Hetong Xu's user avatar
Hetong Xu's user avatar
Hetong Xu's user avatar
Hetong Xu
  • Member for 2 years, 7 months
  • Last seen this week
  • Beijing, China
794 votes
1 answer
43k views

A proof for $\dim(R[T])=\dim(R)+1$ without prime ideals?

510 votes
10 answers
261k views

Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$

492 votes
10 answers
64k views

Best Sets of Lecture Notes and Articles

  • 49.5k
298 votes
9 answers
46k views

V.I. Arnold says Russian students can't solve this problem, but American students can -- why?

  • 7,931
253 votes
6 answers
25k views

In (relatively) simple words: What is an inverse limit?

  • 375k
158 votes
0 answers
3k views

Does every ring of integers sit inside a ring of integers that has a power basis?

  • 1,937
153 votes
2 answers
36k views

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

  • 5,253
139 votes
1 answer
27k views

Classification of prime ideals of $\mathbb{Z}[X]$

  • 40.2k
125 votes
2 answers
8k views

Pullback and Pushforward Isomorphism of Sheaves

  • 7,040
119 votes
2 answers
83k views

Prove that simultaneously diagonalizable matrices commute

  • 3,220
108 votes
8 answers
52k views

Normal subgroup of prime index

  • 6,088
93 votes
1 answer
4k views

In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual?

78 votes
3 answers
69k views

If $G/Z(G)$ is cyclic, then $G$ is abelian

  • 5,136
77 votes
3 answers
10k views

Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$

  • 10.2k
76 votes
3 answers
30k views

Prove that $\prod_{k=1}^{n-1}\sin\frac{k \pi}{n} = \frac{n}{2^{n-1}}$

  • 763
75 votes
14 answers
6k views

"Naturally occurring" non-Hausdorff spaces?

  • 1,552
68 votes
11 answers
5k views

Have there been efforts to introduce non Greek or Latin alphabets into mathematics?

66 votes
3 answers
6k views

How and why does Grothendieck's work provide tools to attack problems in number theory?

  • 12.8k
65 votes
1 answer
19k views

Divisor -- line bundle correspondence in algebraic geometry

61 votes
2 answers
10k views

Path-connected and locally connected space that is not locally path-connected

  • 1,047
61 votes
4 answers
9k views

Examples of morphisms of schemes to keep in mind?

  • 1,819
58 votes
9 answers
17k views

A linear operator commuting with all such operators is a scalar multiple of the identity.

  • 505
57 votes
5 answers
13k views

Subgroups of finitely generated groups are not necessarily finitely generated

  • 4,651
53 votes
1 answer
24k views

Baby/Papa/Mama/Big Rudin

53 votes
3 answers
12k views

$|G|>2$ implies $G$ has non trivial automorphism

53 votes
2 answers
10k views

How do you split a long exact sequence into short exact sequences?

  • 533
52 votes
4 answers
78k views

Multiplication in Permutation Groups Written in Cyclic Notation

  • 5,272
51 votes
3 answers
9k views

Ideals of $\mathbb{Z}[X]$

51 votes
5 answers
22k views

How to prove that the sum and product of two algebraic numbers is algebraic? [duplicate]

  • 10.2k
50 votes
2 answers
10k views

Global sections of $\mathcal{O}(-1)$ and $\mathcal{O}(1)$, understanding structure sheaves and twisting.

  • 935
1
2 3 4 5
38