Forgot your password?
Math Books Media Science

Book Recommendations For Maths To Astrophysics? 276

Posted by kdawson
from the take-a-left-at-newton dept.
sexy_flying_yoda writes "I have just graduated from 3 years doing a BSc in Mathematics in the UK and will be beginning an MSc in Astrophysics and Astronomy in September. I have very limited knowledge in physics, and as my new course of study is basically physics, I'm currently searching for books that will enable me to get up to speed. What books would you recommend that would help a mathematics graduate convert to a physicist?"
This discussion has been archived. No new comments can be posted.

Book Recommendations For Maths To Astrophysics?

Comments Filter:
  • by Anonymous Coward on Sunday July 13, 2008 @05:32AM (#24170983)

    I can heartily recommend "The road to reality" by Roger Penrose, there'll be a lot of stuff that's old-news to a math major, but it's essentially an undergraduate course in mathematical-physics for the lay-reader (of course this normally means scientist from another discipline :-)

    Best of luck!

    • Re: (Score:2, Interesting)

      by efagerho (579859)
      I would assume that what he wants is a physics textbook that assumes that you're very fluent in math (not a book about handwaving), thus making the presentation a lot more dense, thus faster... I'm myself a Ph.D. student in math and I've tried to find such a book myself. It's very booring to read physics books that really do calculations the hard way (e.g. use pages to do something with matrices that directly follows from a theorem concerning linear operators etc.). Unfortunately, I don't think such books
    • by rasputin465 (1032646) on Sunday July 13, 2008 @11:22AM (#24172653)
      I imagine that if he's going into astrophysics, he's probably already familiar with the typical pop-sci material or at least the content.

      No, you will need more technical know-how and fundamentals if you wish to compete in a graduate level program. Here's a list of textbooks that would cover the basics at a bachelor's level. I imagine all of these would be at your University library, and are certainly available on amazon. And IAAP.

      Quantum mechanics: R. Shankar, "Principals of Quantum Mechanics" (the first few chapters should give you a basic foundation of the theory).

      Electricity and Magnetism: D. Griffiths, "Introduction to Electrodynamics"

      Thermo/statmech: C. Kittel & H. Kroemer, "Thermal Physics"

      Particle Physics: D. Griffiths, "Introduction to Elementary Particles" (this covers a little bit of quantum field theory too)

      Statistics: G. Cowan, "Statistical Data Analysis" (as a mathematics major, you might already know the content, but the formalism as used in physics is important to learn).

      Classical Mechanics: S. Thornton & J. Marion, "Classical Dynamics of Particles and Systems".

      Different people mean different things when they say "astrophysics", but if you're doing this with heavy emphasis on Astronomy, then you would be better off focusing more on the classical mechanics and statmech than on quantum mechanics and particle physics.
      • by Beetle B. (516615) <{moc.liame} {ta} {b_elteeb}> on Sunday July 13, 2008 @12:29PM (#24173149)

        Quantum mechanics: R. Shankar, "Principals of Quantum Mechanics" (the first few chapters should give you a basic foundation of the theory).

        In my undergrad, a physics professor told me, "There's no particularly good book on QM". I thought he was being pedantic, but years later I found out he was actually correct. Every book has some serious deficiency (serious if that's the only book you learned it from). I've read only the first few chapters of Shankar, and they're quite decent - I liked them. I tried reading some of the stuff later in the book and didn't feel he did justice to them (either too brief on the topic or hand-waving). Another problem with Shankar is that it doesn't really challenge the reader.

        I can't exactly recommend a QM book, as I learned it from my professor's lecture notes - which were awesome. But from memory, he consulted a bunch when he wrote them. They included the books by Messiah, Davydov, Landau & Lifshitz, Baym.

        At the undergrad level (in case you did not learn it during your BSc), two common books are the ones by Griffith and Liboff. Again, both have weaknesses but they do complement one another well.

        Electricity and Magnetism: D. Griffiths, "Introduction to Electrodynamics"

        Best undergrad book on the topic ever. Well worth reading for its insights even if you think you know E&M very well.

        In the US, at the grad level the standard is the book by Jackson. I hear in some countries they sometimes use that in the final year of undergrad. It's a standard and a must if your program requires you to know EM.

        In general, people speak very highly of the series by Landau & Lifshitz. Might want to keep them as references and read them at some point.

        • Re: (Score:3, Informative)

          by BitterOak (537666)

          In my undergrad, a physics professor told me, "There's no particularly good book on QM".

          I've heard the same thing, and used to think so too, but one book I discovered which I really like is Modern Quantum Mechanics by Sakurai. It is a modern, and reasonably complete treatment which I like.

