**16**

votes

**14**answers

2k views

### Teaching a pedagogy course

At my institution incoming graduate students must take a semester long course on pedagogy taught by current grad students. I may soon be in the position of having to teach this course and I'm looking ...

**21**

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, ...

**0**

votes

**0**answers

436 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

**5**answers

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 ...

**9**

votes

**2**answers

1k views

### Literature on the Springer resolution

Could you suggest me a basic reading list on the Springer resolution? Is there a textbook I can refer to? Or do I need to start with the original paper?
Unfortunately googling for "Springer" and ...

**5**

votes

**5**answers

2k views

### Exponential sums for beginner.

What are the good books, online lecture notes or starting material on exponentials sums with applications in number theory for a beginner, apart from N. M. Korobov's book? The book or notes should ...

**38**

votes

**8**answers

3k views

### Natural transformations as categorical homotopies

Every text book I've ever read about Category Theory gives the definition of natural transformation as a collection of morphisms which make the well known diagrams commute.
There is another possible ...

**1**

vote

**4**answers

1k views

### Textbooks to use as reference for standard calculus and probability topics

I am currently working on a paper to be submitted to a US journal (addressed primarily to non-mathematiciansâ€™ audience) where I use
(1) some standard calculus stuff (e.g. limits, Taylor expansions, ...

**4**

votes

**7**answers

2k views

### probability and math puzzle books/references

Hi All,
I'd like to solve some math puzzles, especially in the context of probability theory, but I'm open to other areas too. The kind of problems that does not require much knowledge of mathematics, ...

**12**

votes

**19**answers

7k 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, ...

**3**

votes

**10**answers

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 ...

**2**

votes

**1**answer

535 views

### Knowledge base about topology [closed]

We are studying topology. There are a lot of definitions and theorems. I wonder if there somewhere knowledge base about topology and reasoning system exists. So I expect some tool that systematizes ...

**10**

votes

**7**answers

3k views

### Leibnizian calculus textbook

Where can I find a calculus textbook that emphasizes differentials?
Is there such a book that I could realistically require my calculus students to use?
I want a textbook that supports me when I tell ...

**10**

votes

**12**answers

4k 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 ...

**9**

votes

**10**answers

3k views

### The best text to study both incompleteness theorems

Hi!
What text on both incompleteness theorems you would recommend for beginner?
Specifically, I'm looking for the text with the following properties:
1) The proofs should be finitistic, in Godel's ...

**12**

votes

**4**answers

3k views

### Textbook or lecture notes in topological K-Theory

I am looking for a good introductory level textbook (or set of lecture notes) on classical topological K-Theory that would be suitable for a one-semester graduate course. Ideally, it would require ...

**13**

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 ...

**19**

votes

**3**answers

2k views

### Real algebraic geometry vs. algebraic geometry

This question is predicated on my understanding that real algebraic geometry (henceforth RAG) is the version of algebraic geometry (AG) one gets when replacing (esp. algebraically closed) fields with ...

**3**

votes

**6**answers

7k 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 ...

**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 ...

**11**

votes

**10**answers

3k views

### Math History books

I'm teaching a course over the summer (it's a sort of make-your-own course for non-majors) and I'm planning on organizing it as a math history course, hitting on major threads through about 1900, and ...

**22**

votes

**16**answers

6k views

### introductory book on spectral sequences

I have studied some basic homological algebra. But I can't send to get started on spectral sequences. I find Weibel and McCleary hard to understand.
Are there books or web resources that serve as ...

**17**

votes

**10**answers

5k views

### Riemannian Geometry Introductory Text

I have studied differential geometry, and am looking for basic introductory texts on Riemmanian geometry. My target is eventually KĂ¤hler geometry, but certain topics like geodesics, curvature, ...

**24**

votes

**11**answers

9k views

### Algebraic Topology Beyond the Basics:Any Texts Bridging The Gap?

Peter May said famously that algebraic topology is a subject poorly served by it's textbooks. Sadly,I have to agree. Although we have a frieghtcar full of excellent first-year algebraic topology ...

**2**

votes

**7**answers

1k 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.

**13**

votes

**13**answers

4k views

### Looking for an introductory textbook on algebraic geometry for an undergraduate lecture course

I am now supposed to organize a tiny lecture course on algebraic geometry for undergraduate students who have an interest in this subject.
I wonder whether there are some basic algebraic geometry ...

**17**

votes

**15**answers

13k 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 ...

**10**

votes

**17**answers

22k 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 ...

**15**

votes

**29**answers

10k 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 ...

**8**

votes

**15**answers

9k views

### Learning Topology

EDIT (Harry): Since this question in its original form was poorly stated (asked about topology rather than graph theory), but we have a list of Topology books in the answers, I guess you should go ...

**10**

votes

**17**answers

9k views

### Undergraduate Differential Geometry Texts

Can anyone suggest any basic undergraduate differential geometry texts on the same level as Manfredo do Carmo's Differential Geometry of Curves and Surfaces other than that particular one?
(I know a ...

**5**

votes

**3**answers

948 views

### Suggested reading for thermodynamic formalism

Are there any good books out there that can serve as an introduction to thermodynamical formalism in dynamical systems?
I know only Zinsmeister's short "Thermodynamical formalism and holomorphic ...

**24**

votes

**11**answers

6k views

### Lecture notes on representations of finite groups

Next term I am supposed to teach a course on representation of finite groups. This is a third year course for undegrads. I was thinking to use the book of Grodon James and Martin Liebeck ...

**5**

votes

**5**answers

991 views

### Texts In Non-Commutative Harmonic Analysis

What texts/books are available for progressing into non-commutative harmonic analysis?

**7**

votes

**17**answers

15k 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?

**27**

votes

**11**answers

8k 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, ...

**76**

votes

**32**answers

46k 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 ...