User SRobertJames - Mathematics Stack Exchange

22 votes

5 answers

2k views

What do physicists mean when they say something is "not a vector"?

asked Dec 19, 2023 at 20:52

19 votes

13 answers

4k views

If two pairs of numbers have equal sums and products, what can we conclude about the pairs?

asked Dec 12, 2023 at 15:00

16 votes

5 answers

1k views

What are examples of Halmos's claim that a single small concrete special case can capture every instance of a concept of great generality?

asked Mar 19, 2023 at 2:30

15 votes

2 answers

1k views

When studying a book (like Rudin ) where the problems are not intended to be fully solvable by a student, what criteria show you're ready to advance?

asked Feb 6 at 15:01

9 votes

2 answers

319 views

An accurate, rapidly converging estimate of $\sum_{j = 1}^{\infty}\frac 1 {j^2}$ (the Basel Problem) using only elementary calculus

asked Jan 23 at 17:01

9 votes

1 answer

133 views

Does the SVD work on an incomplete field?

asked May 31, 2023 at 19:53

7 votes

2 answers

686 views

$e^{e^x} = 10^{10} x^{10}e^{10^{10} x^{10}}$ - Find $x$ (G.H. Hardy)

asked Jan 26 at 1:43

7 votes

1 answer

731 views

Did Paul Halmos state “The heart of mathematics consists of concrete examples and concrete problems"?

asked Mar 17, 2023 at 21:28

7 votes

2 answers

283 views

$f$ is uniformly continuous $\implies |f(x)| < C + D|x|$

asked May 4, 2021 at 0:48

7 votes

1 answer

374 views

The Cantor set + the Cantor set = $[0,2]$

asked Nov 6, 2022 at 23:07

6 votes

0 answers

224 views

Building $\textit{techniques}$ (as opposed to $\textit{concepts}$) for advanced complex analysis

asked Oct 24, 2022 at 19:42

6 votes

2 answers

654 views

How did Feynman produce solutions in under a minute?

asked Jan 3 at 1:29

6 votes

1 answer

525 views

A false "proof" that record setting events are dependent

asked Apr 10 at 13:22

6 votes

2 answers

757 views

If I've learned real analysis, should I go back and (re)learn calculus properly?

asked Jun 9, 2023 at 0:29

6 votes

1 answer

105 views

Does $\sqrt a + \sqrt b$ have a four way conjugate?

asked Jun 23, 2023 at 12:46

6 votes

1 answer

324 views

What algebraic manipulations are needed for real analysis?

asked Jun 28, 2023 at 12:49

5 votes

3 answers

556 views

A tricky system of non-linear multivariate equations

asked Jun 29, 2023 at 3:12

5 votes

1 answer

68 views

Characterize $\frac {ax + b} {cx + d}$ as $x \to \frac {-d} c$

asked Jul 7, 2023 at 3:31

5 votes

1 answer

141 views

Can you critique my exposition of $\int_{-\infty}^{+\infty}e^{-x^2}dx = \sqrt \pi$?

asked Dec 4, 2023 at 3:56

5 votes

3 answers

158 views

Find the lengths of the principal axes of the ellipsoid $\sum_{i \leq j} x_ix_j = 1$ (Arnold 85)

asked Jan 21 at 18:53

5 votes

2 answers

147 views

Prove that $\sum a_n$ converges $\implies \sum \frac {a_n} {2^n}$ converges.

asked May 2, 2021 at 16:45

5 votes

2 answers

269 views

Handling elementary but messy computations in proofs

asked Apr 11, 2021 at 16:17

5 votes

3 answers

1k views

Doing math on paper vs computer

asked Dec 11, 2022 at 23:15

5 votes

1 answer

181 views

Verify: A differentiable function has a continuous approximation function

asked Dec 18, 2022 at 5:02

4 votes

1 answer

59 views

Prove a monotone function at all points of its domain is either continuous or has a jump discontinuity

asked Dec 12, 2022 at 23:42

4 votes

2 answers

84 views

Verify: If $A$ is a bounded set and $f: A \subset \mathbb{R} \to \mathbb{R}$ is uniformly continuous, then $f(A)$ is bounded

asked Dec 7, 2022 at 2:21

4 votes

1 answer

82 views

Improve exposition of this proof: Matrix multiplication is associative, due to commutativity of underlying field

asked Mar 22, 2023 at 20:00

4 votes

2 answers

273 views

Does matrix multiplication require an inner product space?

asked Mar 14, 2023 at 12:51

4 votes

2 answers

282 views

Difference in usage between function, mapping, functional, form, and operator?

asked Mar 27, 2023 at 10:27

4 votes

1 answer

240 views

Prove if in a group $a$ commutes with $b$, it also commutes with $b^k$ for any integer $k$

asked Sep 14, 2021 at 22:41

Stack Exchange Network

285 Questions

What do physicists mean when they say something is "not a vector"?

If two pairs of numbers have equal sums and products, what can we conclude about the pairs?

What are examples of Halmos's claim that a single small concrete special case can capture every instance of a concept of great generality?

When studying a book (like Rudin ) where the problems are not intended to be fully solvable by a student, what criteria show you're ready to advance?

An accurate, rapidly converging estimate of $\sum_{j = 1}^{\infty}\frac 1 {j^2}$ (the Basel Problem) using only elementary calculus

Does the SVD work on an incomplete field?

$e^{e^x} = 10^{10} x^{10}e^{10^{10} x^{10}}$ - Find $x$ (G.H. Hardy)

Did Paul Halmos state “The heart of mathematics consists of concrete examples and concrete problems"?

$f$ is uniformly continuous $\implies |f(x)| < C + D|x|$

The Cantor set + the Cantor set = $[0,2]$

Building $\textit{techniques}$ (as opposed to $\textit{concepts}$) for advanced complex analysis

How did Feynman produce solutions in under a minute?

A false "proof" that record setting events are dependent

If I've learned real analysis, should I go back and (re)learn calculus properly?

Does $\sqrt a + \sqrt b$ have a four way conjugate?

What algebraic manipulations are needed for real analysis?

A tricky system of non-linear multivariate equations

Characterize $\frac {ax + b} {cx + d}$ as $x \to \frac {-d} c$

Can you critique my exposition of $\int_{-\infty}^{+\infty}e^{-x^2}dx = \sqrt \pi$?

Find the lengths of the principal axes of the ellipsoid $\sum_{i \leq j} x_ix_j = 1$ (Arnold 85)

Prove that $\sum a_n$ converges $\implies \sum \frac {a_n} {2^n}$ converges.

Handling elementary but messy computations in proofs

Doing math on paper vs computer

Verify: A differentiable function has a continuous approximation function

Prove a monotone function at all points of its domain is either continuous or has a jump discontinuity

Verify: If $A$ is a bounded set and $f: A \subset \mathbb{R} \to \mathbb{R}$ is uniformly continuous, then $f(A)$ is bounded

Improve exposition of this proof: Matrix multiplication is associative, due to commutativity of underlying field

Does matrix multiplication require an inner product space?

Difference in usage between function, mapping, functional, form, and operator?

Prove if in a group $a$ commutes with $b$, it also commutes with $b^k$ for any integer $k$