          I second the vote for Jackson's Classical Electrodynamics. I used it in my last undergrad year, and it is very good. In order to do the problems, you really need a solid background in solving PDEs, but with a math undergrad degree, you've likely already had a course in that subject.

          For Classical Mechanics

        • by mazarin5 (309432)

          I would like to add to that list "An Introduction to Modern Astrophysics" by Carroll and Ostlie. It's a very comprehensive book. Whenever I can't recall something, or need clarification, it's always the first book I grab. There's almost never a need to go to my second choice, Shu's "The Physical Universe" which covers a lot of odds and ends, but is a fantastic resource for anybody learning the basics of astrophysics. It spends several chapters covering the relevant portions of thermodynamics, E&M, QM, a

      • Penrose's "Road to Reality" is quite a bit more than Pop-Sci. I bought it a few months ago as a refresher. It has been 25 years since I got my degree and while I have kept up with the news it has been quite a while since I "practiced".

        I'd also recommend "High Energy Astrophysics" V1 and V2 by Longair. Fascinating stuff in there.

        Finally, set up a good newsreader and spend some time on the sci.astro and sci.physics newsgroups. If you can't get an education there, at least you will get some more suggestions fr

      • Re: (Score:3, Interesting)

        by ClassMyAss (976281)
        While I mostly agree with you, I'd still suggest picking up "The Road To Reality," as it's a truly fun read, if for no other reason than that Penrose is just a little bit nuts - he's got to be the first person ever to manage to get a "layman's" (i.e. it shows up at Barnes and Noble) book to include detailed calculations involving tensor calculus... Beyond that, though, he really looks at everything in a different light, and in a very non-standard order, so I think it's 100% worthwhile. The 1000 page thing
        • Re: (Score:3, Informative)

          by ClassMyAss (976281)
          Oh, I forgot - I wanted to comment on the rest of those books and add a couple.

          Re: Griffiths books - they are both really good as intros to these topics (both are amongst my favorite "pleasure" reading physics books), but in the field they are often considered too elementary to be "serious," for better or worse. It's not that they are wrong, just that they are a little too user-friendly, which to me is a good thing.

          If you can manage to wade through the extreme density that is that Shankar book, that
      • Although I can give a wholehearted recommendation for the Griffiths and Kittel books (and have heard good things about the Shankar QM book), I had some *serious* qualms about Thornton/Marion's Classical Dynamics book.

        Attempting to work my way through their reasoning, proofs, and explanations was an exercise in frustration and futility. Some important sections were barely described at all, while other trivial topics were covered to death. The texts by Goldstein and Landau/Lifshitz are both vastly better, e

    • by b4upoo (166390)

      I suspect that in the world of modern physics there is plenty of room for people who concentrate on an almost exclusively mathematical approach. Let others conjure up the suppositions and apply mathematics in the search for proofs.

  • by jimmydevice (699057) on Sunday July 13, 2008 @05:39AM (#24171015)
    "Well, with one degree in maths and another in astrophysics, it was either that or back to the dole queue on Monday" DNA
  • Feynman Lectures (Score:5, Informative)

    by Rudisaurus (675580) on Sunday July 13, 2008 @05:40AM (#24171023)
    Try "The Feynman Lectures on Physics", Vol.s I - III. I've never encountered a better reasonably high-level introduction to the topic, and they're eminently readable. Here's [] a site devoted to them.
    • Re: (Score:2, Informative)

      by cjmilne (38848)

      I second this. As far as a general intro to Physics these are by far the best set you can get. Here's the amazon link []. There are audio copies [] of the lectures as well.

      One caveat, many Physics & Astrophysics/Astronomy Departments are separated & have little overlap so take a careful look at your MSc course curriculum before leaping to the conclusion that you need to learn large amounts of general physics.


      • Re: (Score:3, Informative)

        by pallmall1 (882819)
        For a solid mathematical background (and a price that won't force your bank account to violate the second law of thermodynamics), try Fundamentals of Physics [] by Halliday, Resnick, and Walker. Excellent mathematical descriptions, but short on the kind of insight you can find in Feynman's work. A used, earlier edition costs very little and would be good reference for a person with a degree in mathematics.
    • Ooooh, forgot about those. But do get the audiobooks (with course notes) also.
    • by gTsiros (205624)

      came here to say the exact same thing.
      (yes, i am a physicist... just not have completed my studies yet :( )

    • Re: (Score:3, Informative)

      by massivefoot (922746)
      The Feynman lectures are good, and are pretty good at getting you to think about the physics, but are aimed at first year undergrads. I've just completed a BA in maths and I find them interesting, but a little easy.

