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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23
votes
7answers
6k views

Classification of (compact) Lie groups

I would like to study/understand the (complete) classification of compact lie groups. I know there are a lot of books on this subject, but I'd like to hear what's the best route I can follow (in your ...
93
votes
28answers
20k views

Are there other nice math books close to the style of Tristan Needham?

I've been very positively impressed by Tristan Needham's book "Visual Complex Analysis", a very original and atypical mathematics book which is more oriented to helping intuition and insight than to ...
43
votes
19answers
39k views

Linear Algebra Texts?

Can anyone suggest a relatively gentle linear algebra text that integrates vector spaces and matrix algebra right from the start? I've found in the past that students react in very negative ways to ...
8
votes
1answer
318 views

Trinity College, Cambridge, circa 1896 maths scholarship papers [closed]

I've been searching around looking for the (maths component) of the scholarship papers to Trinity College (Cambridge) from around 1890. Can anyone provide a link to a pdf scan of these papers? Was ...
4
votes
1answer
103 views

Bromwich introduction to infinite series or modern counterpart

I'm looking to brush up my analysis after several years out of mathematics (graduated in 1996 and worked in industry since then). I want a hard core treatment of analysis in order to brush up and ...
13
votes
15answers
8k views

undergraduate logic textbook

I am going to teach the standard undergraduate Logic course for math and engineering majors. What are good (bad) text-books and why. I have not taught that course for a while and wonder if there are ...
58
votes
55answers
10k views

Books you would like to see translated into English.

I have recently been told of a proposal to produce an English translation of Landau's Handbuch der Lehre von der Verteilung der Primzahlen, and this prompts me to ask a more general question: ...
104
votes
41answers
37k views

Where does a math person go to learn quantum mechanics?

My undergraduate advisor said something very interesting to me the other day; it was something like "not knowing quantum mechanics is like never having heard a symphony." I've been meaning to learn ...
21
votes
24answers
27k views

Text for an introductory Real Analysis course.

Any suggestions on a good text to use for teaching an introductory Real Analysis course? Specifically what have you found to be useful about the approach taken in specific texts?
46
votes
13answers
5k views

Erratum for Cassels-Froehlich

Edit 25 April 2010: I have a physical copy of the new printing of the book. I can only assume the LMS is now selling it (but have no details). IMPORTANT EDIT: THE RESULTS ARE IN! Ok, the deadline has ...
3
votes
3answers
582 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 ...
1
vote
11answers
4k views

Propositional logic and first order logic textbook

What are in your opinion some good propositional and first order logic textbooks (undergraduate level) ? I need one that focuses mainly on the aspects of logic related to computer science. thanks in ...
19
votes
6answers
7k views

What are some good group theory references?

I'm curious about what books people use for a group theory reference. I don't currently own a dedicated group theory book, and I think I'd find such a book very helpful in my research. What is your ...
6
votes
5answers
1k views

A book explaining power and limitations of Peano Axioms?

Are there books or survey articles explaining the subject to a non-expert? To clarify what I mean, here is a couple of issues that I would like to read about. (I am mainly interested in references but ...
26
votes
0answers
782 views

Greatly expanded new edition of a Bourbaki chapter on algebra?

Recently I discovered by accident that Bourbaki issued in 2012 a radically expanded version of their 1958 Chapter 8 Modules et anneaux semi-simples (like other chapters, initially in French) within ...
21
votes
10answers
13k views

A book for problems in Functional Analysis

I want to know if there's any book that categorizes problems by subjects of Functional Analysis. I'm studying Functional Analysis now a days and I really need to solve some problems in order to ...
25
votes
17answers
37k views

Suggestions for a good Measure Theory book

I have taken analysis and have looked at different measures, but I am currently looking at realizing a certain problem in a different light and feel that I need a better background in various measures ...
122
votes
37answers
16k 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 ...
11
votes
6answers
3k 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 ...
34
votes
12answers
12k views

Homological Algebra texts

I would like to hear the communities' ideas on good Homological Algebra textbooks / references. The standard example is of course Weibel (which I'll leave for someone else to describe). As usual, ...
21
votes
29answers
15k views

Alternative Undergraduate Analysis Texts

Other than the standard baby Rudin, Spivak, and Stein-Shakarchi, are there other alternative and comprehensive analysis texts at the undergraduate level? For example something that has general results ...
129
votes
33answers
77k views

Best Algebraic Geometry text book? (other than Hartshorne)

I think (almost) everyone agrees that Hartshorne's Algebraic Geometry is still the best. Then what might be the 2nd best? It can be a book, preprint, online lecture note, webpage, etc. One suggestion ...
65
votes
66answers
11k 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 ...
44
votes
27answers
14k 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
2answers
813 views

Can I find Fermat's complete works anywhere?

