Questions in which books play a key-role, such as questions on antique books, e-books, difference between various editions of a book, etc. For questions asking for recommendations of books on some subject the tag textbook-recommendation is often more suitable.

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2
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1answer
115 views

books on very large scale linear optimization

Recently in my material science research, I have encountered problems of very large scale linear optimization. I read the introductory book "Introduction to Linear Optimization (Athena Scientific ...
7
votes
2answers
487 views

Survey of the history of calculus?

Boyer 1939 is a nice readable survey of the history of the calculus, but it's showing its age. Discussing the notion of instantaneous velocity, he has: Mathematics knows no minimum interval of ...
0
votes
1answer
204 views

Books to Better Understand Mathematics [closed]

I would just like to quickly provide some background information about why I am asking this question. I'm about to finish my first semester of community college and have finally decided my major, ...
5
votes
4answers
1k views

Advice for number theory library

Hi I just got a faculty position and it comes with a generous start up funds for "office supplies", which I must use or lose. What does a pure mathematician need? I have good computers already. I ...
13
votes
1answer
288 views

Which tools can identify scholarly papers that use the same types of equations?

Many types of equations are being used in multiple contexts, so a search for specific formulas might be one way to identify scholarly papers that are conceptually related. Is any website or tool ...
-4
votes
1answer
268 views

I need following books (soft copies) [closed]

I know this is not the place to ask for such help, but I cant find these books in my country and not even on line and the shipping is very expensive. If someone out there have any of these books (soft ...
3
votes
1answer
238 views

A good reference for learning about super-differentiation & super-integration?

I've looked at a couple of books for basic information for super-differentiation & super-integration - Rogers Supermanifolds, and Khrennikovs Superanalysis. Unfortunately both books lack a clear ...
6
votes
0answers
232 views

Alternative source to Drozd's book on finite dimensional algebras

I am trying to learn classic representation theory of finite dimensional algebras. My main source is the book "finite dimensional algebras" by Drozd and Kirichenko. I did not have too much trouble ...
16
votes
12answers
1k views

Insightful books about elementary mathematics

What are some books that discuss elementary mathematical topics ('school mathematics'), like arithmetic, basic non-abstract algebra, plane & solid geometry, trigonometry, etc, in an insightful ...
6
votes
6answers
635 views

What books approach group theory through transformation/permutation groups?

What are some books that discuss transformation groups (or permutation groups) before abstract groups? Some quotes to motivate the question: from V. I. Arnold, 'On Teaching Mathematics': What ...
4
votes
2answers
297 views

P.J. Hilton notes requested

Does anybody here have the mimeographed notes Homotopy theory and duality, by P.J. Hilton, Cornell University, 1959 ? I guess that those notes were never published online. I believe that some ...
18
votes
2answers
1k views

Papers better than books?

Not so long ago I took a class called "Discrete analysis". I remember that I couldn't find any "novice" level material on Mobius functions in combinatorics. So then I went to the roots and read Rota's ...
2
votes
3answers
307 views

Good Books on the history of Zero

I am looking for books that discuss the origins of the zero, specifically the differences in the use and concept of the zero number among different civilizations (considering also the Mesoamerican ...
4
votes
2answers
293 views

lie algebras, Kac Moody, and quantum mechanics book

Hi all, I've just finished a graduated course on Kac-Moody algebras, and I'm really looking for some reading in regard to their applications to Quantum Mechanics. Can you help?
11
votes
2answers
451 views

Book on the Three body Problem

Hi all, I am looking for a good book about the famous (infamous perhaps?) three body problem - both theoretical and numerical hardless and accomplishments. can you help? Thanks
7
votes
5answers
867 views

Mathematics for ebook readers

Project Gutenberg has a mathematics section, and they prepare their more recent publications in a format that works very well on an ebook reader of moderate size: they generate PDFs in a size of ...
53
votes
61answers
8k views

Old books still used

It's a commonplace to state that while other sciences (like biology) may always need the newest books, we mathematicians also use to use older books. While this is a qualitative remark, I would like ...
2
votes
1answer
428 views

