Does anyone have any book/problem sets that would go well with Dennery and Krzywicki's ? I like the style of the book compared to usual texts like Riley, Arkfen, or Hobson and Bence, and would really like to study from it. The thing is this book has no problems sets and without doing problems, it's worthless to do a math methods course.   So, any pointers to other books, problem sets from professors, your own stuff would be much appreciated!
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I'm looking for texts on mathematical physics. I've seen various other threads, but the texts recommended in those threads were mathematical methods of theoretical physics texts, that is to say those texts focused on the math methods useful for physicists and assumed the applications of those methods would be covered in some other text. What I'm looking for is a book which introduces some math and then looks at its applications (back and forth) rather than a text which just goes over some math. (Example of books which are NOT what I'm looking for: Mathematics for physicists by Dennery, Math methods for physicists by Weber and Arfken etc)  I've taken courses in multi-variable calc, linear algebra, real analysis, and I'm currently taking a course in abstract algebra. But so far I've only seen applications of multi-variable to physics. I'm looking for books which look at the applications of the other subjects mentioned above to physics, of course books which cover subjects beyond those mentioned are also welcome.   So far I'm liking the flavor of the text "A Course in Modern Mathematical Physics" by Szekeres, but I'd prefer a text which got to the physics side of things more quickly (in the Szekeres text the first eight chapters are strictly on pure math).   After some amazon searching it looks like Theoretical Physics by Joos, Mathematical Physics by Henzel, and Physical Mathematics by Cahill may be good bets?
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Also, I want to make it clear: Beginner.  I'm getting really frustrated trying to study for math competitions:   On the one hand, there are books teaching the high school curriculum, but that's it. I don't need these, I know (almost) everything on your regular high school curriculum. On the other hand, there are books for the IMO. But they assume you have a really strong olympiad mathematics background, and they are only there to prepare you for the IMO. They're basically composed of one or two lines of theory per chapter, and then a huge list of hard exercises and problems. I don't need these either: I'm not even near the IMO calliber, and the solutions to the problem seems to rely on theorems and techniques that aren't taught in high school.   What I am really looking is for a bridge between these two extrema: A book that makes a connection between high school basic math and IMO advanced math.  A book that covers  is what I am trying to find. I've never heard about any of these topics, though they seem to be essential for math competitions. Also, I've never found any book that covers them.   I'm not sure whether a single book will contain such a broad range of topics, so I believe that I'll need a book for Algebra, a book for Number Theory, a book for Combinatorics, etc.   But if that's the case, I also want to make it clear that I'm not looking for a book that teaches you college Algebra, college Number Theory, etc. I want something that covers topics that appear on a math competition, but doesn't assume anything other than high school maths.  Thank you in advance.
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I am almost finishing Gilbert Strang's book "An introduction to linear algebra" (plus video lectures at MIT OCW). First and foremost, I would like to suggest this course for everyone. It has been incredibly illuminating.   I would like to continue studying linear algebra, with particular focus on different properties of matrices and the transition to more general linear spaces (I am a physicist so Hilbert spaces and etc. are of particular interest).   Does anyone have a a good recommendation of books/resources/etc.?
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Can someone give me a recommendation on homological algebra textbooks? I would like something that are accessible to a beginner (i.e., someone who have studied abstract algebra) and that have  1) an account on preadditive, additive, monoidal, abelian, triangulated categories, respectively,  2) motivations from algebraic topology exploited, (an elementary example that comes into my mind is the mapping cylinder/cone construction explained in contrast with Puppe sequence,)   3) an explanation on module theoretic topics like injective / projective resolutions,  4) a coverage of sheaf theory, cohomology of groups, and Galois cohomology.
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I've taken up self-study of math. (How smart can that be?) I've just about finished a course in real analysis which spent a lot of time on metric spaces and some time revisiting calculus.  I was thinking of trying abstract algebra. I would appreciate any book recommendations.  Thanks in advance.  Andrew
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Lately I've gotten a friend of mine interested in mathematics. He has no college-level education to speak of, but is well employed as a software engineer. So I feel he's competent to learn this stuff on his own.  He asked me recently if there was a 'mathematical' version of .  The point being, if there was an "introduction to proofs" book which took a more hand-holding approach. He's also expressed fondness for the .  However, metamath's proofs are obviously a bit too low level to learn anything serious.  At one point in our conversation, I mentioned the dependently typed programming language , but I felt it's not quite as helpful until he at least gets some experience with  (for which the target audience of Agda is Haskell programmers, hence the similarity in syntax).  Anyone have any good suggestions on a book?
