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Is my math study plan suitable?

  1. Jun 29, 2015 #1
    Hello, I have been reading the posts on this website and they have really helped me out in finding good books. I will be starting university math next year and have formed the following study plan for the year (the books I list are merely the ones I start with -- I will of course read more books in following years, as continuation):

    Foundations: Algebra and Geometry by Beardon

    Calculus/analysis: Calculus by Spivak

    Linear algebra: Firedberg Insel

    Abstract algebra: Allan Clarke

    This is the main skeleton of my study for the next year. I will also be kept busy by homework assignments, lectures, etc. so I think this is enough, however I am seeking your opinions on how good my study plan is (for someone who doesn't know any university math). I am also open to suggestions for books I should read alongside the current ones (but I am not interested in "further reading" except for calc/analysis -- the rest can wait until next year as I said).

    What I'm thinking for doing alongside are the following:

    Foundations: I think the book I listed is comprehensive enough itself

    Calculus/analysis: As I said, I want to push ahead with calculus/analysis so I'm thinking of reading something like Pugh's analysis right after Spivak.

    Linear algebra: Are there enough problems in Friedberg Insel? If not then would you recommend Schaum's outline for problems? What about Halmos' problem book?

    Abstract algebra: Allan Clarke is basically a "learn through problems" book. There is minimal exposition. I am good at solving problems and did very well in my national olympiad so I thought it would suit me (in fact it was recommended to me by one of the national team's IMO members). But I think I may need a reference in any case, so would Dummit Foote work for that?

    There is also the issue of learning physics. I am interesting in taking some (optional) applied modules in my first year so I can decide if I want to continue with "math and physics" or just pure math. I don't know any physics except for the very basics from high school, such as the kind of thing taught in Hewlitt's conceptual physics. In particular, I don't know any "calculus physics" -- how physics is done using calculus. Any recommendations for starting?

    Thanks for your help!
  2. jcsd
  3. Jun 29, 2015 #2
    From my experience (I'm in second year of math and physics degree), Spivak's quite a good book for single-variable calculus. I don't know your background studies and knowledge, first year of math was all about the begging of think in abstract. I had some trouble with working on abstract vector spaces, so linear algebra in my opinion is very important. I used my class notes and also the book Introduction to linear algebra by Derek J.S. Robinson, who also has another "Introduction to abstract algebra". I really enjoyed the first one and I really got the important concepts.

    About physics... I have the opinion that before studying physics one should have some good mathematical tools very well learned. I had a subject on general introductory physics in my first year, and we had to solve a lot of problems using multivariable calculus and differential-equations-solving that we did not fully understood back then. It was not until this year that we understood what we were doing (integrating inertia moment, calculating electric and magnetic field via line or surface integrals, applying Gauss theorem...). Anyhow, I would still recommend learning a little bit about classical kinematics and dynamics.
    I think a very good application of linear algebra is understanding the motion of rigid bodies, and that would be cool to study right after isometries of the euclidean space. And it's not so difficult to understand once you know what vector and affine spaces are.
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