Spenser

Graduate student in mathematics.

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Show $\sum_{n=0}^\infty\frac{1}{a^2+n^2}=\frac{1+a\pi\coth a\pi}{2a^2}$

sequences-and-series asked Oct 6, 2012 at 18:38

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39 votes

Non-trivial open dense subset of $\mathbb{R}$.

real-analysis general-topology asked Oct 28, 2013 at 2:36

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36 votes

Prove the divergence of the sequence $\left\{ \sin(n) \right\}_{n=1}^{\infty}$.

sequences-and-series asked Nov 17, 2012 at 1:54

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27 votes

Sum of reciprocals of primes factorial: $\sum_{p\;\text{prime}}\frac{1}{p!}$

sequences-and-series prime-numbers asked Nov 2, 2013 at 2:11

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21 votes

Visualizing functions on the integers

tikz-pgf asked Sep 12, 2013 at 21:59

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21 votes

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

calculus integration improper-integrals asked Sep 4, 2012 at 1:07

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17 votes

The absolute value of a Riemann integrable function is Riemann integrable.

real-analysis integration absolute-value riemann-integration riemann-sum asked Feb 27, 2013 at 18:11

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16 votes

Examples of nonlinear ordinary differential equations with elementary solutions.

differential-equations big-list asked May 20, 2013 at 18:08

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15 votes

Show that if $T_1$, $T_2$ are normal operators that commute then $T_1+T_2$ and $T_1T_2$ are normal.

linear-algebra inner-product-space exercises-and-solutions asked Apr 21, 2013 at 21:05

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15 votes

If $F:M\to N$ is a smooth embedding, then so is $dF:TM\to TN$.

general-topology differential-geometry manifolds differential-topology smooth-manifolds asked Jun 1, 2015 at 14:24

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Top Answers

What is an odd prime?

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Is the Lie Algebra of a connected abelian group abelian?

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Why doesn't this operation work?

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How does the Herglotz trick work?

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Function that maps the "pureness" of a rational number?

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Show $\sum\limits_{d|n}\phi(d) = n$.

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Reference for redundance of inversion condition for Lie groups

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Are continuous functions with compact support bounded?

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Why are there four solutions to $x^2-2x-8=0$ in $\mathbb{R}$? Or am I wrong?

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Does trivial fundamental group imply contractible?

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Is the identity matrix the only matrix which is its own inverse?

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Rational or Irrational number

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Is there a matrix $A$ such that: $A^4=\begin{pmatrix}0 & 2 & -1 & 1\\ 0 & 0 & 3 &1\\ 0 & 0& 0 & 4\\ 0 & 0 & 0 & 0 \\ \end{pmatrix} ~?$

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Great contributions to mathematics by older mathematicians

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If $f(x)+2f(1/x)=3x$, find all $y$ such that $f(y)=f(-y)$.

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Extension Lemma for Smooth maps (Lee vs. Lee)

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Modulus of a complex number

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Looking for a good alternative to 'An introduction to manifolds' by Loring W. Tu

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Proving $e^{-|x|}$ is Lipschitz

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Not sure about my proof that orthogonal matrices are a manifold in ${\rm Mat}_{n \times n}(\mathbb{R})$

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Approximation of $\sqrt{ x + y } - \sqrt{ x - y }$

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Do there exist several positive real numbers such that their sum is $1$ and sum of their squares is less than $0.01$

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Does $\sum_{n=1}^\infty \left(e^{\frac{1}{n}} - 1\right)$ converge?

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Is the set of decreasing functions from $\Bbb N$ to $\Bbb N$ countable?

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Which is bigger: $\sqrt{1001} - \sqrt{1000}$, or $\frac{1}{10}$?

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Special Orthogonal Group $SO(2)$

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How can I solve this equation $x^{x^{x^{x^{.^{.^{.}}}}}}-a=0$

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Proof that $\Bbb R/\Bbb Z$ is isomorphic to $S^1$

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Let $f: X \to X$ be such that $d(f(x), f(y)) = d(x, y)$ for all $x, y \in X$. To show that $f$ is onto.

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If $\{f(x)\}^2 = 2\int_0^xf(t)dt $ then $f(x) = x$ for all $x \geq 0$.

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