Basic Mathematics

Yeah, read Basic Mathematics by Lang. Covers all precalculus you need in a rigorous way.

In order: 1. Book of Proof 1a. How to Prove It: A Structured Approach 2. Elements of Set Theory - Enderton 2a. Naive Set Theory - Halmos 3. Foundations of Analysis - Landau 4. Basic Mathematics - Lang 5. Principles of Mathematics - Allendoerfer & Oakley 6. A Transition to Advanced Mathematics 6a. Concept of Modern Mathematics - Stewart 7. Calculus - Apostol or Spivak Don't skip any

That thread recommends many very few good books, but probably mostly books too hard at first for the participant who has posted this new thread. I'll recommend a couple of books from that thread: http://www.springer.com/physics/book/978-0-306-45036-5 http://www.amazon.com/Mathematics-Short-Introduction-Timothy... (http://www.amazon.com/Mathematics-Short-Introduction-Timothy-Gowers/dp/0192853619/) I agree with the recommendation of An Introduction to Mathematical Reasoning in this thread. Another participant has already recommended my favorite for background reading, Concepts of Modern Mathematics by Ian Stewart. http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewar... (http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewart/dp/0486284247/) Get that right away. Sawyer's A Mathematician's Delight is surely also good (I've read other books by Sawyer). http://www.amazon.co.uk/gp/product/0486462404/ Read those for background as you get my favorite overviews of mathematics: Basic Mathematics by Serge Lang and Numbers and Geometry by Joseph Stillwell.…