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Feynman Lectures - Anything similar for Mathematics?

  1. Nov 10, 2012 #1
    Last year I got volume 1-3 of the Feynman lectures but as a soon mathematics major I think it'd be appropriate to read more mathematics lectures (and more enjoyable). Is there anything similar I could ask for for my upcoming birthday?

    Thanks,
     
  2. jcsd
  3. Nov 10, 2012 #2
    Hi converting1,
    it's quite hard to match 'similar' it all depends on what you mean/expect.
    If you haven't heard about it by now, I'd recommend having a look at Michael Spivak books, I don't know if they will meet your specific expectations, but there is no way they will be any kind of a bad gift for your birthday :)
    cheers...
     
  4. Nov 10, 2012 #3
    Bourbaki. :rofl:
     
  5. Nov 10, 2012 #4
    I'm just looking for something which really underlies the foundations of mathematics, something rigorous with a lot of proofs, but still requires a proficiency in mathematics. Here is what I've studied so far:

    Factor, remainder theorm
    Algebraic Division
    Definite intergration
    Coordinate Geometry and Further Differenciation
    Trigonometry
    Geometric Series
    More Differenciation: Product,Quotient,Chain rule
    Trigonemetric manipulation: Double angles, Half angles, reciprocol functions
    Mappings and Functions
    Implicit Differenciation
    Parametric equations
    Further Integration: Substitution, Recognation, Integration by parts
    Partial Fractions
    Vectors
    Matrices
    Proof by induction
    Series
    Basic conics
    Numerical Techniques, iteration etc
    Complex Numbers
    Further Complex numbers: Loci,De Movrie, Roots of Unity etc
    1st Order Differencial Equations
    2nd Order Differncial Equations
    Polars
    Further Series
    Roots
    Taylor expansions
    Hyperbolic functions; inverses etc
    Further coordinate systems: Equations for an ellipse, loci, parametric equations for a hyperbola & ellipse etc tangents normals etc,
    Differentiating hyperbolic functions, inverses & trigonometric functions
    Integration - standard integrals, integrating expressions with hyperbolic functions, integrating inverse trigonometric and hyperbolic functions
    Further vectors- triple scalar product, writing the equation of a plane in the scalar, vector or Cartesian form.
    Further Matrix algebra; determinant, inverse of 3x3 matrix, linear transformations etc

    when working through the topics above I would really have to attempt the proofs myself, and if I couldn't do it it'd take a while to be able to find a proof online, so it'd be nice to have it all summarized in a book or so
     
  6. Nov 10, 2012 #5
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  7. Nov 10, 2012 #6
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  8. Nov 10, 2012 #7

    micromass

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  9. Nov 10, 2012 #8
    why?
     
  10. Nov 10, 2012 #9
    lol!
     
  11. Nov 10, 2012 #10

    micromass

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    They're not very suitable for beginners. And they're quite difficult to read through. It's more like an encyclopedia than a textbook.
     
  12. Nov 10, 2012 #11
  13. Nov 10, 2012 #12
    oh ok,

    any other suggestions?
     
  14. Nov 10, 2012 #13

    micromass

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  16. Nov 10, 2012 #15

    micromass

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    I think it might be worth to try it. You already know a lot of calculus (derivatives, series, integrals, etc.), so that won't be the problem. The hard part of Spivak is going to be the rigor and the proofs. The first two or three chapters are going to be very easy things you know already, but you should make the exercises to get used to the proofs involved. If you can't get used to proofs, then you might want to look at a proof book.

    That said: Spivak has a reputation for having very hard exercises. Don't be discouraged by this.

    But yes, I should try the book if I were you!
     
  17. Nov 10, 2012 #16
    thanks, I'll be sure to get it.

    Also, I hear most undergraduate textbooks don't have any answers attached, wouldn't this be a problem if it has very hard exercises?
     
  18. Nov 10, 2012 #17

    micromass

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    If I'm not mistaken, Spivak gives some solutions (but not all) at the end of the text.
     
  19. Nov 10, 2012 #18
    I see, thanks

    out of curiosity does this book cover calc I-III in the US education system? I'm from the UK and we don't have that sort of system afaik.
     
  20. Nov 10, 2012 #19

    micromass

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    It only covers calc I-II (and a bit of complex analysis). It doesn't do multivariable stuff.
     
  21. Nov 10, 2012 #20
    I see,

    thanks to everyone for responding
     
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