Hottest Questions This Month

46

votes

4

answers

4k

views

What is the size of each side of the square?

modified yesterday Tavish 4,086

26

votes

4

answers

2k

views

How to prove this algebraic version of the sine law?

algebra-precalculus trigonometry systems-of-equations alternative-proof

modified May 15 at 11:51 William McGonagall 907

15

votes

4

answers

2k

views

Are computer integers a finite group (under addition with overflow)?

abstract-algebra group-theory finite-groups computer-science

modified 2 days ago usul 2,894

20

votes

3

answers

2k

views

Why am I getting the wrong answer when I factor an $i$ out of the integrand?

calculus integration algebra-precalculus functions

modified May 25 at 16:02 Xander Henderson 19.5k

15

votes

6

answers

1k

views

Does taking the dot product of two column vectors involve converting one of the vectors into row vectors first?

linear-algebra vector-spaces inner-product-space

answered 2 days ago mrc ntn 1,258

11

votes

3

answers

877

views

Examples of non-continuous, non-piecewise-constant, idempotent map?

real-analysis functions

modified May 21 at 0:53 Vectornaut 3,990

32

votes

1

answer

2k

views

How long can proofs be?

logic computational-complexity provability

modified May 22 at 20:10 Community♦ 1

27

votes

2

answers

103

views

What is the difference between the Jacobian, Hessian and the Gradient?

gradient-descent jacobian

May 18 at 15:00 Pluviophile 483

8

votes

2

answers

956

views

Which field property enables us to multiply on both sides by the same value, while preserving equality? [duplicate]

real-analysis field-theory

answered May 18 at 5:50 Dirk 10.3k

16

votes

3

answers

2k

views

What is the most efficient way to find the inverse of large matrix?

linear-algebra matrices systems-of-equations inverse numerical-linear-algebra

answered May 13 at 20:57 Rodrigo de Azevedo 15.2k

18

votes

2

answers

909

views

Is the AM-GM inequality the only obstruction for getting a specific sum and product?

real-analysis polynomials systems-of-equations a.m.-g.m.-inequality

modified May 8 at 10:39 Asaf Shachar 18.2k

9

votes

5

answers

314

views

Proving $\int_0^{\infty} \frac{\sin^3(x)}{x^2} dx = \frac{3\ln(3)}{4} $

real-analysis calculus integration definite-integrals

modified May 1 at 6:36 robjohn♦ 294k

8

votes

4

answers

768

views

Why matrices commuting with $\small\begin{bmatrix} 0&1\\-1&0\end{bmatrix}$ represent complex numbers?

linear-algebra abstract-algebra matrices ring-theory complex-numbers

modified May 10 at 15:59 user21820 44.9k

6

votes

7

answers

1k

views

Why isn't every metric space a manifold?

general-topology metric-spaces manifolds

answered May 15 at 20:54 Moishe Kohan 60.7k

15

votes

1

answer

1k

views

How does Elo rating scale with games played?

probability mathematical-modeling

modified May 11 at 7:04 joriki 203k

11

votes

3

answers

589

views

Do any proofs/properties rely on the distinction between some uncountable size and a larger uncountable size, in order for the proof/property to hold?

set-theory cardinals infinity

modified May 13 at 22:23 Andrés E. Caicedo 70.5k

12

votes

2

answers

657

views

What is the reason for the term “zero dimensional” in the context of topology?

general-topology

modified May 24 at 10:47 ToBeFree 3

9

votes

7

answers

190

views

Evaluating $\lim_{n\rightarrow\infty} (\frac{(1+\frac{1}{n})^n}{e})^n$

real-analysis limits

modified May 15 at 13:21 xpaul 27.9k

11

votes

6

answers

385

views

+300

Polynomial outputs containing a particular Integer sequence

real-analysis number-theory polynomials

modified May 26 at 6:38 Sharky Kesa 1,866

17

votes

4

answers

369

views

Evaluate $\lim_{n\to\infty} \prod_{k=1}^n \frac{2k}{2k-1}\int_{-1}^{\infty} \frac{{\left(\cos{x}\right)}^{2n}}{2^x} \; dx$

calculus integration definite-integrals infinite-product

modified yesterday Thenard Rinmann 324

8

votes

3

answers

255

views

Evaluate $\sum_{n,k} \binom{n}{k}^{-1} $

real-analysis calculus sequences-and-series summation

answered May 17 at 20:54 robjohn♦ 294k

3

votes

3

answers

586

views

When converting a Riemann sum to an integral, how does one decide the bounds of the converted Riemann sum?

calculus integration

modified May 20 at 16:21 Eric Towers 49.9k

10

votes

3

answers

392

views

Why does $f(z) = z^n$ have no antiderivative only for $n=-1$?

complex-analysis soft-question intuition analytic-functions

modified May 16 at 9:52 Empy2 38.8k

17

votes

3

answers

636

views

Potentially new approach to factoring big numbers

number-theory prime-numbers modular-arithmetic factoring

modified 8 hours ago Dmitry Ezhov 1,150

4

votes

6

answers

168

views

What is the measure of the set $\left\{\frac{1}{2}\right\}\cup\left\{\frac{1}{4},\frac{3}{4}\right\}\cup\cdots$?