      I'd suggest just googling for course notes for the relevant topics. I'm assuming your vector calculus is already good. Other than that you need to know:
      Basic QM
      Probably some fluid dynamics
      Special and general relativity
      Statistical physics / thermodynamics
      Some programming experience might a
      • by ChowRiit (939581)

        Some programming experience might also help, Fortran is still in quite common use in physics and is easy to learn.

        C/C++ is generally better than Fortran these days for physics, as it seems to have overtaken Fortran as the most used langauge, although I'm finding myself having to learn Python for my astrophysics.

        • Not sure which would be better (fortran lets you get away with things that C doesn't, I find I get more runtime bugs), but certainly fortran is still in wide use. I believe that up until last year all Cambridge physics undergrads were still being taught it.
    • by ChowRiit (939581)

      The Feynman Lectures aren't nearly as relevant as one might think, for an astrophysicist. They'd be brilliant if he wanted to do a general physics degree, but there are far better specialist texts which don't require all the pain of quantum.

      They're well worth reading, of course, but Carroll and Ostlie is the better read for the course he wants to do.

      • > They'd be brilliant if he wanted to do a general physics degree, but there are far
        > better specialist texts which don't require all the pain of quantum.

        It's first year general physics. I can't believe that a astrophysicist wouldn't benefit from it. I'm surprised that his astrophysics program doesn't require at least first year physics as a prerequisite.

      • The Feynman Lectures aren't nearly as relevant as one might think, for an astrophysicist. They'd be brilliant if he wanted to do a general physics degree, but there are far better specialist texts which don't require all the pain of quantum.

        For a math major, QM should be a cakewalk. However, nobody should be learning QM from Feynman's lectures, there are far better texts to use for that (Shankar comes to mind, Griffiths if Shankar is too hard, Bohm if you want to be totally weird and pervert your brain).

    • Last time I checked these were the Freshmen text on the subject at Caltech

    • At risk of self-deprecation, I find Feynmann's lectures to be far too brief to gain a sufficient understanding of the subject, and that the lectures would almost immediately dive off into a fairly advanced treatment of the material, and provided few if any examples.

      If you're looking for an introduction to the subject, I can't say that I give them the same sort of recommendations as others are giving here. They're certainly not horrible, but they also take a very different approach to the material than most

    • Agreed about the Feynman Lectures. Halliday and Resnick are ok as well. It's not widely available, but my favorite text book of all time is Thomas M. Helliwell's "Introduction to Special Relativity". Its the only textbook I've ever read cover to cover. The sample problems are great fun, frequently involving a rhinoceros traveling at 0.99c (where c is the speed of light in a vacuum). He also has an excellent two volume introduction to mechanics, but its much harder to find. It basically only exists as
  • Intro Astrophysics (Score:3, Informative)

    by RadicalRhinoceros (1145781) on Sunday July 13, 2008 @05:41AM (#24171027)
    I'm not sure about recommending the intro physics book I had, but as far as intro astrophysics, there's no better than Carroll and Ostlie
    • Re: (Score:3, Informative)

      by ChowRiit (939581)

      Thirded. A lot of people are recommending pop-physics books which are fine for an odd read, but are useless for actually gaining an in-depth knowledge of physics. Carroll and Ostlie is the standard catch-all general reference textbook all the Astrophysics lecturers at my (English) University tend to recommend. I find it very good as a reference text for odd topics I have little knowledge of, but it shouldn't assume too much prior knowledge you don't have - the maths is the important thing to have covered se

  • What books would you recommend that would help a mathematics graduate convert to a physicist?

    The Tao of Physics []
    The Dancing Wu Li Masters []
    To get you thinking the right way, then, for a new classic, try:

    The Road to Reality []
    For some seriously heavy slogging.

    • by gilroy (155262)

      The Tao of Physics
      The Dancing Wu Li Masters

      Guh. I know I'll engender flamage but I found these two books to be little more than dreck. It's been a long while since I read them but at my recollection, there was essentially zero useful science in them. It was a lot of "oh, isn't that coincidence MEANINGFUL...?"

      • Re: (Score:3, Interesting)

        by $RANDOMLUSER (804576)
        I'm afraid I'm old enough to have read both of them when they were first published, which probably colors my view. While I'll admit that neither of them contains any "useful" (i.e: applicable) science per se, I have to say that they were both "mind expanding"/"eye opening" regarding physics.

