How to Prove It: A Structured Approach

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

I couldn't disagree more. I studied Analysis in the Uni, and even in that environment Rudin is pretty bad. For a total newcomer that book will leave you completely helpless. Also, solutions are a must have, without them you are almsot totally lost. In their absence, it is OK to ask on StackExchange or #math on EFnet. First let's start with a few books to prep you for college-level maths: * https://www.amazon.com/How-Study-as-Mathematics-Major-ebook/... (https://www.amazon.com/How-Study-as-Mathematics-Major-ebook/dp/B00B9CIORY) * https://www.amazon.com/How-Read-Proofs-Introduction-Mathemat... (https://www.amazon.com/How-Read-Proofs-Introduction-Mathematical-ebook-dp-B00I8XF6TQ/dp/B00I8XF6TQ) ; or * https://www.amazon.com/Numbers-Proofs-Modular-Mathematics-Al... (https://www.amazon.com/Numbers-Proofs-Modular-Mathematics-Allenby/dp/0340676531) ; or * https://www.amazon.com/How-Prove-Structured-Daniel-Velleman-... (https://www.amazon.com/How-Prove-Structured-Daniel-Velleman-dp-1108439535/dp/1108439535) (I believe you can find solutions to the 2nd edition online) For Single-Variable Analysis…

Math. 1. How to Prove It: A Structured Approach, Velleman (perfectly prepares for reading of pretty much any math book) 2. Higher Algebra and before that Elementary Algebra, Hall (just some intro stuff; general public license, can be freely downloaded from archive.org)

For proof based mathematics, I found "How to Prove It:A Structured Approach" helpful.

Well, if you're looking for an introduction to the basics of mathematics (which I would recommend for anyone looking to delve deeper into any specific area), you can't really beat 'How to Prove It' by Velleman. It covers the fundamental concepts of mathematical analysis and proof-writing (and, perhaps more importantly, reading proofs) and will help give you a great grounding for further reading, especially in the areas of discrete mathematics, set theory, and probability. I can't recommend it enough as an enjoyable introduction to the field. Also, for a good probability textbook, I would point you to 'Probability and Random Processes' by Grimmett and Stirzaker. It may be a bit hard-going at first (which is why I recommend How to Prove It to get you used to rigorous maths), but it is a very thorough text that also happens to concentrate on many areas of interest to the average programmer (Markov chains and the like). Together with the companion book of exercises, it should be fantastic for self-teaching, too.…