User Cameron Williams

96 votes

Am I just not smart enough?

answered Oct 8, 2014 at 1:49

57 votes

Accepted

Why are mathematician so interested to find theory for solving partial differential equations but not for integral equation?

ordinary-differential-equations partial-differential-equations soft-question integral-equations

answered Mar 18, 2014 at 23:43

55 votes

Why is it not true that $\int_0^{\pi} \sin(x)\; dx = 0$?

calculus integration definite-integrals

answered Oct 20, 2015 at 20:00

32 votes

Accepted

Is this solution mathematically "legal"?

sequences-and-series limits

answered Aug 18, 2015 at 16:40

30 votes

Accepted

Why is the derivative of a vector orthogonal to the vector itself?

calculus derivatives vectors orthogonality

answered Feb 25, 2015 at 4:37

25 votes

Accepted

What is the relation between a Banach space and a Hilbert space?

functional-analysis soft-question

answered Aug 20, 2013 at 16:52

23 votes

$\frac1a+\frac1b+\frac1c=0 \implies a^2+b^2+c^2=(a+b+c)^2$?

algebra-precalculus contest-math problem-solving

answered Aug 3, 2013 at 2:42

23 votes

Accepted

Upper Bound vs. Least Upper Bound

real-analysis upper-lower-bounds

answered Aug 12, 2013 at 20:30

22 votes

Accepted

$A^{-1}$ has integer entries if and only if the ${\rm det}\ (A) =\pm 1$

linear-algebra matrices determinant inverse adjoint-operators

answered Apr 20, 2015 at 23:51

21 votes

Accepted

What is the dot product and why do we need it?

geometry

answered Jan 6, 2014 at 18:46

21 votes

Why is zero the only infinitesimal real number?

real-analysis infinitesimals

answered Jun 9, 2015 at 3:58

19 votes

Accepted

Why formulate continuity in terms of pre-images instead of image?

general-topology continuity

answered Jul 30, 2015 at 17:06

17 votes

Accepted

Do row operations change the column space of a matrix?

linear-algebra matrices systems-of-equations matrix-equations

answered Jul 28, 2015 at 1:46

17 votes

Accepted

How to prove $\exp(x)/(\exp(x)+1)^2$ is even?

calculus functions

answered Mar 21, 2016 at 3:19

16 votes

Determine if the following is surjective

functions elementary-set-theory

answered Apr 21, 2015 at 3:51

15 votes

Accepted

Must all Lebesgue integrable functions really be invertible?

real-analysis measure-theory functions notation inverse

answered Jul 28, 2015 at 5:34

14 votes

Accepted

Why it's true? $\arcsin(x) +\arccos(x) = \frac{\pi}{2}$

calculus definite-integrals

answered Jan 23, 2015 at 21:30

14 votes

Find $\lim\frac{1}{\sqrt{n}}\left(\frac{1}{\sqrt{1}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\ldots+\frac{1}{\sqrt{2n-1}+\sqrt{2n+1}}\right)$

limits

answered Jun 23, 2014 at 3:13

13 votes

Accepted

Integral $\int_0^1 \log \left(\Gamma\left(x+\alpha\right)\right)\,{\rm d}x=\frac{\log\left( 2 \pi\right)}{2}+\alpha \log\left(\alpha\right) -\alpha$

integration complex-analysis definite-integrals special-functions gamma-function

answered May 7, 2014 at 4:32

13 votes

Accepted

Importance of groups $(\mathbb R,+)$ and $(\mathbb Z,+)$ for Fourier series

group-theory fourier-series

answered Oct 7, 2014 at 1:59

13 votes

Why do you need to use the chain rule in differentiation of ln?

calculus derivatives

answered Feb 23, 2014 at 17:12

13 votes

Convolution and multiplication of polynomials is the same?

calculus real-analysis algebra-precalculus

answered Sep 22, 2016 at 22:16

12 votes

Intuition about the semidirect product of groups

group-theory intuition semidirect-product

answered Mar 19, 2016 at 17:49

12 votes

Accepted

Solve $2^{x+5} - 2^{x+2} = 7$

algebra-precalculus logarithms exponentiation

answered Apr 23, 2017 at 4:08

12 votes

Show $\sum_{i=0}^\infty {k+i \choose k}a^i=\frac1{(1-a)^{k+1}}.$

sequences-and-series convergence-divergence power-series binomial-coefficients

answered Jan 4, 2018 at 15:26

11 votes

Accepted

Solve equation with $x$ in the exponents

arithmetic

answered Jun 19, 2014 at 23:00

10 votes

Accepted

Finding a rare case where an incorrect rule works?

calculus

answered Jul 5, 2014 at 3:14

10 votes

Change of variable (translation) in complex integral

integration complex-analysis multivariable-calculus

answered Jan 18, 2014 at 19:05

10 votes

Integral of $(3-x)/(x+2)$

calculus indefinite-integrals

answered Jan 31, 2014 at 3:19

10 votes

If $x>0$ and $x^a=x^b$ can one assume that $a=b$?

logic exponential-function

answered May 16, 2016 at 19:16

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778 Answers

Am I just not smart enough?

Why are mathematician so interested to find theory for solving partial differential equations but not for integral equation?

Why is it not true that $\int_0^{\pi} \sin(x)\; dx = 0$?

Is this solution mathematically "legal"?

Why is the derivative of a vector orthogonal to the vector itself?

What is the relation between a Banach space and a Hilbert space?

$\frac1a+\frac1b+\frac1c=0 \implies a^2+b^2+c^2=(a+b+c)^2$?

Upper Bound vs. Least Upper Bound

$A^{-1}$ has integer entries if and only if the ${\rm det}\ (A) =\pm 1$

What is the dot product and why do we need it?

Why is zero the only infinitesimal real number?

Why formulate continuity in terms of pre-images instead of image?

Do row operations change the column space of a matrix?

How to prove $\exp(x)/(\exp(x)+1)^2$ is even?

Determine if the following is surjective

Must all Lebesgue integrable functions really be invertible?

Why it's true? $\arcsin(x) +\arccos(x) = \frac{\pi}{2}$

Find $\lim\frac{1}{\sqrt{n}}\left(\frac{1}{\sqrt{1}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+\ldots+\frac{1}{\sqrt{2n-1}+\sqrt{2n+1}}\right)$

Integral $\int_0^1 \log \left(\Gamma\left(x+\alpha\right)\right)\,{\rm d}x=\frac{\log\left( 2 \pi\right)}{2}+\alpha \log\left(\alpha\right) -\alpha$

Importance of groups $(\mathbb R,+)$ and $(\mathbb Z,+)$ for Fourier series

Why do you need to use the chain rule in differentiation of ln?

Convolution and multiplication of polynomials is the same?

Intuition about the semidirect product of groups

Solve $2^{x+5} - 2^{x+2} = 7$

Show $\sum_{i=0}^\infty {k+i \choose k}a^i=\frac1{(1-a)^{k+1}}.$

Solve equation with $x$ in the exponents

Finding a rare case where an incorrect rule works?

Change of variable (translation) in complex integral

Integral of $(3-x)/(x+2)$

If $x>0$ and $x^a=x^b$ can one assume that $a=b$?