# 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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### Using multiple integrals for tough single integrals

I'm just getting started on double integrals, and I recently saw the super cool way to use double integrals to arrive at $$\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$$ So, I am wondering if ...
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### Math for kids with Cuisenaire rods

I work with kids and i am searching some cool stuff to do with Cuisenaire rods. Thinking about an application i thought that i can show to my students what will be the sum of first $N\in\mathbb{N}$ ...
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### Basis-dependent results on matrices

It is common fashion to try to formulate results about matrices in a basis-free way, using linear algebra. What are some good examples of situations where this is impossible? I illustrate what I have ...
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### Problem sets on Abstract Algebra

Many times we ask about what books should we read to learn or know more about a math topic (Abstract Algebra, in this case). However, I would like to get a list of the exercises what should we solve ...
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### On the alternative stamentes of the famous Sperner's Lemma.

The Sperner's lemma can be stated as follows. Lemma of Sperner. Let $\Omega$ an fintie set with $n$ elements. If a family $\{ A_i \}_{1\leq i \leq N}\subset \Omega$ of subsets satisfies the ...
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### Analogies between finite groups and Lie groups

I believe there are some striking analogous facts between finite groups and Lie groups. One analogue almost too basic to mention is the appropriate notion of subobjects. In elementary group theory ...
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### GRE Mathematics Practice Exams

I will be taking the subject test in the near future. Can you recommend me some sources (online or print) from which I can find realistic practice exams? I would like to get my hands on as many ...
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### What computations would advance math knowledge a lot?

Suppose we where given a super computer that would be capable of computing anything, but only for one day. We could for instance compute many of the Ramsey numbers. What would be some computations ...
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### Deep questions in number theory not accessible by combinatorial results

Number theory and arithmetic geometry were invented to solve many questions about properties of numbers. What are the some of the foundational results or estimates that are accessible to powerful ...
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### Important integral inequalities list.

What are the most important and usefull integral inequalities? I know Chebyshev and Schwarz. Google search provides very few results, mathworld doesn't provide a list.
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### Math software for plotting phase portraits

I'm looking for math software which is possible to plot phase portraits for ODE and systems of differential equations. Is there a software which can create not only simple 2D phase portrait plots but ...
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### Methods to prove axiom independence

What methods have been used to prove the independence of axioms? For instance, in many abstract algebra books the axiom of choice is stated to be independent of all the other axioms of set theory, but ...
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### Is Legendre’s solution of the general quadratic equation the only one?

Legendre famously solved the general quadratic equation $$ax^2+bxy+cy^2+dx+ey+f=0$$ by noting that \begin{equation*} 4a(b^2-4ac)(ax^2+bxy+cy^2+dx+ey+f) = 0 \tag{$\star$} \end{equation*} along with ...
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### Revise high school material

Can you suggest me a comprehensive book to revise high school mathematics (up to besic calculus)? It should be extremely clear and complete and "scientific" (not like most high school books). Thank ...
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### Are there many spaces which have a regular $G_\delta$-diagonal but is not submetrizable?

Are there many spaces which have a regular $G_\delta$-diagonal but is not submetrizable? Submetrizable = if we can choose a coarser topology on the space $X$ and thus make it a metrizable space. $X$...
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### Books similar to “Primes of the form $x^2+ny^2$”

Are there any other books which are similarly to the book "Primes of the form $x^2+ny^2$"? Basically, I want a book which starts with a very important classical problem ( in this case which primes can ...
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### Properties about Matrices that can be proved by only using Block Multiplication of Matrices

I recently proved the property that product of two upper triangular matrices is an upper triangular matrices by using the block multiplication of matrices. The basic fact that was required to prove ...
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### A rigorous book (or preferrably set of notes) on classic multivariable calculus-analysis?

This is different to (Theoretical) Multivariable Calculus Textbooks as I want a classical treatment of line and surface integrals without the notion of a differential form. Prerequisites: Paths, ...
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### Motivating questions for some topics in undergraduate calculus

Being a grad student I'm going to teach a whole class for the first time the coming summer and I'm looking for some motivational problems which I could use to introduce different topics. In other ...
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### Examples of proofs by induction with respect to relations that are not strict total orders.

I have read this Wikipedia article and found it fascinating. I came across it after I tried to prove a certain statement with a method resembling induction in the set of natural numbers but ordered by ...
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### List of large classes of functors providing morphisms

I recently posted this question on mathoverflow and it was closed as being too localized. I am hoping to more precisely say what I mean here. I recently learned, through my Topology coursework, that ...
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### Suggestion of books on Integral Calculus of Several Variables

I'd like recommendations of books on integral calculus of several variables (double integral until Gauss's theorem) that contains challenging(hard) problems. And I'd like books in languages other than ...
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### Machine Learning: are there other functions similar to the softmax?

Recall in probability and machine learning softmax is defined as: $\sigma(\mathbf{z})_j = \dfrac{e^{z_j}}{\sum_{k=1}^K e^{z_k}}$ for $j = 1, ..., K.$ where $\sigma: \mathbb{R}^k \to (0,1)$ ...