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What is the best mathematics book for physicists?

  1. Aug 31, 2015 #1
    what is the best mathematics book for physicists ?or in what way should i study math if i need it for physics? . thanks!
  2. jcsd
  3. Aug 31, 2015 #2


    Staff: Mentor

  4. Aug 31, 2015 #3
    thank you very much . is it better to read both of them or one is enough ?
  5. Aug 31, 2015 #4


    Staff: Mentor

    Hard to say, sometimes you need to look in several books until you find what you're looking for.

    I think Arfken and Weber is good for practicing physicists whereas Boas is a good undergrad book. I've heard a lot of good reviews about the Boas book. I have a copy of Arfken and Weber and like the style of presentation.

    There's also the Nearing book which is available online which you could start with:

  6. Aug 31, 2015 #5
    Absolutely avoid Cahill. It's nearly worthless unless you already know the concepts and just need a refresher.
  7. Aug 31, 2015 #6
    ok . thank you so much
  8. Aug 31, 2015 #7
  9. Sep 5, 2015 #8
    Sean Carroll's lecture notes on general relativity contain a superb introduction to the mathematics of GR (differential geometry on Riemann manifolds). These also also published in modified form in his book, Spacetime and Geometry.

    Spivak's Calculus on Manifolds is a gem. Bishop's Tensor Analysis on Manifolds is a great introduction to the subject, and published by Dover, is very cheap (less than $10 on amazon).

    Georgi's Lie Algebras in Particle Physics is enjoyable and fast-paced, but probably skips around too much to be used as an adequate first exposure.

    Shutz's Geomertical Methods of mathematical physics and a first course in general relativity.

    Despite it's incredibly pompous title, Penrose's The road to reality: A completer guide to the laws of the Universe provides an enjoyable high-level view of a vast expanse of mathematical physics.

    As mentioned by Cedric, I am a huge fan of Sussman and Wisdom's Structure and Interpretation of Classical Mechanics and the associated Functional Differential Geometry memo. The citations in those publications will also point to towards a lot of good material and there's more goodies if you dig around in the source code.
  10. Sep 5, 2015 #9


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    How much math do you already know? How much physics?

  11. Sep 5, 2015 #10
    I know some algebra , some geometry and some calculus only . in physics I know elementary things about classical mechanics and electromagnitism
  12. Sep 5, 2015 #11
  13. Sep 5, 2015 #12


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    In that case, you probably should learn linear algebra, multivariable calculus and basic differential equations before reading even the most basic of the books listed by others here (Nearing: http://www.physics.miami.edu/~nearing/mathmethods/; [Broken] and Boas).

    Books on Lie algebras, general relativity, differential geometry, etc. are way beyond your level at this point. (They are probably beyond my level, too!)

    Last edited by a moderator: May 7, 2017
  14. Sep 5, 2015 #13


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    There are many books on calculus that fit the bill for your next step (multivariable calculus, elementary vector calculus). I learned from Thomas and Finney 7th edition (https://www.amazon.com/Calculus-Ana...eywords=thomas+calculus+and+analytic+geometry) but many folks here think that the 3rd edition is superior to all the rest (https://www.amazon.com/Calculus-Ana...as+calculus+and+analytic+geometry+3rd+edition)

    For linear algebra, a good free book is by Hefferon, free at:
    but you can also buy a paperpack if you like hardcopy better: https://www.amazon.com/Linear-Algeb...08268&sr=8-1&keywords=hefferon+linear+algebra
    Many other books exist - search physicsforums for linear algebra books and you will find many results

    There are many differential equations books. I do not know what is best.

  15. Sep 9, 2015 #14
    thanks very much
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