The exposition tag has no wiki summary.

**9**

votes

**2**answers

456 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 ...

**11**

votes

**4**answers

447 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 ...

**18**

votes

**2**answers

765 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 ...

**9**

votes

**0**answers

338 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 ...

**159**

votes

**7**answers

78k 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 ...

**9**

votes

**0**answers

412 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 ...

**7**

votes

**6**answers

1k 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 ...

**3**

votes

**1**answer

1k 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 ...

**16**

votes

**14**answers

2k 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 ...

**22**

votes

**2**answers

917 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 ...

**4**

votes

**4**answers

2k 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 ...

**17**

votes

**6**answers

853 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 ...

**17**

votes

**9**answers

3k 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

642 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 ...

**143**

votes

**29**answers

13k 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, ...

**14**

votes

**4**answers

900 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 $Y(1)$ ...

**2**

votes

**5**answers

815 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 ...

**1**

vote

**2**answers

318 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) ...

**46**

votes

**1**answer

4k 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 ...

**1**

vote

**4**answers

2k 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 ...

**8**

votes

**3**answers

1k 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.