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502 votes
7 answers
21k views

"The Egg:" Bizarre behavior of the roots of a family of polynomials.

  • 26.1k
152 votes
2 answers
35k views

Example of infinite field of characteristic $p\neq 0$

  • 5,243
133 votes
5 answers
39k views

On Ph.D. Qualifying Exams

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110 votes
12 answers
14k views

Calculating the integral $\int_0^\infty \frac{\cos x}{1+x^2}\, \mathrm{d}x$ without using complex analysis

  • 6,023
109 votes
23 answers
61k views

Complete course of self-study [closed]

109 votes
7 answers
13k views

What are the issues in modern set theory?

102 votes
19 answers
5k views

Good Physical Demonstrations of Abstract Mathematics

  • 12.3k
76 votes
5 answers
28k views

(Theoretical) Multivariable Calculus Textbooks [duplicate]

62 votes
4 answers
4k views

What's the probability that a sequence of coin flips never has twice as many heads as tails?

  • 4,014
50 votes
7 answers
11k views

$\sin 1^\circ$ is irrational but how do I prove it in a slick way? And $\tan(1^\circ)$ is .....

48 votes
3 answers
7k views

How far are the $p$-adic numbers from being algebraically closed?

  • 373k
47 votes
4 answers
11k views

Volume of Region in 5D Space

  • 473
35 votes
1 answer
15k views

Chinese Remainder theorem with non-pairwise coprime moduli

  • 4,260
32 votes
5 answers
3k views

Why is it "easier" to work with function fields than with algebraic number fields?

32 votes
6 answers
1k views

Proofs of $\lim\limits_{n \to \infty} \left(H_n - 2^{-n} \sum\limits_{k=1}^n \binom{n}{k} H_k\right) = \log 2$

  • 53.2k
28 votes
4 answers
7k views

Line integration in complex analysis

  • 5,041
27 votes
1 answer
4k views

Lecture Notes for Hatcher's Algebraic Topology

21 votes
2 answers
2k views

What's the General Expression For Probability of a Failed Gift Exchange Draw

21 votes
4 answers
29k views

How to remember the trigonometric identities

  • 2,327
20 votes
5 answers
902 views

Show $ \int_0^\infty\left(1-x\sin\frac 1 x\right)dx = \frac\pi 4 $

  • 18.6k
14 votes
7 answers
2k views

Solve trigonometric equation: $1 = m \; \text{cos}(\alpha) + \text{sin}(\alpha)$

  • 1,019
13 votes
2 answers
550 views

Exotic maps $S_5\to S_6$

12 votes
2 answers
2k views

The p-adic numbers as an ordered group

  • 920
12 votes
1 answer
5k views

The measure of the image of a set of measure zero

  • 251
9 votes
1 answer
931 views

Under what conditions does a specified conditional distribution exist

  • 1,620
9 votes
7 answers
4k views

Favorite Math Competition Problems

9 votes
4 answers
1k views

Is there a procedure to determine whether a given number is a root of unity?

8 votes
2 answers
6k views

Mean of a Convergent Sequence [duplicate]

  • 111
8 votes
2 answers
3k views

$\epsilon$-$\delta$ limits of functions question

  • 4,872
8 votes
1 answer
784 views

Counting some special derangements

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