        Tao taught me that where there was nothing (literally no thing), there could suddenly be a few particles which would almost instantaneously annihilate themselves, to leave "no thing" behind. The notion of the quantum
        • by John Allsup (987)

          Generally being aware of other directions of thought will, I expect, become more and more important in future -- current directions are getting heavily worked out and it's important to be aware of what might have been missed by the mainstream. Also, a popular science book can be read much more quickly than a serious textbook, so a one-to-one comparison is inappropriate -- read popular stuff for casual-but-enlightening bedtime reading and the more serious textbooks when you're at your best.

  • []

    Coincidentally, I started reading it last night, so a review will have to wait weeks/months(/years?)

  • by Ibag (101144) on Sunday July 13, 2008 @05:56AM (#24171085)

    I recommend "Mathematical Methods of Classical Mechanics" by V.I. Arnold for the classical mechanics side of things. I am not sure what to read for general relativity. The bit that I know I learned from "Semi-Riemannian Geometry" by Barret O'neil, but I don't feel that the book is a good place to learn general relativity unless you already have a very strong background in differential geometry. I hope this helps.

    • Re: (Score:3, Informative)

      by azaris (699901)

      I recommend "Mathematical Methods of Classical Mechanics" by V.I. Arnold

      Seconded, but make sure you have another textbook in mechanics handy for the inevitability that you get confused by Arnold's presentation. Goldstein is probably a good choice.

  • the classic Feynman (Score:3, Informative)

    by e**(i pi)-1 (462311) on Sunday July 13, 2008 @06:01AM (#24171109) Homepage Journal
  • Recommended topics (Score:4, Informative)

    by Anonymous Coward on Sunday July 13, 2008 @06:10AM (#24171161)

    Most astronomy degrees are basically physics degrees with the addition of astronomy classes and without the 400 level physics courses. If you wish to prepare yourself for astrophysics I recommend the following topics:

    1) Classical Electrodynamics (you need to know Maxwell's equations backwards and forwards--this usually takes a year at the undergraduate junior physics level). You need to be able to solve line integrals and surface integrals without blinking an eye.
    2) Mathematical physics. Unless you have an applied math degree or focus, your math education isn't going to be a great help here. Courses in this area would include complex analysis, partial differential equations (that's graduate level physics baby!), and a shitload of knowledge knowing how to work with Fourier transforms, Laplace transforms, and series solutions to ordinary and partial differential equations. Your BSc in mathematics should cover up the other odds and ends (a little group theory, eigenvectors, eigenfunctions, Hilbert spaces, etc.)
    3) Mechanics at the junior level. You need to know mainly how Hamiltonians and Lagrangian operators work. This is not the same thing as introductory mechanics or a statics and dynamics class. The important things you care are about energy functions, potential functions, and conserved quantities.
    4) Quantum mechanics. You will probably get a lot of help at the graduate level here as most schools don't expect astronomy majors to have a lot of knowledge in this topic. Just make sure you know what the postulates of quantum mechanics are and some of the basic concepts (like state vectors, the Schrödinger equation, and Dirac notation). If possible, learn how the Hamiltonian and Lagrangian operators work in quantum mechanics.

    The minimum of all of this that you should learn is the mathematical physics and classical electrodynamics portions. This entire list assumes that you have the 'basic' physics prerequisites for these courses as well.

    • Re: (Score:3, Informative)

      by phobos13013 (813040)
      For number 4), probably your best choice is Steven Weinberg's books: The Quantum Theory of Fields []. It is a three volume set, and can be pretty pricey, but its a gold standard for sure. Many of the studies of Cosmology and Astrophysics are these days bound with QED and QM because quite often you are looking for undiscovered particles hanging out in space. Beyond that, the mathematical systems that explain quanta of fields for instance obviously extrapolate to vast expanses by way of symmetry! Get this bo
  • by strelitsa (724743) * on Sunday July 13, 2008 @06:14AM (#24171175) Journal
    I've audited several of MIT's OpenCourseWare offerings in Physics. Some are ridiculously easy while others have thrashed my intellectual behind back and forth across the Internet. And the best part? They're free. [] []
  • by laughing_badger (628416) on Sunday July 13, 2008 @06:20AM (#24171209) Homepage
    I'll second those people recommending Feynman [] - great series of books.

    Physics to a degree [] will get you thinking like a physicist - it covers most undergraduate topics in physics with tutorial style questions and answers.

    I found Introduction to Modern Astrophysics [] an interesting read after I graduated. It covered most of the stuff we did at Birmingham and did so very well.

    Our introductory book was Introductory Astronomy and Astrophysics by Michael Zeilik, which was ok, and then Astrophysics: Stars Vol 1 by Richard Bowers and Terry Deeming, which was very good and Vol 2 similarly.

