[Math] correct order to learning maths properly

advicelearningsoft-question

I am a high school student but I would like to self-learn higher level maths so is there a correct order to do that?
I have learnt pre-calculus, calculus, algebra, series and sequences, combinatorics, complex numbers, polynomials and geometry all at high school level.
Where should I go from here? Some people recommended that I learn how to prove things properly, is that a good idea? What textbooks do you recommend?

Best Answer

I'm not mathematician. I hold degree in management both bachelor's and master's degree. Anyway, to my knowledge, if you want to learn math from scratch, the order will be

college algebra, algebra & trigonometry, precalculus, calculus, linear algebra, differential equation, intro to analysis (or advanced calculus), functional analysis, real analysis, probability theory

There're some books I recommend

  • College Algebra by Henry Burchard Fine
  • Fundamentals of Algebra & Trigonometry by Earl Swokowski
  • Precalculus by Sheldon Axler
  • Calculus vol.1&2 by Tom M. Apostol
  • Introduction to Linear Algebra by Gilbert Strang
  • Mathematical Analysis by Tom M. Apostol
  • Introductory Functional Analysis with Applications by Erwin Kreyszig

Supplement: How to Prove It by Daniel J. Velleman. You need this book to learn how to do rigorous proofs for mathematical theorems.

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