# Tagged Questions

Questions asking for a "big list" of examples, illustrations, etc. Ask only when the topic is compelling, and please do not use this as the only tag for a question.

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### Best Sets of Lecture Notes and Articles

Let me start by apologizing if there is another thread on math.se that subsumes this. I was updating my answer to the question here during which I made the claim that "I spend a lot of time sifting ...
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### Lesser-known integration tricks

I am currently studying for the GRE math subject test, which heavily tests calculus. I've reviewed most of the basic calculus techniques (integration by parts, trig substitutions, etc.) I am now ...
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### What properties of the real numbers are almost always true and there are no (or very few) known examples of?

What properties of the positive real numbers are almost always true and there are no (or very few) known examples of? Two that come to mind are numbers that are normal in every base and numbers ...
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### Visually deceptive “proofs” which are mathematically wrong

Related: Visually stunning math concepts which are easy to explain Beside the wonderful examples above, there should also be counterexamples, where visually intuitive demonstrations are actually ...
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The Problem Show that the number of possible links in a computer network of $n$ computers ($n \in Z \land n \geq 1$) is $\frac{n(n-1)}{2}$ in as many ways as you can. My Work Solution 1 Given $n$ ...
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### Examples of finite nonabelian groups.

Can anybody provide some examples of finite nonabelian groups which are not symmetric groups or dihedral groups?
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### Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$

As I have heard people did not trust Euler when he first discovered the formula (solution of the Basel problem) $$\zeta(2)=\sum_{k=1}^\infty \frac{1}{k^2}=\frac{\pi^2}{6}.$$ However, Euler was Euler ...
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### Stable and unstable properties of R^n [on hold]

What (interesting?) properties of R^n hold for all large n? What properties hold for only some large n? Put another way, in which senses is {R^n} convergent and in what senses is it divergent (...
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### List of interesting integrals for early calculus students

I am teaching Calc 1 right now and I want to give my students more interesting examples of integrals. By interesting, I mean ones that are challenging, not as straightforward (though not extremely ...
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### Indefinite Integral challenge problems [closed]

This year I am going to participate in an olympiad of indefinite integrals. The level is very high, I would like to know some (hard, olympiad) Indefinite integrals challenge problems Note: Here is ...
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### Large, small but a useful number. [closed]

Today we were discussing in our class about usefulness of a number no problem how large,small may be it's value. As per my knowledge (till grade 11) Avogadro number $N_A=6.022\times 10^{23}$ is a ...
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### Unexpected approximations which have led to important mathematical discoveries

On a regular basis, one sees at MSE approximate numerology questions like Prove $\log_{{1}/{4}} \frac{8}{7}> \log_{{1}/{5}} \frac{5}{4}$, Prove $\left(\dfrac{2}{5}\right)^{{2}/{5}}<\ln{2}$, ...
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### Famous papers in algebraic geometry

I'm reading the Mathoverflow thread "Do you read the masters?", and it seems the answer is a partial "yes". Some "masters" are mentioned, for example Riemann and Zariski. In particular, a paper by ...
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### Explicit examples of (co)limit arguments in other fields

Over the past weeks, I have noticed that high level lecture notes in subjects like algebraic geometry, algebra, and algebraic topology often sketch proofs in the following form: Proof sketch ...
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### Is there a property in $\mathbb{N}$ that we know some number must satisfy but don't know which one?

I have two questions. $(1.)$ Is there a property of the natural numbers such that we know at least one number satisfies it but we don't know which one? Even more, $(2.)$ Is there a property ...
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### What are all the uses of the determinant?

I've learned how to calculate the determinant but what is the determinant used for? So far, I only know that there is no inverse if the determinant is 0.
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So I'm wondering if anybody knows any good math/science related YouTube channels? As for the math channels, I'm currently subscribed to Numberphile, and that is about it. I know few other channels, ...
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### Fake proofs using matrices

Having gone through the 16-page-list of questions using the tag (fake-proofs), and going though Best Fake Proofs? (A M.SE April Fools Day collection) and https://en.wikipedia.org/wiki/...
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### Is there a great mathematical example for a 12-year-old?

I've just been working with my 12-year-old daughter on Cantor's diagonal argument, and countable and uncountable sets. Why? Because the maths department at her school is outrageously good, and set ...
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### Tricks for quickly reading off the eigenvalues of a matrix

I noticed that some mathematicians have an uncanny ability to identify the eigenvalues of matrices without doing much in the way of computation. For instance, one might notice that all the rows have ...
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### List of Local to Global principles

What are some of the local to global principles in different areas of mathematics?