Learn Analysis: Math Skills & Textbook Guide

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To begin learning mathematical analysis, a solid foundation in calculus is essential, which includes a year of differential calculus and some exposure to integral and multivariable calculus. While formal proof techniques are beneficial, they are not strictly necessary if one has a strong grasp of calculus concepts. Spivak's textbook is highly recommended as a bridge from calculus to analysis, as it effectively introduces proof techniques. Rudin's "Principles of Mathematical Analysis" is considered a good resource for those ready for a more rigorous approach, but it may not be suitable for beginners unfamiliar with proofs. Linear algebra is not a prerequisite for learning analysis. For self-learners, starting with Spivak, followed by either Rudin or Terry Tao's freely available analysis notes, is a suggested pathway.
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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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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.
 
So you would say Spivak calculus -> proofs(optional) ->Rudin.
 
If you can get through Spivak, you'll sure know your proofs well enough for Rudin.
 
Yes, if you can make it through Spivak adequately, then you won't need a proofs book (though it would never hurt).
 
Thanks for the information, wish me luck!
 

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