Extended integral in Spivak’s Calculus on Manifolds

On page 48 of Calculus on Manifolds Spivak defines (Riemann) integration over rectangles $[a_{1},b_{1}]\times\cdots\times[a_{n},b_{n}]\subset\mathbb{R}^{n}$. Then on page 55 he extends this integral ...
14
votes
0answers
609 views

Horrible sets and blowups in Hubbard's Teichmuller theory

Edit: I can rephrase this question this way: When blowing up every point in the $x$-axis in $\mathbb{C}^2$ by means of an inverse limit of finite blowups, how can anything be 'left over'? The horrible ...
4
votes
4answers
505 views

Synthetic approach to hyperbolic geometry?

Hello, I am looking for a source that discusses and teaches hyperbolic geometry from a synthetic approach (As opposed to the common analytinc approach in the poincare disk). I am looking for ...
12
votes
3answers
1k views

Erratum for Fulton and Harris

I am currently using Fulton and Harris for a course on representation theory, and I have noticed that there are a few errors throughout the book. A search on google with the keywords "Errata for ...
25
votes
65answers
7k views

Fiction books about mathematicians? [closed]

What are some fiction books about mathematicians? It seems to me rather difficult for writers to create good books on this subject. Some years ago I thought there were no such books at all. There ...
24
votes
14answers
3k views

Essential reads in the philosophy of mathematics and set theory

I am graduate student and have a decent understanding of logic and set theory. Recently I have got interested in the philosophy of mathematics and set theory. I have read a number of papers by ...
8
votes
0answers
585 views

Good introduction to Morse-Novikov theory?

Morse theory investigates the topology of compact manifolds using critical points of real-valued functions $f\colon\, M\to \mathbb{R}$. Motivated by problems in dynamical systems, Novikov (Multivalued ...
9
votes
2answers
564 views

Tor sheaves: what do they tell us about geometry

Hi! I fear that I am up to ask a very vague question, but more than an answer I need a suggestion of references I should look up. I need to know everything about Tor sheaves and what do they tell ...
3
votes
3answers
484 views

Finite, abelian, yet “fugitive” orthogonal subgroups

Update July 29, 2013. I have still not found a good textbook for this topic, if you point one to me I will be grateful :) I have accepted BS's answer anyway, since their explanation was useful to me ...
0
votes
2answers
922 views

Possible errata in Nicolas Bourbaki's General Topology -I, Chapter 1 Exercise 2 ?

Here is the text of Exercise: 2 a) Let $X$ be an ordered set. Show that the set of intervals $\left[x, \rightarrow\right[$ (resp. $\left]\leftarrow, x\right]$) is a base of topology on $X$; ...
8
votes
0answers
438 views

Mathematical literature wiki

Does there exist, either still in development or already on on-line, anything like a wiki-type tool designed for mathematicians and students studying monographs and texts and journal articles---a ...
11
votes
6answers
2k views

Graduate ODE textbook

Suppose that a hypothetical math grad student was pretty comfortable with first-year real variables and algebra, and had even studied some other things (algebraic geometry, Riemannian geometry, ...
13
votes
1answer
866 views

Devlin's “Constructibility” as a resource

It is fairly well-known among set-theorists that Keith Devlin's 1984 book "Constructibility" has flaws in its initial development of fine structure theory. (See Lee Stanley's review 1 of the text for ...
0
votes
1answer
916 views

Any two curves over k homeomorphic [closed]

Why are two curves over a field k homeomorphic? I have been able to prove that any variety of positive dimension over a field k has the same cardinality as k.
4
votes
2answers
505 views

frechet manifolds book

hi, does anyone know a good book or some lecture notes on the theory of frechet manifolds ?
1
vote
1answer
457 views

Principal term of the Dirichlet Divisor problem, from the work of A.F. Lavrik?

