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1500 questions
107
votes
16 answers
What's the difference between stochastic and random?
What's the difference between stochastic and random?
Red Banana
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107
votes
13 answers
Why would I want to multiply two polynomials?
I'm hoping that this isn't such a basic question that it gets completely laughed off the site, but why would I want to multiply two polynomials together? I flipped through some algebra books and have googled around a bit, and whenever they introduce…
user3818
- 1,079
107
votes
4 answers
How did Hermite calculate $e^{\pi\sqrt{163}}$ in 1859?
Pretend you are in 1859. What is a fast, efficient, and accurate way to numerically evaluate constants like that to, say, 20 decimal places, using ONLY pen and paper?
Tito Piezas III
- 61,356
106
votes
15 answers
Problems that become easier in a more general form
When solving a problem, we often look at some special cases first, then try to work our way up to the general case. It would be interesting to see some counterexamples to this mental process, i.e. problems that become easier when you formulate them…
MGA
- 9,869
106
votes
2 answers
Help me put these enormous numbers in order: googol, googol-plex-bang, googol-stack and so on
Popular mathematics folklore provides some simple tools enabling us compactly to describe some truly enormous numbers. For example, the number $10^{100}$ is commonly known as a googol , and a googol plex is $10^{10^{100}}$. For any number $x$, we…
JDH
- 45,866
106
votes
7 answers
Union of two vector subspaces not a subspace?
Union of two vector subspaces not a subspace? I'm having a difficult time understanding this statement. Can someone please explain with a concrete example?
NSjonas
- 1,235
106
votes
8 answers
Has Prof. Otelbaev shown existence of strong solutions for Navier-Stokes equations?
Moderator Notice : I am unilaterally closing this question for three reasons. The discussion here has turned too chatty and not suitable for the MSE framework. Given the recent pre-print of T. Tao (see also the blog-post here ), the continued…
electronp
- 151
106
votes
4 answers
Factorial, but with addition
Is there a notation for addition form of factorial? $$5! = 5\times4\times3\times2\times1$$ That's pretty obvious. But I'm wondering what I'd need to use to describe $$5+4+3+2+1$$ like the factorial $5!$ way. EDIT: I know about the formula. I want to…
akinuri
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106
votes
23 answers
Is math built on assumptions?
I just came across this statement when I was lecturing a student on math and strictly speaking I used: Assuming that the value of $x$ equals <something>, ... One of my students just rose and asked me: Why do we assume so much in math? Is math really…
Anz Joy
- 1,448
106
votes
16 answers
Reference book on measure theory
I post this question with some personal specifications. I hope it does not overlap with old posted questions. Recently I strongly feel that I have to review the knowledge of measure theory for the sake of starting my thesis. I am not totally new…
newbie
- 3,661
106
votes
20 answers
Can the golden ratio accurately be expressed in terms of $e$ and $\pi$
I was playing around with numbers when I noticed that $\sqrt e$ was very somewhat close to $\phi$ And so, I took it upon myself to try to find a way to express the golden ratio in terms of the infamous values, $\large\pi$ and $\large e$ The closest…
Nick
- 7,074
106
votes
6 answers
linear algebra over a division ring vs. over a field
When I was studying linear algebra in the first year, from what I remember, vector spaces were always defined over a field, which was in every single concrete example equal to either $\mathbb{R}$ or $\mathbb{C}$. In Associative Algebra course, we…
Leo
- 11,112
106
votes
6 answers
Why isn't reflexivity redundant in the definition of equivalence relation?
An equivalence relation is defined by three properties: reflexivity, symmetry and transitivity. Doesn't symmetry and transitivity implies reflexivity? Consider the following argument. For any $a$ and $b$, $a R b$ implies $b R a$ by symmetry. Using…
Chao Xu
- 5,986
106
votes
19 answers
Anecdotes about famous mathematicians or physicists
I'm not sure whether this question suits this website, however, I don't know where else I could ask it. It is no mathematical problem or something similar, still I hope it won't be closed. A few weeks ago, our assistant professor in physics told us…
Huy
- 6,897
106
votes
2 answers
What is the solution to Nash's problem presented in "A Beautiful Mind"?
I was watching the said movie the other night, and I started thinking about the equation posed by Nash in the movie. More specifically, the one he said would take some students a lifetime to solve (obviously, an exaggeration). Nonetheless, one can't…
Mlagma
- 1,757