Mathematics Weekly Newsletter
Mathematics Weekly Newsletter

Top new questions this week:

A good way to retain mathematical understanding?

What is a good way to remember math concepts/definitions and commit them to long term memory? Background: In my current situation, I'm at an undergraduate institution where I have to take a lot of …

(soft-question) (self-learning)  
asked by 1mathboy1 55 votes
answered by Jp McCarthy 100 votes

Are there surfaces with more than two sides?

I'm watching a naive introduction to the Möbius band, the lecturer asks if it's possible to construct a one sided surface and then she says that there is one of these surfaces, namely the Möbius band. …

(general-topology) (geometry)  
asked by Igäria Mnagarka 19 votes
answered by Lee Mosher 6 votes

When does $(uv)'=u'v'?$

In any calculus course, one of the first thing we learn is that $(uv)'=u'v+v'u$ rather than the what I've written in the title. This got me wondering: when is this dream product rule true? There are …

(calculus) (real-analysis) (analysis) (differential-equations) (derivatives)  
asked by A little lime 18 votes
answered by David 16 votes

Limit is found using polar coordinates but it is not supposed to exist.

Consider the following 2-variable function: $$f(x,y) = \frac{x^2y}{x^4+y^2}$$ I would like to find the limit of this function as $(x,y) \rightarrow (0,0)$. I used polar coordinates instead of …

(analysis) (limits) (multivariable-calculus)  
asked by James 15 votes
answered by heropup 30 votes

Is it possible that "A counter-example exists but it cannot be found"

Then otherwise the sentence "It is not possible for someone to find a counter-example" would be a proof. I mean, are there some hypotheses that are false but the counter-example is somewhere we …

(logic) (proof-theory)  
asked by ThePortakal 15 votes
answered by Alex Becker 28 votes

Are there contradictions in math?

Someone told me that math has a lot of contradictions. He said that a lot of things are not well defined. He told me two things that I do not know. $1+2+3+4+...=-1/12$ what is infinity $\infty$? …

(soft-question) (education)  
asked by det 15 votes
answered by Ittay Weiss 51 votes

How find this $x,y$ such this equation $x^x+x=y!$

Find all pairs of positive integers $(x,y)$,such $$x^x+x=y!$$ I find the $$(x,y)=(1,2)$$ is such it. and $$(x,y)=(2,3)$$ I think this equation have other roots. and maybe use inequality to …

(number-theory)  
asked by math110 14 votes
answered by Hagen von Eitzen 19 votes

Greatest hits from previous weeks:

Why are mathematical proofs that rely on computers controversial?

There are many theorems in mathematics that have been proved with the assistance of computers, take the famous four color theorem for example. Such proofs are often controversial among some …

(soft-question) (proof-writing)  
asked by Gerard 64 votes
answered by ShreevatsaR 86 votes

Why is Euclid's proof on the infinitude of primes considered a proof?

I've expressed Euclid's proof on the infinitude of primes on Mathematica: f[x_] := Product[Prime[n], {n, 1, x}] + 1 TableForm[Table[{f[x], PrimeQ[f[x]]}, {x, 1, 20}]] Which results in: …

(number-theory) (prime-numbers)  
asked by Igäria Mnagarka 45 votes
answered by Michael Hardy 79 votes

Can you answer these?

Solving integral $\int\frac{\sin x}{1+x\cos x}dx$

How I can find the anti-derivative? $$\int\frac{\sin x}{1+x\cos x}dx$$

(homework) (integration)  
asked by Hamid 3 votes

Use of "I" in mathematics papers

Some people consider the use of "I" in a paper to be a great evil. Others, however, consider the use of the passive voice to be an even greater evil. I will be presenting a paper at a competition, …

(article-writing)  
asked by user1577636 6 votes

Is it easier to publish in certain areas of mathematics?

I was wondering whether there are areas of mathematics that it is easier to publish in than in others. The reason I'm asking this question is not because I would then want to do research there, but …

(soft-question) (publishing)  
asked by Ryker 4 votes
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