I was just wondering if someone would be kind enough to tell me in what order (I know that there is no real "best order") one would most profitably study these subjects/books:
(edited to conform with suggested order of study)
- Pre-Algebra
- Algebra 1
- Geometry
- Algebra 2
- Pre-Calculus/Trig.
- Calculus 1
- Calculus 2
- Combinatorics: Topics, Techniques, Algorithms – Cameron, Peter J.
- Lectures on Probability Theory and Mathematical Statistics – Taboga, Marco
- Classical Mathematical Logic – Epstein, Richard L.
- Calculus, 4th edition – Spivak, Michael
- Linear Algebra – Shilov, G. E.
- Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus – Spivak, Michael
- Naive Set Theory – Halmos, Paul R.
- Elementary Real and Complex Analysis – Shilov, Georgi E.
- Linear Algebra Done Right – Axler, Sheldon
- Ordinary Differential Equations – Tenenbaum, Morris
- Partial Differential Equations: Second Edition – Evans, Lawrence C.
- Abstract Algebra – Dummit & Foote
- Topology (2nd Economy Edition) – Munkres, James
- Introduction to Set Theory, Third Edition, Revised and Expanded –
Hrbacek & Jech (only suggested for those with great interest in Set Theory)
Also, are there any books/subjects missing from a fairly well rounded advanced mathematics education?
Any help would be greatly appreciated.
(edited in) P.S.
I think that I mistook Combinatorics for Discrete Mathematics. Can someone enlighten me on the difference and maybe suggest a good book for discrete mathematics (perhaps a supplement to Cameron's Combinatorics)?
Best Answer
I suggest you not try to stick to some specific order. If something interests you one day then read it. Forcing yourself to stick to a schedule will only cause you to be unmotivated and as a result not get as much out of it. Also, if your going to self study, try and still talk with people about what your doing or make videos in which your try to explain what you've learned. If you really want a challenge test your progress by trying to do problems here on MSE. I hope this helps and good luck. Also, search around for an ebook which shows you some elementary proof techniques because mathematics at this level requires a lot more time and understanding.