>>11718940>>11723900Augmenting to this, I'll give my own list in sequential order. Everything I list within a subcategory can be studied concurrently or relatively quick succession. I assume you know middle school algebra and some basic trig.
Introductory exercises, use khan academy and MIT OCW
>Calc 1-2, vector calculus from your favorite intro calc book. Rogawski's early transcendentals is standard and pretty good.>Basic matrix arithmetic.>ODE's and PDE"s.Transitioning into proof mathematics. MIT OCW and webpages are your best friend
>Book of proof >How to solve it>as much Concrete Mathematics by Knuth you can do. His explanation of techniques is really nice.>proof based linear algebra textCore
>Abbott's Understanding Analysis up to differentiation theory. Then switch to baby Rudin, do up to integration theory.>Algebra by Artin or Dummit+Foote, do group theory, symmetry and isometry, group actoins, and linear representation>Topology either by Munkres or Willard, do at least up to metrization.>Lovasz, combinatorics Core pt. 2
>Folland or papa Rudin for measure theory, integration theory, exact forms, etc>Artin and D+F again for ring theory, number fields, field theory, and galois theoryI've left out topics like logic, graph theory, number theory, etc., which are also great, but you can get into them after or during the core, which will give you enough maturity and experience to go through anything else in the canon.