    You don't mention what your course is going to cover or what its aim is - you are not going to cover the whole of astrophysics in 9 taught months. You also don't mention your interest in astrophysics - numerical simulation? So it is difficult to come up with any more specific recommendations.

    Good luck anyhow. Post below with more info if you want any more detailed recommendations.

  • "What I tell you three times is true." I'm saying it once but two others already have.

    Feynman's "Lectures" + "Tips"

    If you want an expert's opinion, ask the chancellor of John Moore's University in Liverpool. He's an astrophysicist, as well as a member of the Luxuriant Flowing Hair Club For Scientists, which counts for naught save as an indicator of a sense of humor and thus probably approachability. And he's a bit of a musician so I hear. He has a web site with a contact link: []

  • by mako1138 (837520) on Sunday July 13, 2008 @06:21AM (#24171221)

    You're going to be getting into grad-level physics books, like Goldstein (Mechanics), Jackson (Electrodynamics), and Sakurai (QM). They are not really the best places to start your physics education. As you have a math background, the math will not be so much of a problem. Rather, you lack familiarity with physics concepts. What you need is the equivalent of an undergraduate physics education. You can probably skim the Feynman Lectures for the rest of the summer and come out OK. Work through physics problems. Lots of them.

    Popsci books are good too, for getting the big picture.

  • Learning about the basic theories on how galaxies form is going to be underlying a lot of your work if you would like to more than dabble in cosmology. I found this book [] rather useful.
  • by 16384 (21672) on Sunday July 13, 2008 @06:38AM (#24171293)

    The suggestions from other posters about science books for the general public won't help you much. You need to learn the basic physics, such as mechanics, thermodynamics and electromagnetism. Thankfully there are good books that teach all of these areas at a basic level, and you'll be able to go through them quickly.

    Although in a different way, I also changed from math to physics. One thing you should know is that physicists use math as a tool, and don't worry about convergences, approximations, etc. Prepare to be shocked with all the approximations made: Physicists keep expanding stuff in Taylor series and keeping only 1 or 2 terms, without worrying about what they left out, treat differentials basically as numbers, use distribution functions intuitively, without a proper theoretical support, say a differential equation is "solved" when they find one solution that matches what they need, etc.

    I would recommend the introductory physics books by Paul A. Tipler, because they cover the whole physics you need to get up to speed, and are simple.

    Another similar book is "Fundamentals of Physics" by Halliday and Resnick.

    These two books / books series are simple, written for the beggining physics undergrad. I think they are what you need. However, if you are very good at math, and want grad student level physics books, the series "Course of Theoretical Physics" by Landau and Lifshitz is suberb. They are very advanced though.

    After you master the books at the level of Tipler and/or Halliday and Resnick, you should move on to individual books about the various areas, such as mechanics, electromagnetism and thermodynamics.

    "The Feynman lectures on physics" are a classic, and almost required reading for wanting to be a physicist, however they won't teach you much actual day to day physics. It was written to be a physics course, but to me it is more of an inspirational book than a manual, so you can always read these latter.

  • Landau & Lifshitz (Score:2, Informative)

    by RedOctober (10155)

    I wanted to recommend Feynman's lectures also, but it seems many others have done so already. Also Penrose's "Road to Reality", already mentioned.

    What people haven't mentioned are Landau & Lifshitz's series of books, "Course on Theoretical Physics". This is stuff to read AFTER you have got through Feynman, and find his lectures too elementary. Landau is more demanding, but it will be a LONG while before you can finish reading his works.

    • Re: (Score:2, Informative)

      by bierik (575138)
      The Landau & Lifshitz books are quite advanced but absolutely worth reading (well, "reading" is not the correct term to use here; it is very demanding and will take you a lot of time). I've never really been too fond of Feynman's lectures, but the again I'm more of a "lots of equations and exercises" guy.

      Another book worth mentioning is Sakurai's "Modern Quantum Mechanics".

  • His Philosophiæ Naturalis Principia Mathematica [] contains his 3 laws of motion, everything follows from there.
  • one thing i find when talking to mathematicians is that they often have little knowledge of maths for physicists, though they can acquire this knowledge very quickly. for this reason, i'd recommend you have a look at something like "mathematical methods in the physical sciences" by Mary L. Boas. she also covers a great deal of physics from a mathematical perspective.
    • by habig (12787)

      Mathmatical Methods for Physicists [] by Arfken. If it's not in here, you won't be using it in a physics class till you get into some really hard core theory.

