**23**

votes

**1**answer

2k views

### Why not a Roadmap for Homotopy Theory and Spectra?

MO has seen plenty of roadmap questions but oddly enough I haven't seen one for homotopy theory. As an algebraic geometer who's fond of derived categories I would like some guidance on how to build up ...

**2**

votes

**1**answer

468 views

### Books on the Hardy-Littlewood circle method

Are there any good books providing an introduction to the Hardy-Littlewood method that do not require much of a background in complex analysis?

**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 ...

**1**

vote

**1**answer

543 views

### Recomendation of Complex variables book [closed]

I'd like to ask for a book of complex variables that includes a "large" discussion about the Dirichlet problem, Neumann problem, and problems like that, I have now read "basic complex analysis - ...

**1**

vote

**0**answers

559 views

### Linear Algebra Text Book

In our department we do not like our current linear algebra book and so we would want to find a better book. This is for the first course in linear algebra and the title of the course is
Elementary ...

**5**

votes

**1**answer

1k views

### Hodge Theory (Voisin)

I have a strong understanding of Representation Theory but am interested in learning from
Voisin, Hodge Theory and Complex Algebraic Geometry.
What are the prerequisites to learning from this ...

**8**

votes

**6**answers

819 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 ...

**1**

vote

**2**answers

133 views

### Good introductory books on dilation theories?

Are there any good introductory type of books that contain dilation theories of Sz-Nagy, Rohlin and Akcoglu?

**15**

votes

**5**answers

2k views

### Book Recommendation - PDE's for geometricians / topologists

I am looking for recommendations for a book on partial differential equations, which is not written for applied mathematicians but rather focused on geometry and applications in topology, as well as ...

**2**

votes

**1**answer

520 views

### Suggestions on the best introductory Model Theory texts [closed]

Any recommendations on the best texts for introducing Model Theory?

**1**

vote

**2**answers

433 views

### Reference request: learn measure theory for PDEs

I am requesting some references to learn appropriate measure theory for PDEs. Specifically, I would like to learn all the measure theory necessary to understand well-posedness of PDEs with measure ...

**27**

votes

**8**answers

5k views

### An “advanced beginner's” book on algebraic topology?

It has so happened that I have come this far knowing nothing on the subject of algebraic topology (as in homology theories of topological spaces and their applications). I've decided to finally read ...

**11**

votes

**2**answers

517 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

**10**

votes

**4**answers

858 views

### Calculus book in the spirit of the 18th century

I have been reading a lovely 18th century book by John Rowe called An Introduction to the Doctrine of Fluxions. It presents calculus completely motivated by geometric questions - finding tangents to ...

**2**

votes

**0**answers

370 views

### Textbooks on Algorithmic Number Theory

I am looking for a good textbook suitable for graduate or advanced undergraduate students who want to explore algorithmic number theory. Specifically, algorithms for primality testing, and factoring ...

**3**

votes

**4**answers

1k views

### Roadmap to reach Arithmetic Geometry for a Physics Major

Hi Everybody! I am physics major but I read mathematics for myself. my main fields of interest are number theory and geometry. it seems that due to the works of A.Grothendieck, algebraic geometry must ...

**6**

votes

**4**answers

2k views

### Good book on Calculus of Variations

What is a good book on the Calculus of Variations, for a second year PhD student?

**9**

votes

**4**answers

1k views

### Books on advanced galois theory

I have been studying galois theory on my own and find it very fascinating. I have gone through Ian Stewarts book: http://www.amazon.co.uk/Galois-Theory-Third-Chapman-Mathematics/dp/1584883936. I am ...

**3**

votes

**2**answers

253 views

### Book on the Moment Problem

Is there a recently published book on the Classical Moment Problems and related theory?
I have seen a couple of old books by Tamarkin and a few other books by Russian authors. Want to know what else ...

**3**

votes

**6**answers

2k views

### Differential geometry study materials

I want to start studying differential geometry but I can't seem to find a proper starting path. Whenever I try to search for differential geometry books/articles I get a huge list. I know that it is a ...

**1**

vote

**1**answer

229 views

### Recommend a book about compact subgroups

Hi, could you please recommend me some books/articles where I could find information about compact subgroups of metric topological compact (abelian) groups? Thanks in advance for any help.

**13**

votes

**2**answers

2k views

### Learning path for the proof of the Weil Conjectures

Assume you are an algebraic geometry advanced student who has mastered Hartshorne's book supplemented on the arithmetic side by the introduction of Lorenzini - "An Invitation to Arithmetic Geometry" ...

**1**

vote

**1**answer

532 views

### Books on Numerical Methods for Partial Differential Equations

Any good references for undergraduates?

**8**

votes

**8**answers

3k views

### Any good books on numerical methods for ordinary differential equations?

I need to find some masters-level exercises about numerical methods for solving ODEs. Are there any good references?

**9**

votes

**11**answers

3k views

### Textbook for undergraduate course in geometry

I've been assigned to teach our undergraduate course in geometry next semester. This course originally was intended for future high-school teachers and focused on axiomatic, Euclid-style geometry ...

**-3**

votes

**3**answers

658 views

### Books on analytic functions on Banach spaces over a non-Archimedean field

I'm looking for good textbooks on analytic functions on Banach spaces over a non-Archimedean field.
If you know one(s), please let me know.

