**6**

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### Mathematical Physics Book Recommendation

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**14**

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**11**

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Suppose that a hypothetical math grad student was pretty comfortable with first-year real variables and algebra, and had even studied some other things (algebraic geometry, Riemannian geometry, ...

**3**

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Hi,
I am looking for a book on Banach manifolds. Can somebody recommend me something.
Thanks in advance.
leo

**21**

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After having a solid year long undergraduate course in abstract algebra, I'm interested in learning algebra at a more advanced level, especially in the context of category theory.
I've done some ...

**3**

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**3**answers

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**4**

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**22**

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**5**

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First I am interested about the basics and foundations of model theory. ...

**4**

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What is a basic textbook?

**4**

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**3**answers

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I have some paper, but I don't know what is first and what is nice.
Please recommend to me.

**1**

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**2**answers

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Do you know on any good reference on Weil bound for charcter sums over algebraic curves.
I prefer reference which assume few previous knowlage.

**9**

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**4**answers

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**5**

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**2**answers

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**4**

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**1**answer

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**2**

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**2**answers

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**32**

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**1**answer

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### If I want to study Jacob Lurie's books “Higher Topoi Theory”, “Derived AG”, what prerequisites should I have?

I've been told that it's important to know modern physics, Differential Geometry and Algebraic Topology for understanding higher structures. Is there any other prerequisite for understanding Lurie's ...

**11**

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**1**answer

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**6**

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### A book on Banach Manifold for a Dynamicist

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Could you give me a suggestion of suitable book about Banach Manifolds for someone that have background in functional analysis at the level of Conway's book and Do Carmo's book on Riemannian ...

**11**

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**6**answers

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**1**

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Where can I find references that discuss important classes of Infinite Hopf Algebras. By important classes, I mean heavily used in research and of relevance to Hopf Algebraist(s),Physicists, ...

**6**

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**2**answers

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### Book on mixed Hodge structures?

Is there any English textbook about Deligne's mixed Hodge structures? Can you tell me about a reference where they are introduced at least for smooth quasi-projective varieties?

**0**

votes

**1**answer

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### Abelian Variety and Tangent Bundle ----Reference Request

I am looking for the reference where I can find the proof of the following:
If $A$ is an abelian variety then its tangent bundle is trivial.

**1**

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**0**answers

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### What is the MP pseudoinverse's role in statistical learning and Self-Organizing Maps?

During a discussion in our lab last month, a professor mentioned to me that the behavior of Self-Organizing Maps can be described in terms of repeated applications of the Moore-Penrose psuedoinverse, ...

**7**

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**4**answers

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I have studied graduate abstract algebra and would like to learn about Hopf algebras and quantum groups. What book or books would you recommend? Are there other subjects that I should learn first ...

**15**

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**3**answers

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### A reference for geometric class field theory?

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**2**

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**0**answers

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### Elliptic Curves and cryptography. Recommended Reading [closed]

I have been studying RSA cryptography and want to extend this to ECC. I am interested in any books on the topic, that start off with basic principles of elliptic curves as I have almost zero knowledge ...

**22**

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**18**answers

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I'm a student (I've been studying mathematics 4 years at the university) and I like functional analysis and topology, but I only studied 6 credits of functional analysis and 7 in topology (the ...

**15**

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**11**answers

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Walter A. Strauss's Partial Differential Equations: An Introduction is a classic PDE textbook for the undergraduate students. While Folland's Introduction to Partial Differential Equations, is a nice ...

**30**

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**6**answers

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I've been looking high and low for a mathematical Book on String Theory. The only Book I could find was "A Mathematical Introduction to String Theory" by Albeverio, Jost, Paycha and Scarlatti. I only ...

**7**

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**4**answers

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**2**

votes

**0**answers

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### Are there any recommended texts that cover Turing Tilings?

I have read the original paper by Wang, as well as a paper by Boas [1996] entitled 'the Convenience of Tilings', but wanted to know if there were any other texts that people could recommend that ...

**8**

votes

**2**answers

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### good books on Dirichlet's class number formula

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can anyone suggest any good book that gives a complete reference to ...

**5**

votes

**7**answers

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### What is some good introduction to lambda calculus?

I have some background in set theory and automata and I am looking for a good place to start with lambda calculus.

**53**

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**7**answers

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For a student embarking on a study of algebraic topology, requiring a knowledge of basic category theory, with a long-term view toward higher/stable/derived category theory, ...
Is Mac Lane still ...

**4**

votes

**2**answers

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### Reading Material on Couplings

Does anybody have suggestions on what to read to learn more about couplings pertaining to statistics?
I'm working on a research project on Poisson approximations and am looking to perform a coupling ...

**5**

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**2**answers

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### Survey of Algebraic K-Theory Since 1980?

I just came across Charles Weibel's Development of Algebraic K-Theory until 1980, and found it really helpful. Is there been anything analogous which surveys the developments in the last 30 years? ...

**0**

votes

**1**answer

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### Does it make sense that “Representations of groups over finite ring” ?

I am an undergrad student who wants to know about the representation theory over
arbitrary finite fields or finite rings of characteristic p (p a prime). (called modular
representation theory.)
In ...

**16**

votes

**14**answers

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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 ...

**26**

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**3**answers

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### 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

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### 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 ...

**11**

votes

**6**answers

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### 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 ...

**10**

votes

**2**answers

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### 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

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### 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 ...

**43**

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**8**answers

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### 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**

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**4**

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**7**answers

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### probability and math puzzle books/references

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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, ...

**18**

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**21**answers

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### 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, ...

**4**

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**10**answers

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### 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 ...