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Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.

1 vote

Short Course Suggestions For High School Students

I have successfully taught a course for gifted high school students (somewhat shorter than yours, about 9 hours) devoted to the probabilistic method (based, naturally, on Alon and Spencer + some other …
1 vote

How to make a lecture series useful

If possible, it might be a good idea to organize a problem session, with problems/exercises given to participants in advance (say, a day before) and the session devoted to presenting the solution. The …
11 votes

Are there any good websites for hosting discussions of mathematical papers?

You can try SciRate (https://scirate.com/), a site that allows you to rate and comment papers from Arxiv (it updates the list of papers automatically). It doesn't seem to be very popular, though (lack …
37 votes

Most memorable titles

"I know I should have taken that left turn at Albuquerque" by Gady Kozma and Ariel Yadin (https://arxiv.org/abs/1008.4258)
3 votes

Individual mathematical objects whose study amounts to a (sub)discipline?

The Erdos-Renyi random graph model $G(n,p)$ - a single, concrete model that more or less created the field of random graph theory and is still studied.
5 votes

When and how is it appropriate for an undergraduate to email a professor out of the blue?

Above answers give a precise description of what the email should look like, so just a general comment. Profs are (usually) normal people, the fact they're higher in the academic hierarchy than you …
17 votes

What are the most overloaded words in mathematics?

Natural Very often I read things like "Now, it is natural to ask...", ""X is a natural generalization of Y" or "A natural question is..." when the problems are by no means natural, and the feeling of …
10 votes

Introductory text on geometric group theory?

There is a very nice book related to the topic - "Word processing in groups" by David Epstein. It covers some stuff about the combinatorial aspects of geometric group theory, e.g. automatic groups, co …
14 votes

What is the first interesting theorem in (insert subject here)?

Functional analysis: the open mapping theorem.