Ivic writes, at the beginning of chapter 13 of his The Riemann Zeta Function, about a method of expressing the principal terms of the Dirichlet Divisor Problem as polynomials of $log\\ n $ with ...
4
votes
1answer
522 views

On a remark in Foundations of mechanics, 2nd Edition, by Abraham and Marsden

I don't know if this question is appropriate to this site, but I posted here without an answer, so I tried this alternative. Given a $2$-form $\omega$ on a manifold $M$, let us denote by $N$ the ...
22
votes
3answers
3k views

Elementary Number Theory Text from a Categorical Perspective

My question is somewhat similar to this previous question, but from a slightly different perspective. Is there any textbook on elementary number theory that develops the properties of $\mathbb{Z}$ as, ...
0
votes
0answers
437 views

Linear Representations of the Groups

Does anyone know a good book on Linear Representations of the finite Groups which does not assumes a lot of background. Book which will be good to study for computer science and will cover all( at ...
8
votes
5answers
2k views

Good introductory text book on Matroid Theory?

I am looking for a good text book on Matroid theory. Ideally, one that might be better suited to engineers than pure mathematicians...but any book that is well written/organized would do. I have ...
16
votes
17answers
3k views

Which book would you like to see “texified”? [closed]

Let's see if we could use MO to put some pressure on certain publishers... Although it is wonderful that it has been put online, I think it would make an even greater read if "Hodge Cycles, Motives ...
12
votes
19answers
8k views

Textbook recommendations for undergraduate proof-writing class

I am teaching the proof-writing class (for the 3rd time) in the Fall and plan to buck the party line and use a different text than the default Bond and Keane. My parameters are as follows: Logic, ...
0
votes
1answer
435 views

Deeper meanings of Phase Space — any books? [closed]

I often think about the phase space with quite deep interpretations. For example, contraction of phase space means losing energy. But, some of the energy is easily restored (free energy?) while some ...
3
votes
10answers
2k views

Best introduction to probability spaces, convergence, spectral analysis

I'm not sure if this stuff all falls under what most would just term "probability", but I'm researching applied macroeconomics and need to get a handle on the following concepts ASAP: probability ...
3
votes
7answers
2k views

Ask for recommendations for textbook on mathematical logic

I studied mathematical logic using a book not written in English. I would now like to study it again using a textbook in English. But I hope I can read a text that is similar to the one I used before, ...
6
votes
5answers
970 views

Suggestions for mathematics encyclopedia

On daily basis I need to check (and re-check and re-check...) some definitions and main theorems that are not in my research area. Usually I accomplish this by a Google-search and/or a visit to our ...
36
votes
26answers
12k views

A Book You Would Like to Write

Writing a book from the beginning to the end is (so I heard) a very hard process. Planning a book is easier. This question is dual in a sense to the question "Books you would like to read (if somebody ...
11
votes
8answers
2k views

Decent Texts on Categorical Logic

Recently I read the chapter "Doctrines in Categorical Logic" by Kock, and Reyes in the Handbook of Mathematical Logic. And I was quite impressed with the entire chapter. However it is very short, and ...
94
votes
35answers
13k views

Books you would like to read (if somebody would just write them…)

I think that the title is self-explanatory but I'm thinking about mathematical subjects that have not received a full treatment in book form or if they have, they could benefit from a different ...
28
votes
17answers
6k views

Computer Science for Mathematicians

This is a big-list community question, so I'm sorry in advance if it is deemed too soft but I haven't seen anything similar yet. I've seen computer scienctists post questions looking to learn things ...
2
votes
4answers
1k views

Applied linear algebra textbook? [closed]

I have a copy of Linear Algebra Done Right, which I worked through years ago in college. I have been using that book to refresh my knowledge, but it does not have an applied or computational aspect ...
13
votes
1answer
579 views

Website to help track recent research level mathematical book publications?

I'm responsible for recommending purchases of research level monographs to my university library. My job would be vastly simplified if I could find a website (say) that made it easy to scan a list of ...
4
votes
0answers
648 views

Commutative ring Notes by M. Artin

In 1966, Professor Michael Artin gave a course for first-year graduate students at MIT on commutative algebra. In that course he covered many classical topics, (the Spectrum of a commutative ring, ...