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Book Recommendations For Maths To Astrophysics?

Posted by kdawson on 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?"

17 of 276 comments (clear)

  1. Pop-Sci but well worth it... by Anonymous Coward · · Score: 5, Interesting

    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!

    1. Re:Pop-Sci but well worth it... by RedOctober · · Score: 3, Informative

      Disagree. Sure there is some rehashing of material that mathematicians will be familiar with, but unless said mathematicians are familiar with applications in physics, the book will cover plenty of new material for them. Take complex analysis : the initial chapter on complex analysis will be a rehash, but later chapters on its applications in QM, QFT, GR will NOT be a rehash.

      That it is very broad is a good thing: it looks like the reader WANTS an overview. For further detail, good use can be made of Penrose's excellent bibliography.

      I've got a maths background, and found much of the maths in this book new: much of it is idiosyncratic to physics. The holes I had in my knowledge of physics I was able to fill in via Penrose's bibliography.

      I'll finally say that "Dancing Wu Li", "Tao of Physics", etc, are all pop physics that are easy to get through, but useless to learn anything. The danger with these books is that you can walk away with a completely wrong understanding of what they're on about, and you wouldn't be able to tell. They are simply too vague and "new agey", too many slippery concepts that can't be taught properly without mathematics, and dangerous without the appropriate background.

    2. Re:Pop-Sci but well worth it... by rasputin465 · · Score: 4, Informative

      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.

    3. Re:Pop-Sci but well worth it... by Beetle+B. · · Score: 4, Interesting

      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.

      --
      Beetle B.
  2. Potential jobs, Space Pirate? by jimmydevice · · Score: 4, Funny

    "Well, with one degree in maths and another in astrophysics, it was either that or back to the dole queue on Monday" DNA

  3. Feynman Lectures by Rudisaurus · · Score: 5, Informative

    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.

    --
    licet differant, aequabitur
  4. Intro Astrophysics by RadicalRhinoceros · · Score: 3, Informative

    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

  5. Oh Boy, Math to Astro-Physics? by smackenzie · · Score: 4, Funny

    In that case, I recommend:

    Get a Financial Life
    Dating For Dummies
    Paint the Sky with Stars: The Best of Enya
    Getting Things Done: The Art of Stress-Free Productivity

  6. Recommended topics by Anonymous Coward · · Score: 4, Informative

    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.

  7. Always Best To Go To The Source ... by strelitsa · · Score: 5, Informative

    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. http://ocw.mit.edu/OcwWeb/Physics/ [mit.edu]

    --
    No mod points, no meta-moderating/Firehose/all the other free work Slashdot wants me to do.
  8. From an Astrophysicist by laughing_badger · · Score: 5, Informative
    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.

    --
    Help children born unable to swallow - www.tofs.org.uk
  9. General intro to physics books by 16384 · · Score: 4, Informative

    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.

  10. obligatory xkcd comic by frenchbedroom · · Score: 3, Funny

    There's one for every Slashdot discussion !

    http://www.xkcd.com/435/

  11. One of the best by Doofus · · Score: 3, Informative

    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.

    --
    If the Government becomes a lawbreaker, it breeds contempt for law; ... it invites anarchy. - Brandeis
  12. Best Textbooks by E3nder · · Score: 5, Informative

    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.

  13. Astronomy and theoretical physics by golodh · · Score: 3, Informative
    From your post I gather that you will primarily use self-study. As regards reading material I suggest you have a look here: http://www.phys.uu.nl/~thooft/theorist.html 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 http://www.netlib.org/liblist.html 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.

  14. Texts from a PhD Student by DrLudicrous · · Score: 4, Informative

    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!