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I'm looking for a Machine Learning course that would give the maths behind algorithms rather than simply teach how to apply them. I've looked at Udacity Into to Machine Learning and Andrew Ng's course on Coursera, and they both seem too applied to me. Any recommendations of textbooks would also be much appreciated.
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I'm a looking for a good book to self-study differential forms. Particularly, I'm looking for a book that is as similar as possible to Bert Mendelson's "Introduction to topology" (i.e. a book that procede by  following a: "Definition, theorem, proof" style). In addition, the book that I'm looking for should be as much self consistent as possibile. I'm a first year graduate student in nuclear engineering. My prerequisites are a good understanding of (multivariate and vector) calculus,  linear algebra, and a little of functional analysis, Lebesgue integration theory, PDE. I know nothing about differential geometry, but to my (very) poor understanding  differential forms and concept like manifolds and so on are linked to each other.
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What kind of recommendations do you have for a very good source to learn Galois Theory? Is there any Atiyah-MacDonald-type book on Galois theory? What is your opinion on the chapters from Lang, and Dummit and Foote?
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Edit:  Ok, user  made comment that truly helps narrow the focus of my question. Basically, I'm asking for a self-study course of Mathematical Methods.  Thanks to his recommendation I identified a book that is very close to the answer:  Mathematical Methods in the Physical Sciences by Mary L. Boas  Supposedly, the book covers most of the Math a person needs to learn in order to understand the simulations I presented.  Does this book suit my needs?    Hello,  I have always been interested on the idea to study Math at an Undergraduate level to be able to implement simulations like the followings:  Finite Difference Simulation of the Wave Equation    Heat Equation in Two Dimensions    Besides my precollege experience in Math, I have only been able to do very simple simulations due to my lack of knowledge of Advanced Math. Every time I ask about the inner workings of the simulations I get redirected to papers that look like foreign language to me and, unfortunately, I depend on easy-to-read tutorials to understand them, and while I have found   I'm more interested in reaching the solution myself.  I checked some of the questions related to book recommendations for self-study and while they are very helpful I'm interested in learning by example (There is a book called: "Accelerated C++ Practical Programming by Example" that fits very well my study habits)  Thanks in advance.
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I read single variable calculus this semester, and the course is using Thomas Calculus as the textbook. But this book is just too huge, a single chapter contains 100 exercise questions! Now I'm looking for a concise and complete textbook. I'm not interested in routine, computational exercises, but rather some challenging problem sets.  I have quite a strong basic knowledge of calculus from high school, but I still have difficulties in solving a few questions from past exam papers. So I'm looking for more challenging exercises. In fact, I'm looking forward to solving Putnam level questions.  Please suggest some textbooks with these features. Thanks in advance.
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What would be a good book to learn basic number theory? If possible a book which also has a collection of practice problems? Thanks.
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My goal is to pick up some commutative algebra, ultimately in order to be able to understand algebraic geometry texts like Hartshorne's. Three popular texts are Atiyah-Macdonald, Matsumura (Commutative Ring Theory), and Eisenbud. There are also other books by Reid, Kemper, Sharp, etc. Can someone outline the differences between these texts, their relative strengths, and their intended audiences?   I am not listing my own background and strengths, on purpose, (a) so that the answers may be helpful to others, and (b) I might be wrong about myself, and I want to hear more general opinions than what might suite my narrow profile (e.g. If I said "I only like short books", then I might preclude useful answers about Eisenbud, etc.).
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What is a good PDE book suitable for self study?   I'm looking for a book that doesn't require much prerequisite knowledge beyond undergraduate-level analysis.  My goal is to understand basic solutions techniques as well as some basic theory.
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I was wondering if you could tell me about some self-learning resources for linear model theories. My professor has been using "A First Course in Linear Model Theory, Ravishanker and Dey. Publisher: CRC." I found this kinda difficult. My major is mathematics. Thank you so much for your time!
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What are some of the best books on graph theory, particularly directed towards an upper division undergraduate student who has taken most the standard undergraduate courses? I'm learning graph theory as part of a combinatorics course, and would like to look deeper into it on my own. Thank you.
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I am in search of a good book for learning Stochastic Calculus from a purely mathematical/statistical point of view. Almost all the books I see are based on Finance. Also, please specify the pre-requisites for this course.  Actually, I am quite knowledgable in Measure Theory, Markov Chains and Martingale Theory. I believe this knowledge should suffice.  I am planning to self-study this subject. Please suggest me good books.  Thank you.