Questions tagged [reading-list]

Questions about recommended reading on a specific topic or from a specific time period.

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3 votes
0 answers
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Maths books or works by originators or pioneers of fields of mathematics [closed]

I am looking for a (hopefully eventually comprehensive) list of examples of books or works that are: written by an originator of a field of mathematics, and about that field written by a pioneer of a ...
1 vote
0 answers
115 views

Nim variant with minimum number of objects?

I'm wondering where I can find in the literature (if it exists) a discussion of a Nim variant where we impose the additional condition on Nim that we can remove only up to $c$ objects before the game ...
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  • 111
14 votes
1 answer
589 views

Gromov's articles suitable for master students

I'm a master student and I have read "Monotonicity of the volume of intersection of balls" by Gromov and it was a great experience. When trying to fill the gaps, I often end up finding some ...
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  • 309
0 votes
0 answers
73 views

Prerequisites/Preparation for understanding a research paper - global solutions to Einstein field in Bondi Coordinates

I would like to read this paper: João L. Costa, Filipe C. Mena, Global solutions to the spherically symmetric Einstein-scalar field system with a positive cosmological constant in Bondi ...
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  • 101
4 votes
1 answer
74 views

Bounding the number of orthogonal Latin squares from above

As is usual, let $N(n)$ denote the maximum size of a set of mutually orthogonal Latin squares of order $n$. I am wondering what results hold that bound $N(n)$ from above; the only ones I can think of ...
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1 vote
1 answer
410 views

A question of the Schrodinger Semigroup --By B. Simon

The question comes from the paper: B. Simon, Schrodinger Semigroups, Bull. A.M.S., (1982) Vol. 7 (3). On the Theorem C.1.2(subsolution estimate) of the paper, it says that: If $Hu=0$, where $H=-\...
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  • 1,875
9 votes
0 answers
270 views

List of modern points of view simplifying or clarifying classical topics

There are many modern mathematical achievements which greatly clarify or (and) simplify classical important topics. I believe a list of such achievements, among other benefits, would be a big help for ...
90 votes
18 answers
8k views

Short papers for undergraduate course on reading scholarly math

(I know this is perhaps only tangentially related to mathematics research, but I'm hoping it is worthy of consideration as a community wiki question.) Today, I was reminded of the existence of this ...
13 votes
4 answers
4k views

What is the interface between functional analysis and algebraic geometry?

This is a very open ended curiosity of mine and I would be grateful to hear any comments in this direction. In particular I am interested in functional analysis/algebraic geometry books/papers ...
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16 votes
4 answers
1k views

Inverse problem of Chern Classes

For my graduate (master) thesis I am studying the theory of Chern Classes. As a possible personal development the only sensible idea I have so far, and which I frankly think is impossible, is to work ...
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34 votes
13 answers
4k views

Great mathematics books by pre-modern authors

Last summer, I read Euclid's Elements, and it was an eye-opening experience; I had assumed that three thousand years' difference would make the notation incomprehensible and the reasoning alien, but ...
14 votes
11 answers
3k views

Approachable French Masters

It has been my general desire for a few years to acquire the basics in other European languages for the purpose of reading some of the classics in their original language, in a similar vein to this ...
17 votes
17 answers
3k views

Readings for an honors liberal art math course

Our university has an Honors section of our "liberal arts mathematics" course. Typically 10-20 students enroll each Fall, with most of them extremely bright, but lacking the interest and/or ...
4 votes
2 answers
582 views

Reading Material on Couplings

Does anybody have suggestions on what to read to learn more about couplings pertaining to statistics? I'm working on a research project on Poisson approximations and am looking to perform a coupling ...
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9 votes
1 answer
4k views

Is there any book explaining in detail the book "Basic Number Theory" by André Weil as Dirichlet did to "Disquisitiones Arithmeticae" by Gauss?

Is there any book explaining in detail the book "Basic Number Theory" by Andre Weil as Dirichlet did to "Disquisitiones Arithmeticae"? This is because I have read the two books mentioned above and I ...
16 votes
10 answers
11k views

How do I approach Optimal Control?

Other than learning basic calculus, I don't really have an advanced background. I was curious to learn about Optimal Control (the theory that involves, bang-bang, Potryagin's Maximum Principle etc.) ...
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154 votes
22 answers
25k views

Do you read the masters?

I often hear the advice, "Read the masters" (i.e., read old, classic texts by great mathematicians). But frankly, I have hardly ever followed it. What I am wondering is, is this a principle that ...
127 votes
74 answers
19k views

Most helpful math resources on the web

What are really helpful math resources out there on the web? Please don't only post a link but a short description of what it does and why it is helpful. Please only one resource per answer and let ...
30 votes
5 answers
3k views

Handling arXiv feeds to avoid duplicates

I subscribe to feeds from the arXiv Front for a number of subject areas, using Google Reader. This is great, but there is one problem: when a new preprint is listed in several subject categories, it ...
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80 votes
19 answers
98k views

Reading list for basic differential geometry?

I'd like to ask if people can point me towards good books or notes to learn some basic differential geometry. I work in representation theory mostly and have found that sometimes my background is ...
61 votes
14 answers
20k views

A reading list for topological quantum field theory?

Can you suggest a reading list, or at least a few papers that you think would be useful, for a beginner in topological quantum field theory? I know what the curvature of a connection is, know basic ...