**4**

votes

**0**answers

91 views

### Reference for the Banach Manifold structure of $C^k(M,N)$

I'm completely new to the subject of banach manifolds and I'm looking for a reference of the following:
Let $M$,$N$ be smooth (=$C^\infty$) finite-dimensional compact manifolds. Consider the set ...

**0**

votes

**2**answers

216 views

### Linear Algebra classic books [closed]

I'm learning linear algebra at the moment, so I'm looking for some great old classic books. Something like Fermat's or Gauss books of some great mathematians.
I don't really like the nowadays books ...

**1**

vote

**0**answers

400 views

### Commutative algebra books representing the edge of research

Recently I have come across the books Combinatorial Commutative Algebra by Miller and Sturmfels along with Combinatorics and Commutative Algebra by Stanley. I will soon own a copy of each. I also ...

**2**

votes

**1**answer

432 views

### Mathematics equivalent of Feynman's Lectures in Physics? [closed]

I'm looking for an equivalent of "Feynman's Lectures in Physics" in mathematics. I'm specifically looking for book/books that delve into, using Feynman's words, "the meaning of things".

**9**

votes

**2**answers

251 views

### Book on the tetrahedron

Does anybody know of a book containing "all you want to know about the tetrahedron"? What you want to know should include basic geometry of the tetrahedron, study of orthocentric tetrahedra, the Monge ...

**2**

votes

**1**answer

206 views

### Open problems books [closed]

As the title might indicate , I would like to look for recommendations for mathematical book that present open problems in depth with commentary.
The only book of this type that I've come across is ...

**5**

votes

**3**answers

382 views

### Introductory texts to mathematics [closed]

I am interested in texts recomendations for a 14 years old boy who wants to study more mathematics than he does at school. He seems quite talented, but his knowledge of maths is rather low. I would ...

**-1**

votes

**4**answers

473 views

### Studying topology: which first, algebraic or differential? [closed]

I have recently studying the basics of topology (ideas in point set, connectedness compactness) and I want to continue my studies but i'm interested in both differential and algebraic topology. which ...

**1**

vote

**2**answers

176 views

### Mathematical statistical qm book-recommendation

I feel that there are quite a few good and rigorous books on the mathematical foundations of quantum mechanics, but I am currently looking for a book that covers mathematical statistical quantum ...

**2**

votes

**3**answers

392 views

### First Explicit Irreducible Representations

Although the classification of simple Lie Algebras and their representations is fully understood, I wonder whether there is some book with exhaustive tables describing explicit irreducible ...

**5**

votes

**2**answers

314 views

### Combinatorial designs textbook recommendation

Good evening, I am currently taking a class which has combinatorial designs as the first topic, we are using Peter Cameron's book Designs, Graphs, Codes and their Links which I am finding extremely ...

**1**

vote

**2**answers

207 views

### Defining Gauss-Kronecker curvature for submanifolds of $\Bbb R^n$ and relation with ${\rm d}{\bf N}_i$'s

I'm trying to find a definition for Gauss-Kronecker curvature of submanifolds of $\Bbb R^n$, but I'm only finding it for hypersurfaces. I would like to know if someone knows any text which works in ...

**1**

vote

**1**answer

227 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 ...

**3**

votes

**1**answer

325 views

### A More Advanced Version of Aluffi's Chapter 0

This is a crosspost of this question from MSE.
Paulo Aluffi's Book, Algebra, Chapter 0 aims to teach basic algebra from a categorical viewpoint. The first chapters of the book, however, introduce ...

**5**

votes

**1**answer

978 views

### textbooks on modern algebraic geometry for 21st-century starters

As for learners in algebraic geometry in 21st century, is there a textbook, lecture note or anything like that to introduce algebraic geometry utilizing the language of derived categories and stacks?
...

**2**

votes

**0**answers

179 views

### Good Pre-Calculus book? [closed]

I was reading this article and the author mentioned I should come here and get some advice. I'm 17, currently taking Pre-Calc in high schooling doing really good, but I feel like I'm not getting the ...

**12**

votes

**5**answers

940 views

### Differential Algebra Book

I'm looking for a couple good textbooks covering differential algebra. I'm a prospective Ph.D. student, and this is potentially applicable to my specialization. As such, I'm not afraid of depth; I've ...

**8**

votes

**2**answers

464 views

### Are there some tables or handbooks of homology and homotopy groups of every manifold which has been calculated?

Are there some tables or handbooks of homology and homotopy groups of every manifold which has been calculated? Or are there some tables or handbooks which list some common calculated results of ...

