Analysis: With an Introduction to Proof
For "baby" analysis with single variable only. Appropriate for one term courses in analysis and advanced calculus. Text starts with a little logic and how to construct a proof. Revision features: material on the topology of the reals has been expanded and divided into two sections. Two optional sections on metric spaces and continuity in metric spaces have been added.
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Review: Analysis: With an Introduction to ProofUser Review - Cristina - Goodreads
I was scared of this class but I had a good professor and this book was pretty good. I found the proofs to be detailed enough (in general) that I feel like I learned how to construct them pretty well ... Read full review
Review: Analysis: With an Introduction to ProofUser Review - Daniel Babiak - Goodreads
Start here, then go to Rudin. Read full review