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Mathematics

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Awarded 8249 times.
Evaluating $\int_{-1}^{1}\frac{\arctan{x}}{1+x}\ln{\left(\frac{1+x^2}{2}\right)}dx$
Awarded Jul 19 at 14:22
A tetrahedron's vertices are random points on a sphere. What is the probability that the tetrahedron's four faces are all acute triangles?
Awarded Jul 18 at 15:56
Show that $\int\limits_0^1 \left(x^{x}\right)^{\left(x^{x}\right)^{\left(x^{x}\right)^{\left(x^{x}\right)^{⋰}}}}\ \mathrm{d}x=\frac{\pi^2}{12}$.
Awarded Jul 17 at 13:40
The binomial coefficient $n\choose m$ is divisible by $n/\gcd(n,m)$
Awarded Jul 17 at 1:15
Can someone explain to me how a formula for the sine function is derived?
Awarded Jul 16 at 19:03
How to evaluate $\int_{0}^{+\infty}\exp(-ax^2-\frac b{x^2})\,dx$ for $a,b>0$
Awarded Jul 15 at 17:32
Integral $\int_0^\infty\frac{dx}{\sqrt{1+\exp\left(\frac\pi2\left(x^2-\frac1{x^2}\right)\right) }}=\sqrt{\frac\pi2}$
Awarded Jul 15 at 1:17
When is a vector "glued" to the origin?
Awarded Jul 14 at 5:35
Is there a way to describe the pattern this process creates for any set of points in a 2d plane? Will all sets necessarily have a pattern?
Awarded Jul 10 at 1:07
Tricky surface integral of vector field
Awarded Jul 9 at 21:20
Why $\sigma$-algebras represent information, and what information does $\sigma(X)$ represent?
Awarded Jul 9 at 16:27
If nonnegative $a_i$ satisfies $\sum\limits_{i=1}^na_i\ge n^2$ for all $n$, then can $\sum\limits_{i=1}^na_i^2<n^3+n^2$ as well?
Awarded Jul 9 at 4:53
Proving that Tensor Product is Associative
Awarded Jul 8 at 16:00
Subring of a finitely generated Noetherian ring need not be Noetherian? [duplicate]
Awarded Jul 3 at 18:00
Do I maybe have a new formula for the gamma function? Plus proof ideas?
Awarded Jul 3 at 16:12
On the order of elements of $\mathrm{GL}(2,q)$.
Awarded Jul 2 at 19:06
Are fractions with prime numerator and denominator dense?
Awarded Jul 1 at 22:33
Five circles in a rectangle: can the circles move?
Awarded Jul 1 at 12:53
$\int_0^{\pi/2}\int_0^{\pi/2}\frac{(\tan\alpha)(\tan\beta)}{\tan\alpha+\tan\beta} d\alpha d\beta=(0.9999999913...)(\pi/2)$? Seriously?
Awarded Jul 1 at 8:52
An actual attempt to solve $f^{(n)}(x)=f(x)^n$
Awarded Jun 29 at 0:07
Why does dividing both sides of this system of equations to each other yields infinite "incorrect solutions"?
Awarded Jun 28 at 8:42
Prove $\int_0^{\sqrt2/4}\frac1{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)(x-1+x\sqrt{9-16x})}{1-2x}}dx=\frac{\pi^2}{8}$ (from a probability question)
Awarded Jun 27 at 21:51
Dedekind cuts for $\pi$ and $e$
Awarded Jun 27 at 12:28
Does $f(x) = \sum_{k=1}^{\infty} (-1)^{k+1} \sin(x/k)$ have infinitely many real zeros?
Awarded Jun 26 at 19:08
A mysterious limit: probability that a triangle captures the centre of a circle.
Awarded Jun 26 at 16:07
Is the function $f(x) = \sum_{k=1}^\infty (-1)^{k+1} \sin(x/k)$ bounded on $\mathbb{R}$?
Awarded Jun 25 at 4:48
Proving that the arithmetic-geometric mean of $1$ and $\sqrt{2}$ is $\pi/\varpi$, where $\varpi$ is the lemniscate constant
Awarded Jun 23 at 8:23
Functional equations satisfied by both sine and tangent functions.
Awarded Jun 22 at 21:15
Are all Lie groups Matrix Lie groups?
Awarded Jun 21 at 6:31
A way to determine the ideal number of maximum iterations for an arbitrary zoom level in a Mandelbrot fractal
Awarded Jun 20 at 13:06
Why does Zorn's Lemma fail to produce a largest group?
Awarded Jun 20 at 7:34
Hahn-Banach theorem: 2 versions
Awarded Jun 19 at 20:53
Integral $\int_0^\infty\frac{\log(1+\cos x)}{1+e^x}\,dx=0$
Awarded Jun 19 at 4:16
Are all projection maps in a categorical product epic?
Awarded Jun 15 at 8:21
A new pythagorean proof
Awarded Jun 12 at 15:51
If every eigenvalue of $A$ is zero, does this mean $A$ is a zero matrix?
Awarded Jun 12 at 14:01
Locally Lipschitz implies continuity. Does the converse implication hold?
Awarded Jun 12 at 1:08
Multivariate Residue Theorem?
Awarded Jun 11 at 11:12
Prove that $f(x)\in \mathbb{Z}[x]$ such that $f(0)$ and $f(1)$ are odd has no integer roots
Awarded Jun 9 at 12:48
In a PID every nonzero prime ideal is maximal
Awarded Jun 9 at 4:27
Why can we treat differential operators as if they behave like algebraic quantities?
Awarded Jun 8 at 20:16
Do prime of the form $4k+1$ ever lead the greatest prime factor race?
Awarded Jun 6 at 7:51
Motivation for Weil pairing
Awarded Jun 6 at 4:46
Integral: $\int_0^{\pi} \frac{x}{x^2+\ln^2(2\sin x)}\,dx$
Awarded Jun 6 at 1:23
Why must a field whose a group of units is cyclic be finite?
Awarded Jun 5 at 16:47
Intrinsic vs. extrinsic properties of surfaces
Awarded Jun 4 at 6:30
how to generate tessellation cells using the Poincare disk model?
Awarded Jun 3 at 10:49
Finding the 1 of a finite field
Awarded Jun 3 at 9:34
Intuition about the first isomorphism theorem
Awarded Jun 2 at 16:42
Fourier transform of $ |x|^{s} $ and $\log|x| $
Awarded May 29 at 13:27
Lipschitz-constant gradient implies bounded eigenvalues on Hessian
Awarded May 26 at 23:09
Truncated alternating binomial sum
Awarded May 26 at 17:08
In $\mathbb{R}^n$, locally lipschitz on compact set implies lipschitz
Awarded May 26 at 5:52
How to prove that the rank of a matrix is a lower semi-continuous function?
Awarded May 25 at 15:11
Self studying math, how can I learn the most?
Awarded May 25 at 15:11
Minimal path to touch every square's area in an n by n grid
Awarded May 24 at 18:26
Real number $x$ such that $\{ x^n\}$ is constant for all $n\in S$
Awarded May 23 at 18:55
Uniform convergence of $\sum\limits_{n=1}^{\infty} x^ne^{-nx^n}$ on $(0,1)$.
Awarded May 23 at 14:50
For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
Awarded May 22 at 8:42
What kind of knot is this sculpture?
Awarded May 21 at 11:03
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