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1500 questions
126
votes
4 answers
Expectation of the maximum of gaussian random variables
Is there an exact or good approximate expression for the expectation, variance or other moments of the maximum of $n$ independent, identically distributed gaussian random variables where $n$ is large? If $F$ is the cumulative distribution function…
Chris Taylor
- 30,025
126
votes
9 answers
Why is $\cos (90)=-0.4$ in WebGL?
I'm a graphical artist who is completely out of my depth on this site. However, I'm dabbling in WebGL (3D software for internet browsers) and trying to animate a bouncing ball. Apparently we can use trigonometry to create nice smooth curves.…
Starkers
- 1,247
126
votes
0 answers
A question about divisibility of sum of two consecutive primes
I was curious about the sum of two consecutive primes and after proving that the sum for the odd primes always has at least 3 prime divisors , I came up with this question: Find the least natural number $k$ so that there will be only a finite number…
CODE
- 5,197
126
votes
1 answer
How do we know an $ \aleph_1 $ exists at all?
I have two questions, actually. The first is as the title says: how do we know there exists an infinite cardinal such that there exist no other cardinals between it and $ \aleph_0 $ ? (We would have to assume or derive the existence of such an…
anon
- 156,297
126
votes
11 answers
What does it mean to have a determinant equal to zero?
After looking in my book for a couple of hours, I'm still confused about what it means for a $(n\times n)$-matrix $A$ to have a determinant equal to zero, $\det(A)=0$. I hope someone can explain this to me in plain English.
user2171775
- 1,403
126
votes
11 answers
Find the average of $\sin^{100} (x)$ in 5 minutes?
I read this quote attributed to VI Arnold . "Who can't calculate the average value of the one hundredth power of the sine function within five minutes, doesn't understand mathematics - even if he studied supermanifolds, non-standard calculus or…
Please Delete Account
126
votes
26 answers
Examples of problems that are easier in the infinite case than in the finite case.
I am looking for examples of problems that are easier in the infinite case than in the finite case. I really can't think of any good ones for now, but I'll be sure to add some when I do.
Asinomás
- 107,927
126
votes
16 answers
What is the smallest unknown natural number?
There are several unknown numbers in mathematics, such as optimal constants in some inequalities. Often it is enough to some estimates for these numbers from above and below, but finding the exact values is also interesting. There are situations…
Joonas Ilmavirta
- 26,444
126
votes
13 answers
What are some interpretations of Von Neumann's quote?
John Von Neumann once said to Felix Smith, "Young man, in mathematics you don't understand things. You just get used to them." This was a response to Smith's fear about the method of characteristics. Did he mean that with experience and practice,…
125
votes
5 answers
How were 'old-school' mathematics graphics created?
I really enjoy the style of technical diagrams in many mathematics books published in the mid-to-late 20th century. For example, and as a starting point, here is a picture that I just saw today: Does anybody know how this graphic was created? Were…
TSGM
- 1,263
125
votes
4 answers
What is the difference and relationship between the binomial and Bernoulli distributions?
How should I understand the difference or relationship between binomial and Bernoulli distribution?
user122358
- 2,842
125
votes
4 answers
What is the term for a factorial type operation, but with summation instead of products?
(Pardon if this seems a bit beginner, this is my first post in math - trying to improve my knowledge while tackling Project Euler problems) I'm aware of Sigma notation, but is there a function/name for e.g. $$ 4 + 3 + 2 + 1 \longrightarrow 10 ,$$…
barfoon
- 1,499
125
votes
10 answers
How can I find the surface area of a normal chicken egg?
This morning, I had eggs for breakfast, and I was looking at the pieces of broken shells and thought "What is the surface area of this egg?" The problem is that I have no real idea about how to find the surface area. I have learned formulas for…
yiyi
- 7,476
125
votes
7 answers
What remains in a student's mind
I'm a first year graduate student of mathematics and I have an important question. I like studying math and when I attend, a course I try to study in the best way possible, with different textbooks and moreover I try to understand the concepts…
Dubious
- 14,268
124
votes
8 answers
probability $2/4$ vs $3/6$
Recently I was asked the following in an interview: If you are a pretty good basketball player, and were betting on whether you could make $2$ out of $4$ or $3$ out of $6$ baskets, which would you take? I said anyone since ratio is same. Any…
zephyr
- 1,069