Mathematics Stack Exchange
Mathematics Stack Exchange

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1500 questions
70
votes
9 answers

How to effectively study math?

Maybe this is too general for here, but I am having a lot of difficulty studying math. Just got out of the military and I guess I am not use to this yet but when I run into a problem I have trouble with and I just can't get it I get extremely…
Adam
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70
votes
1 answer

Is $a_0=2$, $a_1=a_2=a_3=1$, $a_n=\frac{(a_{n-1}+a_{n-2})(a_{n-2}+a_{n-3})}{a_{n-4}}$ (OEIS A248049) an integer sequence?

The OEIS sequence A248049 defined by $$ a_n \!=\! \frac{(a_{n-1}\!+\!a_{n-2})(a_{n-2}\!+\!a_{n-3})}{a_{n-4}} \;\text{with }\; a_0\!=\!2, a_1\!=\!a_2\!=\!a_3\!=\!1 $$ is apparently an integer sequence but I have no proofs. I have numerical evidence…
Somos
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70
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2 answers

Is Serge Lang's Algebra still worth reading?

Is Serge Lang's famous book Algebra nowadays still worth reading, or are there other, more modern books which are better suited for an overview over all areas of algebra? EDIT: My main concern is that the first edition of Algebra is already 48 years…
Dominik
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70
votes
6 answers

Japanese Temple Problem From 1844

I recently learnt a Japanese geometry temple problem. The problem is the following: Five squares are arranged as the image shows. Prove that the area of triangle T and the area of square S are equal. This is problem 6 in this article. I am…
Larry
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70
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2 answers

Explain this mathematical meme (Geometers bird interrupting Topologists bird)

My knowledge of geometry is just a little bit above high school level and I know absolutely nothing about topology. So, what is the point of this meme? (Original unedited webcomic: “Juncrow” by False Knees)
Hanlon
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70
votes
4 answers

Why does multiplying a number on a clock face by 10 and then halving, give the minutes? ${}{}$

My daughter in grade 3 is learning about telling time at her school. She eagerly showed me this method she has discovered on her own to tell the minutes part of the time on an analogue clock. I wasn't sure at first because I have never heard about…
Sabeen Malik
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70
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1 answer

Simplicial homology of real projective space by Mayer-Vietoris

Consider the $n$-sphere $S^n$ and the real projective space $\mathbb{RP}^n$. There is a universal covering map $p: S^n \to \mathbb{RP}^n$, and it's clear that it's the coequaliser of $\mathrm{id}: S^n \to S^n$ and the antipodal map $a: S^n \to S^n$.…
Zhen Lin
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70
votes
9 answers

Given real numbers: define integers?

I have only a basic understanding of mathematics, and I was wondering and could not find a satisfying answer to the following: Integer numbers are just special cases (a subset) of real numbers. Imagine a world where you know only real numbers. How…
Daniel A.A. Pelsmaeker
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70
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6 answers

Projection is an open map

Let $X$ and $Y$ be (any) topological spaces. Show that the projection $\pi_1$ : $X\times Y\to X$ is an open map.
Alisha
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70
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3 answers

Is $n \sin n$ dense on the real line?

Is $\{n \sin n | n \in \mathbb{N}\}$ dense on the real line? If so, is $\{n^p \sin n | n \in \mathbb{N}\}$ dense for all $p>0$? This seems much harder than showing that $\sin n$ is dense on [-1,1], which is easy to show. EDIT: This seems a bit…
Per Alexandersson
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70
votes
1 answer

Are there infinitely many "super-palindromes"?

Let me first explain what I call a "super-palindrome": Consider the number $99999999$. That number is obviously a palindrome. ${}{}{}{}$ The largest prime factor of $99999999$ is $137$. If you divide $99999999$ by $137$, you get $729927$. This…
celtschk
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70
votes
6 answers

$100$-th derivative of the function $f(x)=e^{x}\cos(x)$

I've got this task I'm not able to solve. So, I need to find the $100^\text{th}$ derivative of $$f(x)=e^{x}\cos(x)$$ where $x=\pi$. I've tried using Leibniz's formula but it got me nowhere, induction doesn't seem to help either, so if you could just…
windircurse
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70
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9 answers

Why is $\pi $ equal to $3.14159...$?

Wait before you dismiss this as a crank question :) A friend of mine teaches school kids, and the book she uses states something to the following effect: If you divide the circumference of any circle by its diameter, you get the same number, and…
gphilip
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70
votes
2 answers

Period of the sum/product of two functions

Suppose that period of $f(x)=T$ and period of $g(x)=S$, I am interested what is a period of $f(x) g(x)$? period of $f(x)+g(x)$? What I have tried is to search in internet, and found following link for this. Also I know that period of $\sin(x)$ is…
dato datuashvili
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70
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11 answers

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

I know the following is not right, but what is the problem. So we want to calculate $$ \int_0^{\pi} \sin(x) \; dx $$ If one does a substitution $u = \sin(x)$, then one gets $$ \int_{\sin(0) = 0}^{\sin(\pi) = 0} \text{something}\; du = 0. $$ We know…
John Doe
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