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Interesting 10 Bountied Hot Week Month
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Determine the convergence behavior of $\sum_{n=1}^{\infty} \frac{a_{n}}{n^x}$

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Prove that $\sum_{k=1}^{n} \left\lfloor \log_{2}\!\left(\frac{2n}{2k-1}\right) \right\rfloor = n$ where $n$ is a natural number.

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Rishit Garg
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Obtain (or close to) Identity matrix by multiplying two vectors such as: $D * (C)^H = I$

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Modelling a dice game without straightforward computation

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Jack Meow Meow
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1 answer
55 views

How many components does an arc meet in a continuum

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David Hartley
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1 answer
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Analytic sum of an alternating series involving $n/(n+\sqrt{a^2+n^2})^2$

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PierreCarre
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2 votes
2 answers
443 views

Terminology: Why is it called sheaf Cohomology?

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Amelia Tearheart
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3 answers
854 views

Showing $x^4+x^2+x+1$ irreducible over $\mathbb{Z_3}$

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Jianing Song
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2 votes
1 answer
771 views

Absolute value of derivative of complex analytic function

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1 vote
2 answers
416 views

Kolakoski sequence

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Ciro Santilli OurBigBook.com
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Closed form for a symmetric sum of squared binomials

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Alex
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1 answer
485 views

No eigenvalue of a graph is larger than the maximum degree

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minh quý lê
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2 answers
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The only area–preserving linear symmetry of a strictly convex body fixing a boundary point is the identity?

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Christophe Boilley
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12 votes
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Is the transfer principle useless?

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Mikhail Katz
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1 vote
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23 views

Most general Logarithm of a matrix

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lambda
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12 views

Ideal of maximal minors is radical when rank never drops by more than 1 [Reference request]

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Leobeth
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3 votes
1 answer
128 views
+50

For which real $\beta$ there exist concave(convex upwards) functions $f, g: (0;1) \to (0;+\infty)$ such that $\frac{f(x)}{g(x)}=(1+x)^\beta$?

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pioo
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Homeomorphic smooth Vector bundle that aren't diffeomorphic

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Manuel Bonanno
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3 answers
2k views

What is $\mathbb{C}^{\mathrm{Aut}(\mathbb{C}/\mathbb{Q})}$?

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Martin Sleziak
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9 views

Study of non linear dynamical system

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thibault_student
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2 answers
782 views

The relation $R$ defined on $\mathbb{Z}$ by $aRb$ if and only if $a=(2^n)b$ prove/disprove symmetry, transitive and reflexive

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artemetra
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Prob. 7, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: Is $S_{\Omega}$ first-countable? second-countable? separable? Lindelof?

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Tankut Beygu
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65 votes
2 answers
4k views

When are nonintersecting finite degree field extensions linearly disjoint?

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Martin Sleziak
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2 votes
1 answer
960 views

How to translate math technical terms?

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1 answer
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Markov chain having unique stationary distribution

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If $f$ is absolutely continuous and $g$ is Lipschitz, then $f \circ g$ is absolutely continuous.

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Venediktov
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Calculate the expected value of a bivariate function

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Jeremy_J
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4 votes
2 answers
260 views
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What sets of digits can be used to represent all of the real numbers in a ternary numeral system?

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Dark Malthorp
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9 votes
8 answers
1k views

Is there a nice way to find this integral $\int_0^1\frac{ \arcsin x}{x} \mathrm{d}x$?

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Integreek
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4 votes
2 answers
70 views

Construction of a dense linear order with $2^\kappa$ cuts

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Holo
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1 answer
45 views

A question concerning the duality bracket of $W^{-1,p'}(\Omega)$ with $W_0^{1,p}(\Omega)$ relevant to $L^2(\Omega)$ inner product

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daw
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Why doesn't Montel's Theorem imply the space of analytic functions is locally compact?

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2 answers
122 views

Evaluate (when possible) $\sum_{n=0}^{+\infty}\ln\left(2\cos\frac{\alpha}{2^n}-1\right)$

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zaknenou
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2 answers
68 views

Intuition behind using $\pi$-system in Measure Theory

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Michael Greinecker
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Converse of Holder's inequality in the finite case

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The nature of elements in local rings and local parameters

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zyy
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Asymptotic Variance

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SATYA
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325 views

Why isn't this a correct triangulation of the torus/projective plane?

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Wei Xia
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2 answers
4k views

Determining whether a number is a 'factorial number'

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Will.Octagon.Gibson
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1 answer
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Formula for the number of divisors of an integer

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Dietrich Burde
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3 answers
33k views

Finding the equation of a circle given two points on the circle

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2 votes
1 answer
32 views

Upper-bounded version of the Gale-Ryser theorem

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Sacha Bernheim
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1 answer
39 views

Counterexample request: $\sigma$-algebra with no smallest set containing a given (non-measurable) set?

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Michael Greinecker
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3 votes
1 answer
152 views

Real function such that $|f'(x)|\le|f(x)|$ has fixed sign

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van der Wolf
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3 votes
1 answer
70 views

Must every sheaf be a covering space?

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Elia Immanuel Auer
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18 views

Prob. 7, Sec. 30, in Munkres' TOPOLOGY, 2nd ed: Is $\overline{S_\Omega}$ first-countable? second-countable? separable? Lindelof?

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Saaqib Mahmood
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29 views

Does Blaschke’s characterization of ellipsoids extend to non-compact convex body?