      The Amazon links to a newer version than I have, but presumably it's the same beast.

  • by frenchbedroom (936100) on Sunday July 13, 2008 @06:56AM (#24171369)

    There's one for every Slashdot discussion ! []

  • by Bazman (4849)

    I did a BSc in Physics with Astrophysics, and the astro classes were more maths than even my friends who were doing maths had in their mathiest maths classes.

    For our stellar structure course the lecturer used every letter of the alphabet in his equations. Upper and lower case. Latin and Greek. He may even have sneaked in an aleph when we weren't looking (which was often). We used to test ourselves by someone picking a random letter, say 'p' and someone else going 'partial gas pressure!' or whatever it was.


    • Actually, as an English clever person with a doctorate and everything (I has a smarts, I do), I've found myself using just 'Math' recently as it seems to make more sense. Certainly in tutorial material.

      It just sounds better really, not least because the word it's shortened form of isn't 'Mathsematics'. I may be committing an Englishness sin by doing this, but since I never studied Mathematics as a single subject, I may be able to plead insanity.

      • Seriously, did you study Mathematic or Mathematics? If the latter, you should shorten it to Maths. English is really quite simple.
    • Why do so many people insist on confusing the two? Mathematics is merely the language used to describe the Physics. It's a tool folks, and nothing more.

      That said, having a Maths degree can be either a very good or very bad basis for pontgrad physics. If you insist on seeing Physics as nothing more than messy but fun maths, you'll never be a great Physicist. If however you see the Maths as a succinct and powerful way to describe the Physics you are on the way to being good at Physics. A lot has to do w

  • One of the best (Score:4, Informative)

    by Doofus (43075) on Sunday July 13, 2008 @07:42AM (#24171529)
    One of the best, and most consistently relied upon, physics texts is Fundamentals of Physics [], by Halliday and Resnick. The link leads to the 2007 edition - prior editions are still available for lower cost.

    I used this book in high school, and then had the opportunity to use it again during several courses in college. The text is now in its 8th edition, and has been regularly updated and improved. Depending on where most of your colleagues went to school, its likely some or many have been exposed to H&R.

    H&R does not spoon-feed; some of the exercises are difficult. Working through the text is assuredly not going to be a random walk in the park.

    A number of the other comment threads discuss Feynman's lectures, which are also excellent.
  • Having gone through a physics undergrad, an astrophysics-slanted grad and currently teaching undergrad physics, I am always on the lookout for good texts. Here are my suggestions...

    Firstly, if you have never taken undergrad physics or are looking for a reference, you will want a good intro text. Feynman is good for conceptual understanding but is a bit short on worked examples and problems for you to try. There are several good intro texts out there, my personal favorite is Physics for Scientists and
  • Best Textbooks (Score:5, Informative)

    by E3nder (908983) on Sunday July 13, 2008 @08:11AM (#24171647) Homepage
    I think the important thing to realize in your situation is that whatever you _need_ to know to do your masters your classes and your professor will point you to the right books. As such, what you really need to do is go back and fill all the wholes that were left from a non-physics undergraduate degree. Most of these textbooks that I will list are the standard for MIT, and Harvard and the like. So let's begin.
    Classical Mechanics:
    Kleppner and Kolenkow []
    If you have time: Goldstein []

    Electricity and Magnetism:
    This one is a little tricky, I'll give you the 1st undergrad, the Junior level undergrad and then the two Grad texts. You can probably just read the Junior level text.
    Purcell []
    Griffiths []
    Jackson [] and Schwinger []

    Statistical Mechanics and Thermodynamics:
    There are really no agreed upon texts here (sorry), I used Baierlein [] at MIT but that seems to switch every year.
    Same goes for graduate texts, BUT the MIT profesor who has been teaching grad stat mech just put out his own books which I hear are quite good. We'll call them Kardar 1 [] and Karadar 2 []

    Quantum Physics:
    What you really need is an introduction to two fundamental ideas, the wave-function formalism and the linear-algebra formalism.
    Wave-function: French and Taylor []
    Linear Algebra: Griffiths [] - Best Book in this list in my opinion.

    Special Relativity and General Relativity:
    Special: French []
    General: Carroll []

    That should fill in everything that you missed. What we are skipping is every other specialty in physics, but, it seems like you've already chosen one, so no big loss.
  • by golodh (893453) on Sunday July 13, 2008 @08:24AM (#24171693)
    From your post I gather that you will primarily use self-study. As regards reading material I suggest you have a look here: [] Prof. 't Hooft is a Nobel-prize winner in physics and he has put together a page with "open source" reading material on physics which he recommends to anyone with aspirations of becoming a theoretical physicist.