real-analysis measure-theory elementary-set-theory

modified May 10 at 0:07 Michael Hardy 235k

21

votes

4

answers

525

views

A simple geometric problem, solving $f'(x)=\frac{f(x)}{\sqrt{r(x)^2-f(x)^2}}$, given $r(x)$.

geometry ordinary-differential-equations trigonometry physics

answered May 18 at 23:51 G Cab 26.5k

9

votes

3

answers

519

views

Coordinate-Free Proof of the Orthogonal Decomposition Theorem

linear-algebra functional-analysis

modified May 4 at 14:25 Martin Argerami 151k

5

votes

3

answers

673

views

Difference between a number and a set with one number

real-analysis elementary-set-theory

modified May 25 at 16:47 fleablood 96.2k

11

votes

4

answers

415

views

Can elementary row operations be done by both left and right multiplication?

linear-algebra matrices

modified May 16 at 13:52 levap 52.7k

6

votes

3

answers

406

views

Spivak Calculus. Why is the books proof valid? Is my attempt at a proof valid?

real-analysis calculus

modified May 10 at 6:38 ruakh 587

11

votes

3

answers

500

views

Probability zero vs impossible

probability probability-theory probability-distributions

answered May 12 at 19:22 D. Zack Garza 313

6

votes

5

answers

182

views

Does $a^2 + b^2 = 2 c^2$ have any integer solution?

diophantine-equations parametric pythagorean-triples

answered May 21 at 21:19 Adam Bailey 2,815

4

votes

3

answers

126

views

Prove that $\frac{1}{1 - \sqrt{ab}} + \frac{1}{1 - \sqrt{bc}} + \frac{1}{1 - \sqrt{ca}} \leq \frac{1}{1 - a} + \frac{1}{1 - b} + \frac{1}{1 - c}$

inequality contest-math cauchy-schwarz-inequality a.m.-g.m.-inequality

modified May 9 at 16:11 robjohn♦ 294k

8

votes

2

answers

507

views

If $T_n = \{\frac{a}{n} \mid a \in \mathbb{Z}\}$, then what are $\bigcup_{n\in\mathbb{N}}T_n$ and $\bigcap_{n\in\mathbb{N}}T_n$?

elementary-number-theory elementary-set-theory

modified May 9 at 15:31 Gone 1

9

votes

3

answers

239

views

Evaluating $\lim_{n \to \infty} \int_{0}^{\pi} \frac{\sin x}{1+\cos ^2(nx)} dx$

calculus limits definite-integrals

modified May 19 at 23:04 Asaf Karagila♦ 334k

7

votes

3

answers

499

views

Which vectors have unique representation when it isn't a direct sum?

linear-algebra

modified May 15 at 5:15 Fred 62.9k

27

votes

1

answer

623

views

Number of ways to stack LEGO bricks

combinatorics reference-request recreational-mathematics discrete-geometry statistical-mechanics

modified May 5 at 7:33 joriki 203k

9

votes

4

answers

367

views

Understanding Fraleigh's proof of: Every finite integral domain is a field

abstract-algebra field-theory proof-explanation domain-theory

answered May 24 at 15:18 Andreas Blass 56.7k

0

votes

6

answers

124

views

Comparison of two numbers without calculator [closed]

number-theory

modified May 25 at 15:56 saulspatz 34.2k

7

votes

3

answers

398

views

Why does $AB + BC + CA = (A\oplus B)C + AB$ not imply $BC + CA = (A\oplus B)C$ in boolean algebra?

logic propositional-calculus boolean-algebra

modified May 25 at 9:49 user21820 44.9k

5

votes

5

answers

238

views

What should I do when I get stuck?

soft-question education

answered May 22 at 13:05 G Cab 26.5k

6

votes

5

answers

174

views

Factorise $x^4+y^4+(x+y)^4$

algebra-precalculus polynomials contest-math factoring binomial-theorem

modified May 1 at 19:04 User2020201 599

11

votes

3

answers

202

views

Can this complete metric space be a Banach space?

functional-analysis metric-spaces banach-spaces complete-spaces

modified 16 hours ago Oliver Diaz 3,114

10

votes

3

answers

1k

views

If $f$ is a nonconstant entire function such that $|f(z)|\geq M|z|^n$ for $|z|\geq R$, then $f$ is a polynomial of degree atleast $n$.

complex-analysis polynomials cauchy-integral-formula entire-functions

modified May 13 at 21:34 zhw. 87.4k

4

votes

5

answers

317

views

Why can a linear “ordinary” differential equation have non-linear coefficients of independent variable?

calculus ordinary-differential-equations derivatives differential-geometry

modified May 2 at 0:47 Will Orrick 15.9k

6

votes

4

answers

234

views

Why should the real numbers interact with number fields and Galois theory?

field-theory galois-theory galois-extensions

modified May 5 at 11:47 Ricardo Buring 4,412

9

votes

2

answers

181

views

Prove $\lim_{n \to \infty}\int_0^1 \dots \int_0^1 f(\sqrt[n]{x_1\dots x_n})dx_1\dots dx_n = f(\frac{1}{e}).$ $f$ is continuous on $[0;1].$

real-analysis calculus integration limits

modified May 19 at 10:29 Arjang 9,024

2

votes

4

answers

287

views

Arithmetic Puzzle

logic arithmetic puzzle

modified May 10 at 10:31 user21820 44.9k

Top Questions

Looking for more? Browse the complete list of questions, or popular tags. Help us answer unanswered questions.