Questions tagged [exposition]

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13 answers
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Exposition of Grothendieck's mathematics

As Wikipedia says: In Grothendieck's retrospective Récoltes et Semailles, he identified twelve of his contributions which he believed qualified as "great ideas". In chronological order, ...
8 votes
1 answer
470 views

Exposition of concrete constructions

I am frequently interested to find less technical proofs of results which already appear in the literature, at least in some special cases of these results. Sometimes a published proof shows that an ...
23 votes
1 answer
2k views

Is an interpretation mathematics (fit for publication)?

Background I am a mathematician with two published papers. The first is based on my PhD thesis and generalised a tool to a more general setting. The thesis was cited a number of times by the time the ...
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67 votes
5 answers
5k views

A better way to explain forcing?

Let me begin by formulating a concrete (if not 100% precise) question, and then I'll explain what my real agenda is. Two key facts about forcing are (1) the definability of forcing; i.e., the ...
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8 votes
0 answers
251 views

Motivating derived stacks via Euclidean geometry

Here (see Section 3) triangles in Euclidean plane are used to motivate the notion of DM stack (an equilateral triangle has more symmetries than a generic triangle). Can something similar be done to ...
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5 votes
4 answers
586 views

mixing theorem with definition (definition with proof)

I often find myself writing a definition which requires a proof. You are defining a term and, contextually, need to prove that the definition makes sense. How can you express that? What about a ...
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6 votes
2 answers
2k views

Wasserstein distance and the Kantorovich-Rubinstein duality

The only few references I could find on this topic are either amateur blog posts (http://n.ethz.ch/~gbasso/download/A%20Hitchhikers%20guide%20to%20Wasserstein/A%20Hitchhikers%20guide%20to%...
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39 votes
4 answers
2k views

Important open exposition problems?

Timothy Chow, in his article A beginner's guide to forcing, defines an open exposition problem as a certain concept or topic in mathematics that has yet to be explained "in a way that renders it ...
19 votes
3 answers
2k views

What is a sieve and why are sieves useful?

I have been trying to understand what is exactly a sieve and why sieves are useful. I have read Wikipedia articles about sieve theory but they don't provide a definition of what is a sieve or why they ...
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25 votes
4 answers
9k views

What is a good poster for a math conference?

I'm going to participate to a conference and they ask me to do a poster on my research. I've never made a poster for a conference/seen a poster session in a conference. So what is important? What do ...
19 votes
4 answers
3k views

Analogy between the nodal cubic curve $y^2=x^3+x^2$ and the ring $\mathbb{Z}[\sqrt{-3}]$?

I'm trying to motivate a bit of algebraic geometry in an abstract algebra course (while simultaneously trying to learn a bit of algebraic geometry), and I thought that it might be nice to present an ...
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19 votes
2 answers
2k views

First occurrence of "by the usual compactness argument"?

In his blog, Jeff Shallit asks, what was the first occurrence of the exact phrase, "by the usual compactness arguments," in the mathematical literature? He reports that the earliest appearance he has ...
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10 votes
0 answers
505 views

Where to find NSF Reports (For mathematical expository purpose)? [closed]

This is not asking about how to apply for funding. I just find that some NSF funding report (near the end of the funding cycle) is quite interesting read. In particular, it's almost like a research ...
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289 votes
8 answers
136k views

Philosophy behind Mochizuki's work on the ABC conjecture

Mochizuki has recently announced a proof of the ABC conjecture. It is far too early to judge its correctness, but it builds on many years of work by him. Can someone briefly explain the philosophy ...
10 votes
0 answers
606 views

Is there any elementary text unravelling the definitions of 2-category, lax functor and lax transformation, allowing people who do not know in the first place what these things are to really understand the definitions?

The question is in the title. My current research subject is the homotopy theory of $2$-categories. It may be slightly unreasonable to expect my PhD thesis to be read or even looked at by people ...
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10 votes
6 answers
3k views

How do you present a non-existence theorem?

(This question might be too vague, feel free to edit or vote for closing.) In math there are usually lots of non-existence theorems. When someone presents such a theorem, one natural response is "why ...
14 votes
1 answer
7k views

Intuitive understanding of the Stieltjes transform

I have been using random matrix theory in signal processing and have some trouble understanding what the Stieltjes transform does. The gist of my work is that I have an $N\times N$ true covariance ...
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17 votes
14 answers
3k views

Teaching a pedagogy course

At my institution incoming graduate students must take a semester long course on pedagogy taught by current grad students. I may soon be in the position of having to teach this course and I'm looking ...
23 votes
2 answers
1k views

Finding citations for 'well-known' results

I am almost ready to submit my most recent paper, and I find myself in a problem that has already occurred multiple times in my short publishing career. In this paper, I wish to state a result which ...
13 votes
8 answers
5k views

Has anyone found an error in an early version of Neukirch?

I remember a friend in graduate school throwing an early edition of Jurgen Neukirch's Algebraic Number Theory book against a wall (so hard that it split the binding) after he had worked for a number ...
18 votes
6 answers
974 views

How should one present calculations?

It is often necessary to present calculations, or at least their outlines, in a proof. However, when I need to do it, if the calculation takes more than one line (or perhaps two at the most), I feel ...
20 votes
9 answers
5k views

General Equilibrium for Mathematicians

I've been reading up a lot on the recent financial crisis, and central to the story is the existence of general equilibrium models in economics, say, as proven by Arrow and Debreu (and MacKenzie?). ...
9 votes
2 answers
693 views

Expository treatment of Schubert Cells Paper

I was wondering about the paper by Bernstein, Gel'fand, and Gel'fand on Schubert Cells. This paper is fairly old(and often cited) so I figured someone must have represented this material. In ...
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280 votes
34 answers
34k views

Which journals publish expository work?

I wonder if anyone else has noticed that the market for expository papers in mathematics is very narrow (more so than it used to be, perhaps). Are there any journals which publish expository work, ...
15 votes
4 answers
1k views

Introductory text for the non-arithmetic moduli of elliptic curves

I'm looking for an introduction to the non-arithmetic aspects of the moduli of elliptic curves. I'd particularly like one that discusses the $H^1$ local system on the moduli space (whether it's $Y(1)$ ...
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3 votes
6 answers
2k views

Source needed (at final-year undergrad level) for the double cover of SO(3) by SU(2)

This is a bit of an ill-defined question, and I feel I should have been able to resolve it by combining Google with a few library trips, but I'm having difficulty narrowing down the search results to ...
2 votes
2 answers
367 views

Use of the word "data" not in the statistical sense [closed]

Occasionally I see the use of the word "data" in definitions. For instance, one definition of an exact sequence starts off by saying, "An exact sequence of abelian groups (or modules or vector spaces) ...
49 votes
1 answer
5k views

Is it best to run or walk in the rain? [closed]

According to the Norwegian meterological institute, the answer is that it is best to run. According to Mythbusters (quoted in the comments to that article), the answer is that it is best to walk. My ...
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3 votes
4 answers
29k views

Is it alright for STD error bars to be below zero?

I have some statistical data from which I want to graph the means and use the standard deviations as error bars. However this produces a graph with some of the error bars passing below zero. A ...
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13 votes
4 answers
2k views

Short Introduction to Planar Algebras

Are there any good short expositions of planar algebras out there? I am interested primarily in seeing the main definition and some explicit examples.
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