I admire the mathematician very much and want to look at his writings. Is there anywhere in book or web form that has a collection of his writings?
9
votes
6answers
872 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 ...
12
votes
1answer
475 views

Springer GTM Reprints in China?

I apologise if this is not the sort of question appropriate for MO; it does however seem that mathematicians are the most likely to know the answer: Many of the Chinese mathematicians and graduate ...
45
votes
34answers
7k views

Are there any books that take a 'theorems as problems' approach?

Are there any books that present theorems as problems? To be more specific, a book on elementary group theory might have written: "Theorem: Each group has exactly one identity" and then show a proof ...
65
votes
61answers
28k views

Favorite popular math book [closed]

Christmas is almost here, so imagine you want to buy a good popular math book for your aunt (or whoever you want). Which book would you buy or recommend? It would be nice if you could answer in the ...
19
votes
6answers
3k views

Euclid with Birkhoff

I'm looking for an short and elementary book which does Euclidean geomety with Birkhoff's axioms. It would be best if it would also include some topics in projective (and/or) hyperbolic geometry. ...
14
votes
2answers
481 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 ...
1
vote
1answer
164 views

university press specialized in math books [closed]

I am thinking of writing a book for graduate students, on graph theory. Apart from AMS book, does someone of you could suggest a university press that acccept submission on these arguments. I ...
25
votes
3answers
2k views

Is “problem solving” a subject to be taught?

I am witnessing a new curriculum change in my country (Iran). It includes the change of all the mathematics textbooks at all grades. The peoples involved has sent me the textbook for seven graders (13 ...
6
votes
1answer
1k views

In studying maths, do you tend to go through books one at a time? [closed]

Or do you read a lot of books on the same subject (say Topology)? Consider these two cases: Case 1: Suppose you want to study point set topology. You pick up a good book and work thoroughly on it. ...
23
votes
14answers
2k 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 way?...
60
votes
35answers
7k views

Books about history of recent mathematics

I draw on this question to ask something that has always been a pet peeve of mine. It is very easy to find books about the history of mathematics, much less so if one wants books about the recent (say ...
5
votes
5answers
3k views

book recommendation on data analysis and statistics

I am looking for a book on data analysis and statistics. My objective is to better analyse and understand data over time (like trends or events) and extract useful information from raw statistics. I ...
2
votes
2answers
684 views

Popular books written by great mathematicians [closed]

I read: H. Poincare. Value of science F. Klein. Development of Mathematics in the 19th Century J.E. Littlewood. A Mathematicians Miscellany G.H. Hardy. A Mathematician’s Apology R. Courant, H....
1
vote
1answer
304 views

Book on Convergence Concepts in Probability without Measure Theory [closed]

I am looking for a comprehensive book on Probability which discusses Convergence of Random Variables in detail, excluding portions of Measure Theory. Allan Gut's "Probability: A Graduate Course" seems ...
30
votes
15answers
6k views

Learning LaTeX properly [closed]

I have never learned how to use Latex properly. Whenever writing a paper, I use hacks to override behavior of the underlying template. What would be an intermediate to advanced book on learning how to ...
10
votes
7answers
2k views

Geometric flavored textbook on algebra

I am interested in topology, while I am not so comfortable with some algebraic flavored textbook on algebra. Actually, it was not until I learned some topology that I began to understand some ...
74
votes
29answers
12k views

Where does a math person go to learn statistical mechanics?

The more math I read, the more I see concepts from statistical mechanics popping up -- all over the place in combinatorics and dynamical systems, but also in geometric situations. So naturally I've ...
6
votes
4answers
1k views

Good lecture notes/books on Jacobian of hyperelliptic curve

I want to understand what the Jacobian variety is from an algebraic (or arithmetic?) perspective. I want to know: What is the definition of the Jacobian? Widely know facts about it. Why the ...
2
votes
1answer
163 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 ...
25
votes
14answers
4k 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 ...
7
votes
2answers
633 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 ...
3
votes
7answers
3k views

Books about polynomials [closed]

Hi,have you a good reference (books) for the study of polynomials with one variable or many variables ? Thanks for your help. Don't hesitate to correct my English.
9
votes
4answers
2k 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 ...
5
votes
6answers
747 views

CLT for stationary sequences with infinte variance

There is a well-known central limit theorem for as a stationary sequences. If $( X_n )_n$ is a sationary sequence and $E X_n=0$ then under suitable mixing conditions the sequence $S_n := n^{-1/2}\...
8
votes
8answers
4k views

Book recommendations on cellular automata?

I have been looking for books on cellular automata, and I really can't afford more than one book right now, so I really need to make the right choice. What would be the right book for someone with a ...