# Questions tagged [big-list]

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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### Applications of the 5/8 Theorem

The 5/8 theorem for compact groups says the following: Theorem (5/8 Theorem for Compact Groups) Let $G$ be a compact Hausdorff topological group with Haar measure $\mu$. If $G$ is not abelian then ...
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### Big list: Free textbooks and resources

We have had multiple book-recommendation, but I have not found a question where the many free (yet legal) books are available under one umbrella. Therefore I propose a thread where all the best, free ...
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### Optimal algorithm to find maximum value of dot product of two lists

I am looking for an optimal (fastest) way to find a maximum value of dot product of two lists. A list can be rearranged freely in order to maximize the result. My idea for this was to quicksort two ...
488 views

### Examples of subgroups where it's nontrivial to show closure under multiplication?

Usually when a subgroup is declared, it is trivial (or at least straightforward to a sophomore) to prove that it is a subgroup under multiplication. For example: Homomorphic image and preimage of a ...
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### Examples of contravariant functors

I understand the definition and usefulness of the notion of functor. But I am worrying about the usefulness of the notion of a contravariant functor. Wikipedia writes: There are many constructions ...
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### Is there a list of all the possible operations for a certain object? (Wording might be wrong)

I have been thinking about this for some time and I think this is the question I wanted to ask here, since it's more straightforward than asking "When is a mathematical operation/symbol manipulation ...
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### Real Examples of Misleading Statistics

I need to give a presentation to a group of students on Tuesday about why one needs to be careful when examining statistics or mathematical results in the media or online. In his book How Not To Be ...
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### Most important non-elementary functions in Math

I am looking for non-elementary function that is Well behaved over $\mathbb{R}$ and $\mathbb{C}$ like piecewise smooth, not like Weierstrass function Ubiquitous and well studied Simple to compute ...
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### Collection of less well-known, non-trivial, elegant story proofs (ie, “double counting proofs”) of combinatorial identities

By story proof I mean proving a combinatorial identity by counting the number of elements of some carefully chosen set in two different ways to obtain the different expressions in the identity. The ...
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### Pathological, continuous functions

Today in my introduction to measure theory course, the professor said that often when we think of continuity, what we're actually thinking about is smooth functions. We've studied the Cantor set and ...
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As an olympiad-participant, I've had to solve numerous inequalities; some easy ones and some very difficult ones. Inequalities might appear in every Olympiad discipline (Number theory, Algebra, ...
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Here, I am trying to collect as many "I wish I had read that textbook first" textbook names as possible, for as many different topics in mathematics as possible. The "I wish I had read that textbook ...
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### “Milk” the integral $\int_0^\infty\left(\frac{x^2}{x^4+2ax^2+1}\right)^r\frac{x^2+1}{x^2(x^s+1)}\mathrm dx$

I found the following integral in chapter $13$ of Irresistible Integrals, and I would like to see which conclusions you can reach from it. My goal in asking this question is to see which methods I can ...
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### What natural ways of partitioning a group $G$ are there?

What natural, or at least useful, ways are there to partition a finite group $G$? The two examples that come to mind are: Partitioning $G$ into all the left (or right) cosets of a subgroup $H$ of $G$....
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### Html5 Math Applets. Interactive free online

I was an aficionado at collecting links from websites with math java applets that allowed interaction to learn mathematical concepts visually and interactively. My favorite was http://www.ies-math.com/...
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### Killing a butterfly with a bazooka [duplicate]

Let $n\ge3$. Prove that $\sqrt[n]2\notin\Bbb Q$. Let us suppose that $\sqrt[n]2=p/q$, that is $2q^n=p^n$, so $q^n+q^n=p^n$, against FLT. Do you know similar examples, in which simple problems are ...
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### Collection: Results on stopping times for Brownian motion (with drift)

The aim of this question is to collect results on stopping times of Brownian motion (possibly with drift), with a focus on distributional properties: distributions of stopping times (Laplace ...
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### Sequence $\rightarrow$ Generating function simple practice problems

I am trying to teach myself more about generating functions and how they "generate" sequences. Specifically I am trying to learn more about how to go from sequence to function and I would like some ...