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hbghlyj
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94 views

Show that $\frac{\cos(\alpha + \beta)}{\sin(\alpha - \beta)} = \frac{1}{3}$

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Renato C
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2 answers
221 views

General relation between Jordan measure and Riemann integral

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D.R.
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1 answer
769 views

Proof that a uniform continuous function preserves uniform convergence of sequence of measurable functions

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7 votes
3 answers
282 views

Closed form of $\Omega = \int\limits_3^\infty {\frac{{{x^4}}}{{\sqrt {{{\left( {{x^4} + 2{x^2} + 4} \right)}^3}} }}dx} $

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Paramanand Singh♦
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2 votes
2 answers
184 views

Does the Axiom Schema of Separation in any sense "provide" only countably many definitions of subsets of $\mathbb{N}$?

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Chad K
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1 answer
784 views

Folland Real Analysis Chapter 7 Exercise 12

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1 vote
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Casting shadows of parametric convex surfaces to arbitrary planes

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hbghlyj
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19 views

complete theory where cannot omit all non-isolated types

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Anonymous Anonymous
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7 votes
1 answer
280 views

How can we calculate the sum of sines or cosines where the angles are in geometric progression?

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Dhairya Kumar
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3 answers
2k views

$R = \mathbb{Z}[ i ] / (5)$ is not an integral domain? Why?

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19021605
  • 1,305
2 votes
1 answer
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Difference of statistics of order of a exponential distribution

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7 votes
2 answers
922 views

In which sense are the Cauchy-Riemann equations elliptic

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subrosar
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2 answers
677 views

How do I calculate the first n digits and last m digits of $3^{3^{3^{3^{3}}}}$?

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Gonçalo
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-1 votes
0 answers
61 views

Why is the connection necessary?

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Pierre MATSUMI
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1 vote
0 answers
28 views

degeneracy maps when computing limits

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user14411
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11 votes
4 answers
725 views

Closed form solution for $ \int_0^1 x^x (1-x)^{1-x} dx $

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Sangchul Lee
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3 votes
1 answer
77 views

Conditions to a linear map between tangent spaces being the differential of a isometry

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Moishe Kohan
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1 answer
1k views

Fourier transform of Gaussian noise

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CommunityBot
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1 vote
1 answer
27 views

Family of i.i.d. random variables is ergodic under shift

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kodlu
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6 votes
1 answer
64 views

Does the sequence of Stieltjes measures build concentrations?

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Sangchul Lee
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1 vote
0 answers
19 views

Number of critical points of a homological sphere with dimension three

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Horned Sphere
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34 views

What makes the category of isocrystals over non-algebraically closed field non-semisimple?

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KReiser
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0 answers
52 views

Convergence of Poincaré Series

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Tommy Soon
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1 answer
37 views

Show that these intervals are either disjoint or identical and their union has Lebesgue measure lower bound independent of $N$

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Bruno Andrades
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10 votes
2 answers
336 views

Evaluation of $\int_0^{\frac{\pi}{2}}\frac{f(x)}{2+\sin(x)}dx$

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homo_morph
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2 votes
2 answers
3k views

Show that $\min(X,Y)$ has geometric distribution

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Bowei Tang
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0 answers
11 views

Good Textbook or Relevant Literatures for Learning Graph Embedding

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psmuler
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3 votes
1 answer
854 views

How to draw level curves for $\frac x{x^2+y^2}$

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CommunityBot
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37 views

Is it true that $s\in mM$ and $t\in mN$ implies $s\otimes t\in m(M\otimes N)$?

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王夏辉
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23 views

How to prove that the moduli space $\mathcal{M}_g$ is Hausdorff using Kuranishi families?

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Framate
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if p is equivalent to 1 (mod d), then $x^d$ being equivalent to 1 (mod $p$) has exactly $d$ solutions modulo $p$.

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J. W. Tanner
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2 votes
1 answer
191 views

Continuous solutions to a first order PDE

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Gonçalo
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1 vote
0 answers
14 views

Looking for authors/papers in GGT involving piecewise isometries, free group actions, and twisted Ihara zeta functions

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J. Zimmerman
  • 1,159
3 votes
1 answer
32 views

Does the long exact sequence of a pair for a simplicial complex and a face delete split when the connecting maps are zero?

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John Palmieri
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2 votes
0 answers
53 views

How do you think about uniform continuity?

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Lourenco Entrudo
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3 votes
1 answer
87 views

solving $\int \frac{\sqrt{\sin\theta}}{1+\sin^{2}\theta} \, d\theta$

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OscarTheGrumpyGrouch
  • 120
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0 answers
20 views

Are the motion equations of an optimal control problem geodesics on a manifold?

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Meclassic
  • 502
1 vote
0 answers
17 views

What could have been a good motivation / intuition behind the Dorfman Bracket condition?

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Kishalay Sarkar
  • 4,406
4 votes
1 answer
96 views

Can a hemispherical surface be flattened if tearing is allowed but no stretching is allowed in the interiors

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san
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3 votes
0 answers
36 views

Do fiberwise homotopy groups define a local system?

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Frank
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3 votes
1 answer
30 views

Known properties of these generalized Cauchy distributions

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van der Wolf
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4 votes
1 answer
184 views

Examples of countable non-commutative division rings

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Noah Schweber
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1 answer
61 views

Where does this partition-of-unity argument not work in general?

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Paul Frost
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5 votes
2 answers
320 views

Checking if a matrix has support

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Rodrigo de Azevedo
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0 votes
1 answer
97 views

Ahlfors Laurent Series Coefficients

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Paul Frost
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1 answer
75 views

First Chern class of a line bundle

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the_dude
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11 votes
2 answers
1k views

Is this formula for cosine correct? (And is it significant)

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Bruno Andrades
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3 votes
1 answer
95 views

Compactness through Scott topology on the poset of open subsets

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Julián
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1 vote
1 answer
73 views

Topology literature focusing on continuous functions and measures

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Michael Greinecker
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