**6**

votes

**5**answers

973 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 ...

**25**

votes

**0**answers

591 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 ...

**20**

votes

**10**answers

12k 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 ...

**20**

votes

**17**answers

33k 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 ...

**119**

votes

**37**answers

15k 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

**6**answers

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 ...

**33**

votes

**12**answers

11k 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, ...

**17**

votes

**21**answers

24k 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?

**21**

votes

**29**answers

14k 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 ...

**121**

votes

**33**answers

69k 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 ...

**56**

votes

**55**answers

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:
...

**65**

votes

**66**answers

10k 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 ...

**42**

votes

**27**answers

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

**2**answers

782 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?

**8**

votes

**6**answers

833 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

**1**answer

399 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

**34**answers

6k 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 ...

**64**

votes

**61**answers

27k 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 ...

**18**

votes

**6**answers

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.
...

**10**

votes

**14**answers

7k 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 ...

**14**

votes

**2**answers

461 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

**1**answer

151 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 ...

**35**

votes

**16**answers

34k 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 ...

**25**

votes

**3**answers

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 ...

**5**

votes

**1**answer

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.
...

**20**

votes

**14**answers

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 ...

**58**

votes

**35**answers

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

**5**answers

2k 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

**2**answers

633 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, ...

**1**

vote

**1**answer

272 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

**15**answers

5k 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

**7**answers

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 ...

**68**

votes

**29**answers

11k 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

**4**answers

834 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 ...

**89**

votes

**28**answers

18k views

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

Hello, 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 ...

**2**

votes

**1**answer

157 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

**14**answers

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

**2**answers

617 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

**7**answers

2k 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

**4**answers

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 ...

**4**

votes

**6**answers

660 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 := ...

**8**

votes

**8**answers

3k 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 ...

**19**

votes

**15**answers

18k views

### Good Algebraic Number Theory Books

I have just finished a master's degree in Mathematics and want to learn everything possible about algebraic number fields and especially applications to the generalized Pell equation (my thesis ...

**111**

votes

**22**answers

15k views

### Why do so many textbooks have so much technical detail and so little enlightenment? [closed]

I think/hope this is okay for MO.
I often find that textbooks provide very little in the way of motivation or context. As a simple example, consider group theory. Every textbook I have seen that ...

**5**

votes

**5**answers

1k views

### Textbooks on SINGULAR and Macaulay 2

Recently, I'm tired of those theoretical parts on commuative algebra. So I hope that someone could recommend me some good textbooks on SINGULAR and Macaulay 2. And I'm wondering whether SINGULAR is ...

**0**

votes

**2**answers

1k 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 $X$; ...

**28**

votes

**32**answers

5k views

### What out-of-print books would you like to see re-printed?

It's excellent news that the LMS are to re-publish Cassels & Fröhlich. There are many other excellent mathematics books which are just about impossible (or at least very expensive) to get hold ...

**15**

votes

**1**answer

5k views

### Matsumura: “Commutative Algebra” versus “Commutative Ring Theory”

There are two books by Matsumura on commutative algebra. The earlier one is called Commutative Algebra and is frequently cited in Hartshorne. The more recent version is called Commutative Ring ...

**2**

votes

**2**answers

794 views

### Help with Griffiths & Harris, Surfaces

I believe to have found a typo in Griffiths & Harris.
In the chapter on surfaces, section Rational Surfaces 1, I am trying to read the result that a holomorphic vector bundle over ...

**18**

votes

**19**answers

14k views

### Good combinatorics textbooks for teaching undergraduates?

Hello, can anyone recommend good combinatorics textbooks for undergraduates? I will be teaching a 10-week course on the subject at Stanford, and I assume that the students will be strong and motivated ...