**4**

votes

**2**answers

351 views

### what is the definition of the Picard group of a (non necessarilly commutative) Ring?

Hi. I have only able to find the definition of $Pic(R)$ for a commutative ring $R.$ Which is the isomorphism classes of projective $R$-modules of rank $1,$ and the product given by $[A][B]=[A\otimes_R ...

**5**

votes

**4**answers

557 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 ...

**8**

votes

**5**answers

2k views

### What is a good book on topological groups?

I am looking for a good book on Topological Groups. I have read Pontryagin myself, and I looked some other in the library but they all seem to go in length into some esoteric topics.
I would love ...

**9**

votes

**5**answers

1k views

### Measure theory treatment geared toward the Riesz representation theorem

I'm looking for recommendations for books (or lecture notes) that develop measure theory in sufficient detail to state and prove the Riesz representation theorem (which is the characterization of the ...

**7**

votes

**6**answers

2k views

### Discrete Mathematics textbooks for undergraduates

For the first time, I will be teaching a course on Discrete Mathematics for electrical and computer undergraduates students.
I intend to focus on practical applications.
I would be grateful if ...

**6**

votes

**0**answers

539 views

### Recommendation textbooks on D-module

I am going to take part in a seminar on D-modules and applications, the textbooks that will be used are : D-modules, Perverse Sheaves, and Representation Theory, A Primer of Algebraic D-Modules
...

**25**

votes

**6**answers

2k views

### A toolbox for algebraic topology

This question has a very general part and a rather concrete part.
General:
When one wants to prove something in algebraic topology (actually in all parts of mathematics) one obviously needs some ...

**8**

votes

**10**answers

6k views

### College (Euclidean) geometry textbook recommendations

I will be teaching a mid-level undergraduate course in Euclidean geometry this fall. Has anyone taught such a course, who can recommend a good textbook?
My students will mostly be future high school ...

**3**

votes

**1**answer

495 views

### Searching for text for studying Spectral sequence

I'm a graduate student studying algebraic geometry
I saw Spectral sequence is important in deformation theory, and many other places in algebraic geometry.
Can you recommand me some good text for ...

**4**

votes

**5**answers

1k views

### searching for text for studying representation theory

I'm a graduate student studying algebraic geometry.
Recently, When I studying Hodge theory, I saw sl2-representation is used in Hodge theory.
So I think that studying representation theory may be ...

**12**

votes

**11**answers

2k views

### Approachable French Masters

It has been my general desire for a few years to acquire the basics in other European languages for the purpose of reading some of the classics in their original language, in a similar vein to this ...

**3**

votes

**1**answer

755 views

### Books on logic for someone aiming to go to grad school in the field?

I have taken two introductory courses on logic. One was an undergraduate level and the second one was at the graduate level. Both used a set of notes written by the instructor. I'm thinking about ...

**3**

votes

**1**answer

508 views

### Math background needed for Stakgold's Boundary Value Problems & Green's Functions Book

I saw a reference in Jackson's "Classical Electrodynamics" book for Stakgold's book on "Boundary Value Problems and Green's Functions" as a reference for Green's functions. The text is sort of clear, ...

**9**

votes

**2**answers

639 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

**3**answers

492 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 ...

**5**

votes

**3**answers

986 views

### Signal Analysis/Processing Textbook

Can anybody recommend me a decent Signal Analysis/Processing textbook. If possible one that deals a little with MATLAB. I have an little knowledge of Real Analysis and fourier transforms. Wavelets i ...

**13**

votes

**10**answers

3k views

### Good book on Riemann surfaces and Galois theory?

I'm supervising an undergraduate project on Galois theory and covering spaces. I want to have him read about the fact that from a branched cover of a Riemann surface you get an extension of its field ...

**-1**

votes

**1**answer

398 views

### Fuzzy topology : references [closed]

Hey. I'm looking for references in fuzzy topology. Does anyone know a good book ?

**7**

votes

**4**answers

2k views

### Help me find good math questions for my students

I am a teacher at 西铁一中。 I teach mathematics in English for students going abroad.
Now this is my problem, there are few mathematics books written in English that are at the level of high school, ...

**1**

vote

**1**answer

849 views

### Algebraic approaches to modular forms

I'd like to learn about modular forms. My background is mostly computational algebra and group theory, and I've had little-to-no training in complex analysis. I've briefly seen modular forms in a ...

**4**

votes

**2**answers

1k views

### Any suggestions for a course in Mathematical Logic?

I am teaching a topics course for Mathematics majors (at Temple), and am considering Logic as the topic. I was wondering if people (a) have suggestions for an appropriate text and (b) how much might ...

**16**

votes

**12**answers

7k views

### A book in topology

I will have to teach a topology course:
it starts in point set topology and ends at fundamental group of $S^1$.
In the past I have used two different books:
Elementary Topology. Textbook in ...

**6**

votes

**5**answers

4k views

### Mathematical Physics Book Recommendation

I want to learn contemporary mathematical physics, so that, for example, I can read Witten's latest paper without checking other sources again and again to find some basic definitions and theorems. I ...

**13**

votes

**9**answers

3k views

### Book recommendation for ergodic theory and/or topological dynamics?

Hello,
I'd like to hear your opinion for ergodic theory books which would suit a beginner (with background in measure theory, real analysis and topological groups). I am looking for something well ...