**0**

votes

**4**answers

454 views

### Which are the recommended books for an introductory study of complex manifolds? [closed]

Are there any good introductory type of books that is focus on complex manifolds?
Thanks.

**17**

votes

**19**answers

5k views

### Math books for advanced high school students

I'm working in a program for teaching a group of students selected in a Olympiad competition. The program is aimed to acquaint the students with the diverse aspects of higher mathematics in a way ...

**4**

votes

**3**answers

474 views

### Textbook request for class field theory [duplicate]

I am studying class field theory. I need good reference books, notes, or other materials which explain the following topics: ideles and ideals, Haar measure and integration on local fields, Fourier ...

**2**

votes

**1**answer

142 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 ...

**3**

votes

**2**answers

448 views

### Textbook for Partial Differential Equations with a viewpoint towards Geometry

I don't know whether I should ask this question here or not but I asked this question on MSE but didn't get any answer so I am posting it here.
Though similar questions have been asked at ...

**0**

votes

**2**answers

233 views

### A book about almost periodic functions [closed]

Can anyone give me suggestions for new books about Besicovitch's almost periodic functions? Thanks a lot.

**5**

votes

**1**answer

479 views

### Serious introduction to the Langlands program for nonspecialist

I recently became interested in the Langlands program and hope to learn more.
For context, I am an analytic number theorist but have some light background in algebraic number theory and modular ...

**5**

votes

**1**answer

270 views

### Where can I find resources for creating a mathematics “bridge course”?

My department is in the very early stages of developing a "bridge course" or "introduction to proofs" course, motivated by our lower-level courses not currently doing a good job of preparing our ...

**1**

vote

**1**answer

178 views

### Which book will discuss torsion tensor and affine connection in detail? [closed]

Which book about differential geometry will have these formula about torsion tensor?
$$\nabla_{j}T^{i}_{kl}+\nabla_{k}T^{i}_{lj}+\nabla_{l}T^{i}_{jk}=R^{i}_{jkl}+R^{i}_{klj}+R^{i}_{ljk}$$
...

**1**

vote

**2**answers

247 views

### Introductory text on Group Cohomology [closed]

What are good introductory textbooks available on Cohomology of Groups?

**8**

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 ...

**5**

votes

**1**answer

330 views

### Learning representation theory of real reductive lie groups

I am interested in any sources that can be helpful for learning the representation theory of real reductive groups.
I am currently reading Wallach book, but I feel that I don't understand the subject ...

**2**

votes

**0**answers

96 views

### Learning resources for Probability Distributions/Models [closed]

I've a good background in basic probability. I need to learn and get a good grip on the probability distributions and stochastic processes, counting processes, and other related topics.
I am already ...

**3**

votes

**3**answers

330 views

### undergraduate handle decomposition. Reference

As the title says, I'm searching for a nice textbook for introducing the theory of handle decomposition of manifolds to undergraduate students.

**7**

votes

**2**answers

508 views

### Ergodic theory and dynamical systems books references

I am arranging a weekly meeting of 2 hours with postgraduate students in ergodic theory (for a period of 3 weeks).
I am asking here for an advice of a book (or maybe a set of papers) to look at ...

**45**

votes

**1**answer

2k views

### Wanted: a “Coq for the working mathematician”

Sorry for a possibly off-topic question -- there are four StackExchange subs each of which could be construed as the proper place for this question, and I've just picked the one I'm most familiar ...

**5**

votes

**4**answers

1k views

### “Introduction to mathematical logic” book from a formalist perspective

I'm looking for books that introduce the reader to mathematical logic assuming the perspective of a formalist.
I've found that many books are more or less written for the platonist - like Kunen's ...

**6**

votes

**1**answer

386 views

### Background to understand Gromov's green book

I have a decent background in differential geometry. I have read John Lee's introduction to smooth manifolds and doCarmo's Riemannian Geometry. I was trying to read Misha Gromov's Metric structures ...

**13**

votes

**6**answers

1k views

### Text for Algebraic Number Theory

I have the privilege of teaching an algebraic number theory course next fall, a rare treat for an algebraic topologist, and have been pondering the choice of text. The students will know some ...

**1**

vote

**6**answers

760 views

### Good books on Geometric Theory of Dynamical Systems

I am looking for a good book on Geometric Theory of Dynamical Systems . I found Geometric Theory of Dynamical Systems by Jr. Palis myself,but it's very old, anyway i would like to find a pure ...

**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

436 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?

**18**

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

470 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

527 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 ...

**6**

votes

**6**answers

697 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

128 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

1k 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

478 views

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

Any recommendations on the best texts for introducing Model Theory?

**1**

vote

**2**answers

412 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 ...