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William
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490 votes
10 answers
64k views

Best Sets of Lecture Notes and Articles

127 votes
5 answers
12k views

Why does L'Hopital's rule fail in calculating $\lim_{x \to \infty} \frac{x}{x+\sin(x)}$?

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75 votes
9 answers
6k views

Is it bad form to write mysterious proofs without explaining what one intends to do? [closed]

  • 1,331
67 votes
7 answers
11k views

Intuition on group homomorphisms

38 votes
5 answers
2k views

What other tricks and techniques can I use in integration?

36 votes
5 answers
59k views

What is the intuitive meaning of the basis of a vector space and the span?

  • 999
36 votes
6 answers
4k views

The formalism behind integration by substitution

  • 28.2k
27 votes
2 answers
1k views

Why this $\sigma \pi \sigma^{-1}$ keeps appearing in my group theory book? (cycle decomposition)

26 votes
3 answers
851 views

Evaluate $\lim\limits_{n\rightarrow \infty}\frac{n+n^2+n^3+\cdots +n^n}{1^n+2^n+3^n+\cdots +n^n}.$

  • 13.2k
23 votes
7 answers
4k views

How can I visualise groups in Group Theory?

21 votes
1 answer
15k views

counting the number of elements in a conjugacy class of $S_n$

19 votes
2 answers
10k views

Permutation groups and symmetric groups

  • 3,745
18 votes
4 answers
2k views

How to simplify $\int{\sqrt[4]{1-8{{x}^{2}}+8{{x}^{4}}-4x\sqrt{{{x}^{2}}-1}+8{{x}^{3}}\sqrt{{{x}^{2}}-1}}dx}$?

12 votes
2 answers
2k views

What does it mean when people say that groups are a study of symmetry?

11 votes
4 answers
5k views

The meaning of various equality symbols

  • 459
10 votes
3 answers
456 views

Integrating $\int_0^1 \frac {\log(1-x)\log^2(1+x)}x \mathrm{d}x$

  • 3,998
10 votes
2 answers
582 views

What is an intuition behind conjugate permutations?

  • 515
7 votes
3 answers
1k views

What are the most popular techniques of proving inequalities?

5 votes
3 answers
333 views

Why are units called units?

  • 237
5 votes
1 answer
374 views

What is the geometrical meaning of the total differential?

4 votes
1 answer
192 views

If $f(f(x)) = 2x+1$, what is $f(13)$? [SOLVED by @DonThousand]

3 votes
1 answer
207 views

Explanation for how limit of a sum can be converted to definite integration

2 votes
0 answers
152 views

True or False : What are some tricky questions in calculus? (or in overall) [closed]

  • 1,101
1 vote
3 answers
7k views

Is this discontinuous function Riemann Integrable?

  • 369
1 vote
1 answer
135 views

What motivated hyperbolic functions?

  • 2,955
1 vote
1 answer
90 views

How to prove that the sequence (${x_n}$) converges and calculate $\lim _{n\to \infty }\left(x_n\right)$

1 vote
0 answers
66 views

How many positive divisors of 7560 are coprime to 15?

0 votes
2 answers
79 views

Does $\left\{a_n\right\}$ converges to $0$ or $3$

0 votes
1 answer
145 views

Intuition behind : If rank of a matrix is $r$ then it has a maximum of $r$ non zero eigen values

0 votes
2 answers
160 views

Reference book for problem solving (Multivariable Calculus).

  • 4,435