As someone who also went back to study math after not doing it for a long time, I would recommend doing a book that focusses on teaching how to prove things, using the math you already know. Most upper div math courses either assume you know how to prove things, or try and teach it in passing while also teaching the topic itself (classically linear algebra and calc 3 were taught this way, though now many places now have separate "proof" classes instead)
I would strongly recommend Chartrand and Zhang's "Intro to mathematical proofs", once you know how to prove things, every other more advanced math class you take will be much easier than it would have been otherwise.
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In particular, do the book, including the chapters on "proofs in calculus" and "proofs with real and complex numbers" before doing real analysis - you'll enjoy it much more that way!
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I went through most of this book a few years ago, now about to finish my MS in math :)
Agreed. I'm trying to move from being a secondary mathe teacher to actually learning pure math, and proofs are the killer. I feel like I understand topics, but creating proofs kills me.
I would strongly recommend Chartrand and Zhang's "Intro to mathematical proofs", once you know how to prove things, every other more advanced math class you take will be much easier than it would have been otherwise.
[Edit] In particular, do the book, including the chapters on "proofs in calculus" and "proofs with real and complex numbers" before doing real analysis - you'll enjoy it much more that way! [/Edit]
I went through most of this book a few years ago, now about to finish my MS in math :)