    As an aspiring astronomer your profile will strongly resemble that of a theoretical physicist. And you'll certainly need to know about just about everything he lists on that page: from classical mechanics, optics, special and general relativity, quantum mechanics, statistical mechanics, thermodynamics, plasma physics, plain old electromagnetism, to electronics. 't Hooft lists freely downloadable high-quality reading material on just about every topic!

    And although you didn't ask, don't forget the computational side of things! Most astronomers I know are heavy computer users and very good programmers.

    So make sure you know about Fortran and the libraries that are written in it (e.g. have a look at [] and acquaint yourself with Lapack, Sparsepack, fftpack, cephes etc). Many of those routines can also be found in Matlab, Octave, Scilab, etc., but if you need full control and a standalone executable on a big supermini you might have to go back to Fortran and C++), And make sure (well ... I hardly need tell a mathematics undergraduate but I can't omit it) that you know about Maple and/or Mathematica.

    But ... if I may be so bold ... whilst reading and self-study are an indispensable element of learning physics they are rarely sufficient. You'll also need to learn a special way of thinking that sometimes comes hard to people with a background in mathematics. Which is to know when and where to cut corners and use approximations, and sometimes even go beyond the mathematics you know.

    Think of Paul Dirac (of the Dirac Delta function). His "function" isn't a function at all, it's a distribution, and trying to think of it as a function will lead you to contradictions. But Dirac set up a formalism using it (and got the properties right !) without knowing about distributions (they were invented later partly to put what he had done on a firm mathematical basis). He simply let mathematical firmness go hang at the appropriate moment. Now I'm not comparing you to Dirac (and I'm certainly not encouraging you to take liberties with mathematics), but Dirac was a physicist first and a mathematician second. That's what I mean. Someone suggested the Feynman Lectures ... they're great (if sometimes a tough read) exactly because Feynman makes this very point.

    You see ... in Physics, the physics comes first and the mathematics second; meaning that in thinking about physics problems you'll have to think in terms of physics (of course greatly helped by the mathematical formalisms in which physical laws are couched) but if you'll need to be able to think through a physical line argument without necessarily working through all the maths. Physicists do this as a second nature, and you'll need to learn how.

  • Your Professor?

    A quick check on your universities web site should also furnish a list of your prof's group, (Phds and post-docs). Track them down. What you don't really need at this stage is a full physics degree. That is why they chose a mathematician, right? So find out the specifics of your project, and read around that.
    Also, it shows the people who count that you're interested.....
  • Tough material, great book. Remember that Einstein had the physical theory first and then looked to mathematicians to help him put it into formal equations. One can't help but feel closer to "God" (whatever that may be) after learning about GR and seeing the implications as truths in our telescopes. Good luck to you!

  • A good classical mechanics textbook: Classical Mechanics, Herbert Goldstein. It it IMHO the defacto standard for graduate classical mechanics, and very very well written. It requires advanced math to understand (but that shouldn't be a problem for you :)).

    A good statistical mechanics book, I can't think of one off the top of my head, but I've used serveral, there doesn't seem to be much of a shortage of good stat-mech books.

    Since you are going into astro I'd suspect it would be good to either/or/both re

  • For a very lightweight text that goes surprisingly deep into the physics theory, I suggest this book: "Astrophysics With a PC - An Introduction to Computational Astrophysics" []. It's intended for amateur astronomers with an interest in astrophysics, source code in Basic is printed along with the text.

    Take a look at the table of contents in the link I gave and see what you think, it costs only $19.95, which is a very low cost for a book these days.

  • it's hard to believe no one has recommended Gravitation [] yet. This comprehensive, well-written, and authoritative book on general relativity is tailor-made for the mathematically sophisticated. One of its strong points is it does everything twice using both coordinate-free and coordinate-based differential geometry to help solidify your understanding and so you can do both theory (coord-free) and calculations (coords).

  • Two of the books I kept after graduating in nuclear physics might help to get a quick rough overview in about 10% of the pages of the Feynman lectures. None of them replace the other suggestions, but they might work well as a kick start and quick reference.

    -From Newton to Mandelbrot []. The fractals section is probably completely out of fashion now, but the first 2/3rds of the book are a lightning fast course through most of theoretical mechanics, electrodynamics, relativity and quantum physics

    -Princeton Guide

  • Course of Theoretical Physics by Landau and Lifshitz

  • by DrLudicrous (607375) on Sunday July 13, 2008 @11:25AM (#24172671) Homepage

    The vast majority of the recommendations here are top notch. A lot of which book to use really is personal preference and background. Here are my personal choices after having been in 3 separate Physics departments. Also, you should consider looking at ANY of the Landau-Lifshitz texts. These Soviet scientists wrote comprehensive texts that might be right up your alley as someone with a math background. I only wish I could understand them more, their physics is really beautiful.

