Jason Polak
  • Member for 12 years, 2 months
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Periods and commas in mathematical writing
77 votes

This is something I've never paid attention to until graduate school, but virtually every book uses the convention that formulae in display mode are part of the text. Every Springer text for instance ...

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What should be offered in undergraduate mathematics that's currently not (or isn't usually)?
45 votes

Inequalities! I don't think I've ever seen a course on inequalities, and there's certainly enough elementary material to cover in a one-semester course. Very few undergrads know much about ...

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Depressed graduate student.
38 votes

There are several different approaches you can use. As mentioned, health is important and you should go to the gym or exercise in some way, preferably with someone. Also reading about a variety of ...

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Justifying/Explaining math research in a public address
30 votes

I‘m all for talking about the applications of math and your research. I think such things can be very interesting. However, let me add one more point. I feel you should also express to the audience ...

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Memorizing theorems
18 votes

Try coming up with counterexamples when you remove hypotheses. Play with the mathematics. The best way to know a theorem is to prove it. Try coming up with a different proof. Explain the theorem to ...

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The "derived drift" is pretty unsatisfying and dangerous to category theory (or at least, to me)
14 votes

I think the answer is obvious. If you want to stay in mathematics, quit HTT and go back to the basics of what got you interested in math in the first place. It's easy for young people to be seduced ...

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First group homology with general coefficients
Accepted answer
11 votes

In the trivial case the abelianization comes from the short exact sequence $0\to J\to \mathbb{Z}G\to \mathbb{Z}\to 0$ where $J$ is the augmentation ideal. The homology $H_*(G,-)$ are just derived ...

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How can I tell if a group is linear?
8 votes

Since this is not purely group theoretical and not a complete answer, this maybe should be more of a comment, but since you mentioned simplicial complexes perhaps you should check out the following ...

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Open source mathematical software
8 votes

Kenzo and Chomp are for computing homology. Kenzo for instance can take an arbitrary abstract simplicial complex and compute the simplicial homology groups, and it has various spaces already built in. ...

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What motivations for automorphic forms?
7 votes

The following answer will be an attempt for the 'general mathematical audience', and so contains a little imprecision. Here are two reasons (somewhat?) related to number theory why one might consider ...

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Applications of Chevalley Restriction Theorem
7 votes

Let $G$ be a split reductive group over a finite field $k$ (of sufficiently large characteristic), $X$ a smooth geometrically connected projective curve over $k$ and $\mathcal{M}$ the algebraic stack ...

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Geometric invariant theory for geometers
7 votes

If you just want to get a feeling for invariant theory, here are some books that aren't necessarily comprehensive but nevertheless are enlightening at a more leisurely pace as compared to GIT, which ...

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What out-of-print books would you like to see re-printed?
7 votes

"Essays In Group Theory" edited by S.M. Gersten, which in particular contains Gromov's paper "Hyperbolic Groups".

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Criteria for accepting an invitation to become an editor of a scientific journal
6 votes

What strikes me most is that this letter is generic and not directed at you specifically, in the sense that there is no explained reason why they contacted you and not someone else. And "highest ...

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Meaning of fibration in Kazhdan and Lusztig's paper on affine flag manifolds
5 votes

According to Lusztig, it means locally trivial in the Zariski topology.

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Tools for collaborative paper-writing
5 votes

For joint collaboration I've used subversion. Having a central repository I think is a really good idea for a paper, although you can set up central repositories in bzr and git. I would stay away ...

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What is a good reference (preferably thorough) for the Derived Category of a scheme/orbifold/stack?
4 votes

I'll just mention some sources that are not already in the other question indicated by Franz's answer, in case you need to become more comfortable with the derived machinery itself. (The book by ...

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What arithmetic information is contained in the algebraic K-theory of the integers
4 votes

Let $p$ is an odd prime and $C$ the $p$-Sylow of the class group of $\mathbb{Q}(\zeta_p)$. If $C^\sigma$ denotes the group fixed by complex conjugation then Vandiver's conjecture is that $C^\sigma = 0$...

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Taking lecture notes in lectures
4 votes

Yes. It's essential for me to take notes or else I learn almost nothing unless it's something I've been thinking about for a while. I've discovered that my best learning technique is seeing symbols on ...

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How does one find out what's happening in contemporary mathematics research?
3 votes

This doesn't directly answer your question, but some universities give guest access to visitors for limited periods of time (e.g. an hour a day), so if there are any resources you really want to check ...

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Nonstandard Methods ( or Model Theory ) and Arithmetic Geometry
3 votes

Since you also mention algebraic geometry, you may want to take a look at "Model Theory and Algebraic Goemetry" edited by Elizabeth Bouscaren (Springer LNM 1696). Its primary purpose is to introduce ...

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Linear Algebra Texts?
3 votes

There's also Nicholson's Elementary Linear Algebra or the slightly more advanced Linear Algebra: With Applications. If your students react negatively to the intro of abstract vector spaces, I don't ...

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Sources for Bibtex entries
3 votes

There's also Lead2Amazon which can export in a variety of formats.

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Reductio ad absurdum or the contrapositive?
3 votes

There does seem to be a difference, although I don't know how to distinguish them formally, but here are two cases which distinguish the two: *Let V be a vector space. A linear map f on V is ...

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The Importance of ZF
3 votes

People use whatever is most useful. ZFC just happens to be a fairly simple formalization of the way people think of sets such that we can eliminate imprecision sufficiently to do good mathematics. ...

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Resources for getting maths on to the web.
2 votes

You can also install MediaWiki, the software used for Wikipedia, with LaTeX support, on your own server (say, your own domain or a department server); http://www.mediawiki.org/wiki/MediaWiki ...

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Injective Modules over Group Rings
1 votes

The notion of Frobenius algebra is still useful in the general case, but then group rings that are Frobenius algebras aren't necessarily quasi-Frobenius rings, as your example notes. However if $M$ is ...

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