I'm interested in giving The Geometry of Physics a read, and I was wondering what the mathematical and (more importantly) physical prerequisites are.  My background is a bit stronger on the mathematical side, and I'm worried that if heavy (or even moderate) exposure to physics is required that I'll miss out on a lot.  If someone has read it and has a good sense of this sort of thing, I'd very much appreciate the input!  A link to the .
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How and from where does a mathematician learn physics from a mathematical stand point? I am reading the book by Spivak . The first couple of pages of Lecture 1 of the book summarizes what I intend by physics from a mathematical stand point. I wanted to find out what are the other good sources for other branches of physics.
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I'm a PhD student in math and am really excited about celestial mechanics.  I was wondering if anyone could give me a roadmap for learning this subject. The amount of information about it on the internet is overwhelming, and I honestly don't know where I should start.  Any help would be greatly appreciated.
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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 finished Introduction to Manifold by Loring Tu and I am interested to study this book by Milnor. But I didn't take a course in topology (other than the one I learnt from the appendix of Tu's book). Is this sufficient for me to read the book by Milnor?
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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 am looking for a preferably introductory text on Yang-Mills theory with mathematical basis and language. (Differential forms) I have a background in QCD and QED, however, I want to go more in details in geometrical interpretations of Yang-Mills theory. I am sorry if this question has asked before. Thanks in advance.
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It seems that Geometric Complexity Theory requires much knowledge of pure maths such as algebraic geometry, representation theory.   While I am a CS student and do NOT have classes of very abstract and pure mathematics, I am interested in this program.  Is there a list of "minimum knowledge" for learning this theory ?     This list includes lecture notes of CS or math departments, surveys of any journal or conferences, and text books of pure math.  [EDIT: Added later] Thank you for your comments.  General theory of computing: I read Sipser's book with the title "Introduction to the Theory of Computation"  Complexity Theory :In particular, I am interested in concrete models for lower bounds of complexity. Thus I read the part of the "concrete lower bounds" in Arora-Barak's text book. I also have basic knowlede in the several chapers of the communication complexity book written by Nisan.  Basic Mathematics : I have learnt about proof-based linear algebra such as general definition of the vector space etc and precicely argument of calculas based on epsilon-delta argument.   Algebra: I have learned about definition and examples of group, ring, and field. I had a class for cs students, and have not learned about general thoery of this algebraic systems.
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I’m studying a PhD in Theoretical Physics (quantum field theory, to be specific), but I would like to learn more about black holes (and related areas. Does anyone have any suggestions for textbooks/available notes on these subjects for people without much background in them? Obviously I’m very comfortable with mathematics and physics in general so I’m not looking for “pop science” material.
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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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This question has been posted before, but I need book with specific qualifications. I do not need books for engineers, book that is centered around calculations and stuff. I need to find a book that is theoretical, proves the statements and has good presentation of the theoretical structure. I have had the book by Tenenbaum, I did not like it. I would be very very thankful if someone shared their knowledge with us about this matter.
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So, as your usual physics undergrad, I read Griffiths's derivation of the general   uncertainty principle. I understood it but there was no physical intuition given behind it in the book. It was basically a bunch of manipulations and inequalities used to get just the right result.  Other than "It's because of the statistical interpretation." is there a more intuitive reasoning behind uncertainty. Like commutators, behavior of particles, etc.  Thank you for the replies and as always, much obliged.
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Note: I will expand this question with more specific points when I have my own internet connection and more time (we're moving in, so I'm at a friend's house).  This question is broad, involved, and to some degree subjective.  (I started out as a physics-only student, but eventually decided to add a mathematics major. I am greatly interested in mathematics; the typical curriculum required for physics students is not deep or thorough enough; mathematics is more general (that means work!); and it only requires a few more classes. Naturally, I enjoy  immensely.)  This question asks mainly of undergraduate-level study, but feel free to discuss graduate-level study if you like.  Please do not rush your answer or try to be comprehensive. I realize the StackOverflow model rewards quick answers, but I would rather wait for a thoughtful, thorough (on a point) answer than get a fast, cluttered one. (As you probably know,  produces clear, useful writing; and a properly-done comprehensive answer would take more than a reasonable amount of time and effort.) If you think an overview is necessary, that is fine.  For a question this large, I think the best thing to do is focus on a specific area in each answer.    Update: To Sklivvz, Cedric, Noldorin and everyone else: I had to run off before I could finish, but I wanted to say I knew I would regret this; I was cranky and not thinking clearly, mainly from not eating enough during the day. I am sorry for my sharp responses and for not waiting for my reaction to pass. I apologize.  Re: Curricula:   Please note that I am not asking about choosing your own curriculum in college or university. I did not explicitly say that, but several people believed that was my meaning. I will ask more specific questions later, but the main idea is how a physics student should study mathematics (on his or her own, but also by choosing courses if available) to be a competent mathematician with a view to studying physics.  I merely mentioned adding a mathematics major to illustrate my conclusion that physics student need a deeper mathematical grounding than they typically receive.   And now I have to run off again.
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It seems there are a lot of respected physicists appearing on pop-sci programs (discovery channel, science channel, etc.) these days spreading the gospel of   Three examples, quickly: 1) Many programs feature Michio Kaku saying that he is on a quest to find an equation, "perhaps just one inch long," which will "describe the whole universe."  2) Max Tegmark has come out with  in which he expresses the gut feeling that "nothing is off-limits" to science.  The subtitle of this book is My Quest for the Ultimate Nature of Reality.  3) In the series  there is talk about a search for the "God equation."  (A good counter-example would be Feynman, but his self-described "non-axiomatic" or "Babylonian" approach does not seem popular with physicists today.)  Is there any sense among physicists that it might be impossible to articulate the "ultimate nature of reality" in equations and formal logic?  It seems to me that physicists are following in the footsteps of the 19th century mathematicians (led by Hilbert) who were on a similar quest which was put to rest by Gödel's incompleteness theorems in 1931.  Is there any appreciation for how the Incompleteness Theorems might apply to physics?  Has any progress been made on  for the 20th century?  Shouldn't this be addressed before getting all worked up about a "God equation?"
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I am looking for a textbook that treats the subject of Special Relativity from a geometric point of view, i.e. a textbook that introduces the theory right from the start in terms of 4-vectors and Minkowski tensors, instead of the more traditional "beginners" approach. Would anyone have a recommendation for such a textbook ?  I already have decent knowledge of the physics and maths of both SR and GR ( including vector and tensor calculus ), but would like to take a step back and expand and broaden my intuition of the geometry underlying SR, as described by 4-vectors and tensors. What I do not need is another "and here is the formula for time dilation..." type of text, of which there are thousands out there, but something much more geometric and in-depth.  Thanks in advance.
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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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I am in the last year of MSc. and would like to read string theory. I have the Zwiebach Book, but along with it what other advanced book can be followed, which can be a complimentary to Zwiebach. I would like a more mathematically rigorous book or lecture notes along with Zwiebach.   Specifically, mention whether the book discusses string theory   Rigorously? Intuitively?   What's the scope of the book? Does it cover the advanced materials, e.g. Matrix string theory, F-theory, string field theory, etc. Maybe even String Phenomenology?
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I find differential equations in physics to be quite challenging so I'm looking for a book to help me master them.  I'm familiar with solving ordinary differential equations via seperation of variables but haven't really gone much further than that.  I was thinking about buying this:   However I'm open to recommendations on books that are specifically targeted to physics, or will help me in general to solve any differential equation.