I am looking for a good introductory book about Group Theory for physicists.
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I am looking for a good source on group theory aimed at physicists. I'd prefer one with a good general introduction to group theory, not just focusing on Lie groups or crystal groups but one that covers "all" the basics, and then, in addition, talks about the specific subjects of group theory relevant to physicists, i.e. also some stuff on representations etc.  Is Wigner's text a good way to start? I guess it's a "classic", but I fear that its notation might be a bit outdated?
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I'm a mathematician. I have good knowledge of superior analysis, distribution theory, Hilbert spaces, Sobolev spaces, and applications to PDE theory. I also have good knowledge of differential geometry. I would like to study the Semiclassic Analysis, but perhaps I must first study the foundations of quantum mechanics. So I would like to know what book you recommend me to begin studying quantum mechanics. I'm primarily interested in a mathematical point of view. I have seen some books of this type, but I would like to have some other opinion.  Thanks for every reply
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I am from mathematical background, and I always hated the way they teach elementary probability theory in schools without giving any clue about measure theory.   I want a theoretical book in probability theory, which starts with measure theory and defines everything in mathematical terms. I am also not looking for a measure  theory book. If there is such a book that instead of giving only an intuitive introduction to probability theory, it rather defines everything in details, I would be really grateful to know it.  I would be happy to hear about any reading experience. Being exact in mathematical  language and maybe exercises.  Thanks a lot.
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I have background in category theory and I am familiar with the very basics of algebraic geometry - Chapters I and II of Hartshorne. What would be a recommended (self-contained, maybe?) text for learning about Grothendieck's Galois theory ?
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Can someone recommend a good basic book on Geometry?  Let me be more specific on what I am looking for.  I'd like a book that starts with Euclid's definitions and postulates and goes on from there to prove thereoms about triangles, circles and other plane shapes.  I'm not interested (at this time) in a book that ties geometry in with linear algebra or explains non-euclidean geometry.  All the books I've seen seem to be of two types 1) Let us use linear algebra and other techniques to put geometry on a firm footing. Let us assume you already know Eucliean geometry and move on to more interesting stuff. These are probably too advanced for me. 2) Let us skip all that complicated postulates/proofs and make geometry fun.  Too easy.  When I was in 9th grade Honors Geometry way back in 1981/82 we had a textbook that, as I recall through my foggy memory, was very good and did systematically build up geometry from the propositions (5 of them?).  And it certainly didn't attempt to address Hilbert's contributions to geometry or explain non-Euclidean geometry. Unfortunately, I don't recall the title or author.  I suspect the book was used nationally though and for quite a number of years, so perhaps someone with a better memory than me can provide a title/author.  I do recall it had all the postulates and most major thereoms listed at the end of the book.  My motivation is two fold... 1.  Review the material myself in preparation for my advanced texts. 2.  Help my children in a few years when they take geometry.    Books I could get for the iPad/Kindle or free books (Google?) would be most appreciatied, but I'm not opposed to killing a tree either :) Thanks for all the help. Dave
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I studied basic field theory from J.A. Gallian in U.G. and Fraleigh. and a year ago I self studied it from Galois Theory by David A. Cox, and I got pretty good at it. But in last year I was mainly studying groups and non-commutative ring theory, so now I feel like I have lost my sharpness in Field theory and now I want to reread whole Galois field theory. But doing Cox again will feel boring so I was thinking to switch to a  new book. After googling a lot I have shortlisted these small and interesting book-  1) Fields and Galois theory by Howie 2) Galois Theory by Rotman 3) Field and Galois theory by Morandi 4) Galois Theory by Escofier  Which one of these texts is most interesting and insighting? Which one should I buy first, e copies of all of them looked great, but which one I should purchase and read first.  If there are any other suggestions, you are welcome!
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What are some of the best books on Representation theory for a beginner? I would prefer a book which gives motivation behind definitions and theory.
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What are some good books for learning general relativity?
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I'm interested in quantum mechanics book that uses high level mathematics (not only the usual functional analysis and the theory of generalised functions but the theory of pseudodifferential operators etc, certainly the modern mathematics). If there isn't something similar please give me a reference to the book that is strictly supported by mathematics (given a set of mathematically descripted axioms author develops the theory using mathematics as a main tool).
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Is there any good book on Electromagnetism from a more mathematical point of view? By this I mean a book which makes use of differential forms and maybe De Rham cohomology. I was also searching for something that would include E&amp;M in the big picture of Gauge theories.
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Can anyone recommend me some nice books about ? I'm looking for complete references.
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Does anyone have any suggestions for abstract algebra books particularly suited to self-study?     Here is some background and motivation, if it's helpful.  I'm currently a junior in high school, but I have some familiarity with groups, rings, polynomials and fields, as I went through Fraleigh's book. I liked its writing style, but many of the problems were not helpful. I would like to get better at algebra with some other book, particularly one that's aimed at someone who already has a little familiarity with the objects, but is by no means completely comfortable.  One of my longer-term goals is to learn a bit of algebraic number theory, as I've only been studying elementary number theory. That's why I feel it  good to learn more algebra first. (I'd also be interested in suggestions of other good subjects to learn prior to tackling algebraic number theory.)  I was considering using one of Lang's books, since they seem pretty universal, but I've heard rumors that they are very terse and not good for self-learning.
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I am taking abstract algebra in this semester. I find that my lecturer didn't provide enough examples for understanding. So I would like to ask what are the recommended books which has lots of solved problems and exercises? The lecturer said in this semester, he will cover group theory, ring theory and a bit of field theory. Which book contains extensive information in these three fields?
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I'm looking for a textbook or set of lecture notes on gauge theory for mathematicians that assumes only minimal background in physics. I'd prefer a text that uses more sophisticated mathematical concepts like principal bundles and connections, and categorical language whenever convenient.
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I have recently been reading Intro to Lie algebras and representation theory by Humphreys, and when I am finished I am interested in reading about Lie groups and Lie algebras and their applications to particle physics.     Is there a book that assumes basic knowledge of Lie algebras, and no knowledge of lie groups and particle physics/quantum mechanics?   I have seen Howard Georgi's book, but it assumes good knowledge of particle physics.   In addition, I do not know differential geometry.
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I just started to learn mathematical logic. I'm a graduate student. I need a book with relatively more examples. Any recommendation?
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I'm interested in learning about the basics of group theory. My background is in statistics so I have barely any knowledge about group theory. I've had some work with proofs and I have also taken classes at university such as multivariable calculus, linear algebra, and differential equations. Any beginner resource would be helpful but nothing too technical.