    First off, a general reference book. I recommend the Halliday and Resnick series. Buy this used. It is basically an encyclopedia of physics that is presented at the intro undergraduate level. I use it frequently when working through problems outside my specific area of expertise.

    Electricity and Magnetism: Three books. Griffiths, Purcell, and Jackson. The first is a classic undergrad text, the second is a more advanced undergrad text, and the last is the standard graduate text in E&M.

    Quantum Mechanics: Griffiths' undergrad text is a must, though it is not very mathematically rigorous. I recommend Shankar as a supplement- Shankar is used as both a grad and undergrad text. I'm an experimentalist who stopped learning formal quantum mechanics after 1 year of graduate study, so Shankar may not be enough for you depending on your interests. Check out other's recommendations. Griffiths and Shankar are very good intro and reference books.

    Statistical Mechanics- I used Kittel and Kroemer as an undergrad, and it's OK, a little dated. Huang was my grad text, and it is also OK. I don't have strong feelings here. Landau and Lifshitz may be better for you

    Classical Mechanics- Marion and Thorton was my undergrad text. Personally, I don't think the CM text really matters. They are all equally bad. The basics they teach you are what a Langrangian is, and unfortunately always underemphasized what a Hamiltonian is (used REPEATEDLY in QM).

    Finally, make sure to get a good Mathematical Methods book, even if you really understand math well (I am sure you do). I recommend Arfken as a reference tome, and the Schaum's outline as a handy desktop reference for solving various partial differential equations. Past that, you should be able to pick up texts cheap used from fellow students, or on eBay. Good luck!

    • by BitterOak (537666)

      Personally, I don't think the CM text really matters. They are all equally bad. The basics they teach you are what a Langrangian is, and unfortunately always underemphasized what a Hamiltonian is (used REPEATEDLY in QM).

      Try Goldstein. A solid treatment of both the Lagrangian and Hamiltonian formulations, as well as canonical transformations, Poisson brackets (which become commutators in QM), and the least action principle.

  • Buy some previous editions of textbooks. For less than the price of one new textbook, you can probably get a whole undergraduate course of learning, as long as you read a lot.

    But, make sure any books you buy have answers to problem sets in the back. I learned that lesson the hard way.

  • There are a series of "classic" physics textbooks published by Dover. They're not hardcovers with glossy paper and amazing color diagrams, but they are about $5-$10. They're generally reproductions of text books which went out of print a few decades ago. Given that most core undergraduate physic curricula stop at ~1930, that's not too bad.

    A better suggestion may be to ask the professors at your university, that's what they're there for. If you walk in to someone's office, they may just hand you the perf

  • Lots of people here are suggesting a super-broad physics education focusing on everything from themo to relativity to quantum mechanics. These are VERY diverse areas and I really don't think you have time to learn any of them very good, let alone all of them. Therefore, I'd focus on the areas you're likely to delve into first - things like relativity and basic mechanics/dynamics.

    In that regard, Feynman's Lecture series is excellent. For a quick read, I'd recommend Feynman's Six Not So Easy Pieces. You m

  • I think you will find this one [] is right up your ally.

    Pricey but worth it.

  • I wouldn't worry too much about this. What I'd recommend is:

    Boas, "Mathematical Methods in the Physical Sciences"

    That'll take you from proving things to applying the actual Math that you've learned. Given your background, you should be able to go through this quickly. You'd probably also benefit from:

    D'Inverno, "Introducing Einstein's Relativity"

    Since Relativity is in there quite a bit. But, as astrophysics applies many different fields of Physics, you'd probably benefit from:

    Serway, Jewett "Physics for

  • I seem to be the only one thinking, that maybe if you don't know anything about physics, a Masters in "basically physics" is not a great idea?

    I mean, supposing you don't like physics?

    When I was doing my Maths degree I foolishly signed up for a physics course. I was learning real rigor in my Maths classes, then had to sit a squirm as the physicists did some terrible things to equations. Should have gone for English instead.

  • Grab yourself a copy of Ohanian (Physics, combined, 2nd edition)

    After that, go to a Blackwell's, and sit in the physics section. Pick some books off the shelf, examine them, see what resonates. Rinse, repeat.

It is the quality rather than the quantity that matters. - Lucius Annaeus Seneca (4 B.C. - A.D. 65)