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Results tagged with textbook-recommendation
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user 3106
Questions asking for recommendations of textbooks on some subject. It can be helpful to indicate whether the request is for self-study, for use in a course one teaches, for use accompanying a course one takes etc., and to give some additional details on the context. Typically, additional tags are used to indicate the subject. For other questions on books, please use the tag books. Also, see reference-request for a related tag.
38
votes
Are there textbooks on logic where the references to set theory appear only after the constr...
There's a fundamental difficulty with your claim that
a mathematician can't use a term before giving its accurate definition.
Mathematical definitions are always in terms of things that are alre …
- 82.7k
21
votes
Accepted
Suggestions for good books on class field theory
When you are first learning class field theory, it helps to start by getting some idea of what the fuss is about. I am not sure if you have already gotten past this stage, but if not, I recommend B. …
18
votes
Good "casual" advanced math books
Based on your first paragraph, I would highly recommend the series What's Happening in the Mathematical Sciences. These provide excellent summaries of a wide variety of cutting-edge mathematics topic …
15
votes
Roadmap to learning the classification of finite simple groups
A natural place to start would be Volume 1 of the so-called GLS project.
Daniel Gorenstein, Richard Lyons, and Ronald Solomon, The Classification of the Finite Simple Groups, Mathematical Surveys and …
- 82.7k
13
votes
Problems in advanced calculus
Section 3.3 of Putnam and Beyond by Răzvan Gelca and Titu Andreescu (Springer, 2007) is entitled "Multivariable Differential and Integral Calculus" and has a number of interesting, non-routine problem …
13
votes
Accepted
Lang's "Algebra" as a self-study book
In my opinion, Lang's Algebra has an excellent choice of topics for someone who wants to do further work in algebraic number theory or algebraic geometry. I'm not sure whether I'd recommend it for sel …
10
votes
Exposition of Grothendieck's mathematics
For topic 4 (schemes), I'd suggest Schemes: The Language of Algebraic Geometry, by Eisenbud and Harris. This book is out of print, and is generally regarded as having been "superseded" by its success …
7
votes
"Introduction to mathematical logic" book from a formalist perspective
I'd like to elaborate a bit on the suggestion, mentioned by some others, that your complaint is not really about platonism versus formalism, but about the common practice of being not completely clear …
6
votes
Canon in algebraic combinatorics and how to study
I would suggest that much of what I said in my answer to another MO question applies here, in spades. To a first approximation, the canon is the empty set. Start with a problem, and learn what you nee …
- 82.7k
6
votes
Recommendation for learning mathematical statistics and probability
You might want to spend some time reading about the philosophy of probability. One book you might try is Philosophical Theories of Probability by Donald Gillies, which lays out many different philoso …
- 82.7k
5
votes
Looking for a mathematically rigorous introduction to game theory
Daniel Litt's suggestion of Fudenberg and Tirole is a good one. Another standard text that takes a mathematically rigorous approach is Game Theory: Analysis of Conflict by Roger Myerson.
4
votes
A book about model theory
Based on our discussions in your other MO question, I believe that what you want to see is not a book about model theory, but a tutorial about how to formalize ordinary mathematics in ZFC, with model …
4
votes
Accepted
Intuitive explanations of the Carlitz-Scoville-Vaughan theorem
This is more of an extended comment than an answer, but maybe you will find it helpful. I agree with Sam Hopkins that it is fruitful to think of the Carlitz–Scoville–Vaughan (CSV) theorem as a combin …
- 82.7k
2
votes
Good introductory text book on Matroid Theory?
I agree that Tony Huynh's suggestions of Oxley and Welsh are good ones. Depending on what you mean by "suited to engineers," another option might be Lawler's Combinatorial Optimization: Networks and …
- 82.7k