**9**

votes

**18**answers

17k 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?

**86**

votes

**33**answers

51k 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 ...

**5**

votes

**4**answers

488 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 ...

**81**

votes

**28**answers

14k 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

118 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 ...

**24**

votes

**14**answers

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 ...

**54**

votes

**61**answers

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 ...

**7**

votes

**2**answers

499 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 ...

**12**

votes

**19**answers

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, ...

**2**

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.

**5**

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 ...

**46**

votes

**49**answers

9k 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:
...

**0**

votes

**1**answer

211 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, ...

**4**

votes

**6**answers

486 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 := ...

**6**

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 ...

**17**

votes

**15**answers

14k 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 ...

**97**

votes

**22**answers

10k 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 ...

**13**

votes

**1**answer

292 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

**1**answer

271 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 ...

**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 ...

**26**

votes

**16**answers

24k 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 ...

**60**

votes

**28**answers

8k 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 ...

**0**

votes

**2**answers

926 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 $X$; ...

**26**

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

**29**answers

11k 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 ...

**14**

votes

**1**answer

4k 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

776 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 ...

**14**

votes

**19**answers

11k 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 ...

**22**

votes

**3**answers

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, ...

**19**

votes

**8**answers

4k views

### How to start Game theory?

Hi everybody,
I recently got interested in Game Theory but I don't know where should I start.
Can anyone recommend any references and textbooks?
And what are the prerequisites of Game Thoery?
Thanks ...

**36**

votes

**26**answers

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 ...

**3**

votes

**1**answer

242 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 ...

**58**

votes

**61**answers

23k 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 ...

**6**

votes

**0**answers

234 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 ...

**6**

votes

**6**answers

639 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 ...

**3**

votes

**6**answers

8k views

### What are your favorite calculus books for math majors of various levels? [closed]

Since I'll be working ("I" being the original poster, Andrew L) as either a high school math teacher or adjunct at a university as well as private tutoring, to make ends meet for the next year or so ...

**61**

votes

**13**answers

12k views

### Statistics for mathematicians

I'm looking for an overview of statistics suitable for the mathematically mature reader: someone familiar with measure theoretic probability at say Billingsley level, but almost completely ignorant of ...

**24**

votes

**9**answers

5k views

### Introductory text on geometric group theory?

Can someone indicate me a good introductory text on geometric group theory?

**56**

votes

**34**answers

6k 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 ...

**16**

votes

**12**answers

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 ...

**18**

votes

**2**answers

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 ...

**4**

votes

**2**answers

298 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 ...

**2**

votes

**3**answers

310 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 ...

**3**

votes

**3**answers

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 ...

**6**

votes

**4**answers

873 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 ...

**3**

votes

**7**answers

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, ...

**11**

votes

**2**answers

453 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

**4**

votes

**2**answers

295 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?

**13**

votes

**9**answers

9k views

### A book for problems in Functional Analysis

Hello everybody,
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 ...

**7**

votes

**5**answers

874 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 ...