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Where do I start with self learning linear algebra

  1. May 12, 2012 #1
    Hi. Im a physics major and Id probably go with mathematical/theoretical physics path.

    Where do I start with self learning linear algebra? I'm good with proofs but I'm not comfortable with learning math without intuition or motivation behind the axioms. Still, I hate math without rigor (cookbook engineer math).

    I'm looking for an intro book for linear algebra. Thanks. May be my first exposure to pure math excluding intro to proofs.
  2. jcsd
  3. May 12, 2012 #2
    Try to get "linear algebra" by Serge Lang. It's an excellent book to study from.

    Another good book is "linear algebra" by Friedberg, Insel and Spence.
  4. May 12, 2012 #3
    Very nice intuitive approach to algebra provides Meyer's Matrix Analysis and Applied Linear Algebra. It is great for intuition but as the title indicates, it is far from being a rigorous mathematical text.
  5. May 12, 2012 #4
    Hi micromass. Which edition should I get?
  6. May 12, 2012 #5
    Doesn't matter. If you can find a cheap old edition, then it'll probably be fine.
  7. May 12, 2012 #6
    Thanks!! As I've said, this is my first exposure to pure math. Is it okay if I can't at first answer the exercises? That is, can I skip the hard exercises? This happened a lot in Spivak and I just gave up on the book. Kind of a downer.
  8. May 12, 2012 #7
    I'm no expert but... If I were to buy a textbook to self-study from, I would check a homework-help site like Cramster and see whether that book is covered. Since you won't have anyone to really help you with the problems, having Cramster go over problems step-by-step can help a lot.
  9. May 12, 2012 #8
    Was Spivak your first encounter to calculus?? It really shouldn't be the first calc book you study. It's more something like a second exposure to calculus/intro real analysis book.

    It's ok to skip the hard exercises, but you should try them nevertheless. Ask for help if you really can't do them. This forum has a lot of opportunities for help.
  10. May 12, 2012 #9
    Yes it was. I hope Lang's would be different. And its been a year since my first dreadful take on Spivak.
  11. May 12, 2012 #10
    I take it, that it's your first encounter with linear algebra as well?? That is: do you know something about matrices, determinants and linear systems?? If you don't know anything about them, then perhaps another book would be good. Meyers book, mentioned earlier here, would be a nice first book.
  12. May 12, 2012 #11
    Hey micro, since I've got your attention, I'd like to ask some more. I'm trying to get as good an education in math as I can cause its fun and exciting and I need it. I wouldn't be able to take any course in math (besides math methods, which isn't really math).

    I've taken pre calc and methods single variable calculus. I'll be taking a course on DE on November. The class will consist only of physics majors - so It would probably be non-mathy.

    Right now my plan is to learn linear algebra and will relearn calculus with Spivak and then use Fleming of Spivak on Manifolds for several variable calculus. Would this be okay for a physics major self-learning math?

    Might be the case that all this math theory would be useless in physics. Still, I get the feeling that if I'd be using math, then, at least I should use it properly.
  13. May 12, 2012 #12
    Whether it is enough highly depends on what kind of physics you want to do. For example, if you want to study general relativity, then courses on topology and differential geometry would also help. If you want to study quantum mechanics rigorously, then courses on functional analysis would be good.

    So if you know what kind of physics you want to do, only then can we say what math you need.
  14. May 12, 2012 #13
    Ugh, yes. I don't know anything about matrices and stuff. What a waste.. I found Lang to be quite entertaining. And the Mayer book is large.
  15. May 12, 2012 #14
    You can always get Schaum's outline on linear algebra. It's usually easy with lots of nice exercises. I think that would be a nice first exposure.
  16. May 12, 2012 #15
    I mean, for now as an undergraduate, without any particular field in mind, i.e. the maths that all physics majors (who will probably go with theory) should know.
  17. May 12, 2012 #16
    Calculus (single-variable and multi-variable), ODE's, PDE's and linear algebra. That seems to be the bare minimum.

    Try to get hold of Boas "mathematics mathods in the physical sciences". It might be nonrigorous but it's an excellent book and contains everything a physics major should know.
  18. May 12, 2012 #17
    Okay, thanks, micromass. Guess I'll first study the Boas book to get a feel for the maths.
  19. May 12, 2012 #18


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    if you want a slightly more advanced first exposure to linear algebra, try Linear Algebra by Jim Hefferon or Linear Algebra Done Wrong by Sergei Treil. Both are free online from the authors' websites.
  20. May 29, 2012 #19
    In my view, no better place to start than Klaus Jänich's "Linear Algebra".

    This is the translation into English of one of the common textbooks for the first semester of first year at German universities for students studying maths and/or physics.

    It is thoroughly modern in its approach. The author is a master expositor. He explains concepts with simplicity and great clarity, showing how linear algebra is used.

    There are separate exercises for physics students.

    It is published by Springer in its Universitext series.
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