, (6-2z)/(4z)-(-z^2+6z-1)/(4z^2) if 1/3<z<1 and 0 elsewhere.
Jan
16
comment Fun but serious mathematics books to gift advanced undergraduates.
+1 for "Proofs and Confirmations" by David Bressoud. It is ridiculously good.
Nov
29
comment Example of two dependent random variables that satisfy $E[f(X)f(Y)]=Ef(X)Ef(Y)$ for every $f$
@NateEldredge: that is what I figured. So if you do the arithmetic, it does not work out. f(1)P(X=1)+f(2)P(X=2)+f(3)P(X=3)=(5x+9y+12z)/30, not (3x+3y+4z)/10....unless I'm seriously caffeine deficient right now.
Nov
29
comment Example of two dependent random variables that satisfy $E[f(X)f(Y)]=Ef(X)Ef(Y)$ for every $f$
Can you pls explain how you got E(f(X))?
Jul
17
comment What does the variance/SD of a set signify?
See the chebyshev inequality.
May
17
comment What's the sum of $\sum_{k=1}^{\infty} e^{-k(x-k)^{2}}$?
Look up the Euler Maclaurin formula....Mathematica can do the integral, and it involves the erf function.
Mar
9
comment Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$
@RobertIsrael: Phew - now I can drink the coffee slowly, rather than chugging it. That helps a huge amount, much appreciated!
Mar
9
comment Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$
@RobertIsrael: Thanks much. There are still (at least) two things I'm not getting. You say $\exp(n \log(1-p^k)) \approx \exp(n p^k)$, shouldn't it be $\exp(n \log(1-p^k)) \approx \exp(-n p^k)$ (negative sign)? And why are we solving $npk \approx 1$ Since this is the size of the term $f(k,n)$, wouldn't we want it to be $\exp(n p^k) \approx 1$?
Mar
9
comment Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$
@RobertIsrael: Thanks for the helpful comments. I too had thought about splitting the summation into two parts, one with terms close to zero, the other with terms close to one, but didn't see how to choose the splitting point appropriately. How did you decide on $\frac{\log n}{\log\frac{1}{p}}$?
Jul
25
comment Help solving: Problem on Normal Distribution of Data
Clearly this is a fictional example. Phone call durations do not come from a normal distribution - calculate the probability that a call takes less than 0 seconds, it is not zero!
May
10
comment Need good material on multifractal analysis
When I read it, I already knew why multifractals were interesting and what I needed to analyze & why. What I needed was the 'how', and I got that from this book. Riedi does have some interesting papers though, I remember really liking "The Multiscale Nature of Network Traffic: Discovery, Analysis, and Modelling". Also have a look at "Why study multifractal spectra?" by Peter Morters at people.bath.ac.uk/maspm/whystudy.pdf
Mar
29
comment How to show that $\sum\limits_{k=1}^{n-1}\frac{k!k^{n-k}}{n!}$ is asymptotically $\sqrt{\frac{\pi n}{2}}$?
Thanks for all the help. I was expecting something simpler when they said " elementary asymptotic methods", but this will certainly do.
Nov
7
comment Best Maths books for non-mathematicians
Loved this too!
Oct
22
comment Kindle as a Tool for Mathematicians?
I am also very interested in this question. I am particularly interested in how .pdf files display - are they all good, or do some look wonky, under different magnification levels, etc.