Learn Analysis: Math Skills & Textbook Guide

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In summary, the conversation discusses the topic of learning mathematical analysis. The person asking the question has a basic understanding of calculus and multivariable calculus and is wondering if they need to learn formal proofs in order to learn analysis. The expert recommends using Spivak's textbook as a bridge between introductory calculus and analysis, and suggests either Rudin or Tao's analysis notes as further resources. It is also mentioned that linear algebra is not necessary for learning analysis. The expert advises starting with Spivak and possibly going through an introduction to proofs book before moving on to Rudin. Finally, the expert wishes the person luck in their learning journey.
  • #1
Callmejoe
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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.
 
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  • #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.
 
  • #3
So you would say Spivak calculus -> proofs(optional) ->Rudin.
 
  • #4
If you can get through Spivak, you'll sure know your proofs well enough for Rudin.
 
  • #5
Yes, if you can make it through Spivak adequately, then you won't need a proofs book (though it would never hurt).
 
  • #6
Thanks for the information, wish me luck!
 

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