I'm an Industrial Engineering graduate looking to make a switch into Pure Math at the Masters Level/PhD. I have undergrad experience in Calculus (upto Differential Equations) and Probability and Statistics.
I have an MSc/PhD entrance exam exactly a year from now and I shall need to self study topics in:
1) Real Analysis: 7 chapters of Baby Rudin, upto Sequences and Series of Functions
2) Complex Analysis: Introductory Chapters into AV Ahlfors' Complex Analysis
3) Linear Algebra: Artin's Algebra
4) Abstract Algebra: Artin's Algebra, D&F topics like Sylow's Theorem, Finite Field, Maximal and Prime Ideal
5) Differential Equations: Undergrad Level, Tom Apostol Calc II
- I'm diligent, possess strong work ethic
- Consistently place 10-12hr work days
- Large repository of grit and patience
- Appreciate Mathematical theory and intuition very dearly
My Question: In what order of topics must I cover the above topics, and which courses can/must be taken parallely so that I don't miss any foundation intuition and iteratively cover all topics prior to April-May 2019?
I'd especially appreciate advice from those Math mavericks who'd decided to veer off their traditional path and into Math
@s-stein @jack-bauer @user204305 @ericam @quasar @louis (Since I'd seen ya'll have similar experiences/questions as mine)