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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What's so special about characteristic 2?

I've often read about things which do not work in a field with a characteristic $2$, mainly things which have to do with factoring, or similar things. I'm not exactly sure why, but the only example of ...
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Applications of Nagata's Lemma

In the spirit of this MO question I would like to ask for applications of a (somewhat lesser known?) lemma. Lemma. (Nagata) Let $R$ be an atomic domain. TFAE: $R$ is a UFD There exists a ...
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Undergraduate group theory Aha facts [closed]

I am learning group theory. I found out that there are a lot of (more or less) simple facts that are completely trivial for working mathematicians (e.g. my professor), but that are nowhere explicitly ...
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Is there more RBF's kernel?

I am working on a sfde(stochastic fractional differential equation),I use some of Radial basis function to find solution.like this list ...
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What are Different Approaches to Introduce the Elementary Functions?

Motivation We all get familiar with elementary functions in high-school or college. However, as the system of learning is not that much integrated we have learned them in different ways and the ...
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Recommendations on visualizing basic linear algebra

I am teaching linear algebra this semester, and I would really like to recommend my students some cool youtube videos visualizing some simple stuff like the span of a set of vectors, linear ...
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Learning multivariable/vector calculus through guided discovery

I am asking this question as a question similar to what has been asked previously for other topics as well as math in general. But I'd like to ask for text references specifically in the domain of ...
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What are some things we can prove they must exist, but have no idea what they are?

What are some things we can prove they must exist, but have no idea what they are? Examples I can think of: Values of the Busy beaver function: It is a well-defined function, but not computable. It ...
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Different ways finding the derivative of $\sin$ and $\cos$.

I am looking for different ways of differentiating $\sin$ and $\cos$, especially when using the geometric definition, but ways that use other defintions are also welcome. Please include the ...
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Books that emphasize physical applications

I made a book recommendation thread recently which got deleted, so I'm hoping this one doesn't have the same fate as the question seems much more defined. I was reading an interesting article by VI ...
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Composition of non-differentiable functions to produce a differentiable one

What are examples of non-differentiable functions which when composed form a differentiable function? It would even better if they are $C^\infty$ I am hoping this will turn into a big list, if it ...
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Useful matrix inner products

What are some interesting/useful examples of matrix inner products on square complex matrices, other than $\langle A, B \rangle = Tr(A^{\dagger}B)$?
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List of textbooks that take a historical approach

As the title suggests my aim in this topic is to make a big list of textbooks on any mathematical topic that take a historical approach. I will start with the ones I know: Thomas Muir - The theory of ...
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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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Applications of algebraic graph theory

What are some subtle, or non-obvious applications of algebraic graph theory? Obviously it can be used to study anything directly involving graphs (for instance, the wikipedia page mentions ...
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What families of transcendental equations do we have solved?

I'm particularly interested in transcendental equations but searching in internet gives me only results about the classical linear-exponential equation (which is solved with Lambert's W) and its ...
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$32$ Goldbach Variations - Papers presenting a single gem in number theory or combinatorics from different point of view

A short time ago I found the nice paper Thirty-two Goldbach Variations written by J.M. Borwein and D.M. Bradley. It presents $32$ different proofs of the Euler sum identity \begin{align*} ...
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Elementary topology examples

I'm preparing (to teach) my first class of undergraduate topology and I'm looking for some elementary, motivating applications of topology for the first day. We'll be following Munkres, starting with ...
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A beautiful book on arithmetic doesn't treat you like a little baby

The state of arithmetic today is disgusting. The textbooks on it are absolutely repelling, the authors treat it like a subject that will be of concern to only babies. They don't show any love, they ...
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