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Learning Analysis

  1. Jun 15, 2015 #1
    Hello, I would like to start learning mathematical analysis. I have a basic year of calc( on course in differential, one integral) and a course in multivariable calculus. Will I be able to learn analysis or do I need to learn formal proofs of some sort? Is linear algebra necessary? Also any recommendations on a starting textbook, bonus points if its good for self learning.
  2. jcsd
  3. Jun 15, 2015 #2
    I used Spivak to bridge the gap between introductory calculus and introductory analysis. Rudin is good if you're just looking for straightforward analysis, but I wouldn't recommend it if you haven't been exposed to proofs yet. Linear algebra isn't necessary.

    My recommendation would be Spivak, then perhaps Rudin, or go through an intro to proofs book, then either Rudin, or Terry Tao's (freely available) analysis notes.
  4. Jun 15, 2015 #3
    So you would say Spivak calculus -> proofs(optional) ->Rudin.
  5. Jun 15, 2015 #4
    If you can get through Spivak, you'll sure know your proofs well enough for Rudin.
  6. Jun 15, 2015 #5
    Yes, if you can make it through Spivak adequately, then you won't need a proofs book (though it would never hurt).
  7. Jun 16, 2015 #6
    Thanks for the information, wish me luck!
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