I am a college student in computer programming, who has developed an intense passion for mathematics. After graduation I wish to pursue a University degree in mathematics, and perhaps a Master's degree and Ph.D.
Some posts that I read include, but are not limited to:
- How can I read numbers and mathematical symbols comfortably, at a university level?
- What books must every math undergraduate read?
- How much proof knowledge is necessary to begin Spivak's Calculus?
- Recommendations for books with solutions, to review wholly high school math?
During the next two years I wish to learn, not rote, the required mathematics for the "undergraduate" portion and beyond if possible.
I know of some various areas of mathematics such as: Algebra (elementary, linear, multi-linear and abstract), Geometry (discrete, algebraic and differential), Calculus (single/multi-variable), Set Theory, Number Theory, Combinatorics, Graph Theory, Topology, Differential Equations, Logic, Proofs & Proof Writing, etc...
I wish to make a "road map", but how do I plot it? What books are prerequisites? I understand that various areas may cross paths. I would like to state that I have not studied linear algebra or any form of calculus/pre-calculus yet; I am currently brushing up my "elementary" algebra.
I have come across How to become a Pure Mathematician, but ran into a snag. For instance, I had followed the very first link following the "Stage 1" heading which lead to the following book:
Barnard S. and Child J.M., Higher Algebra
After scanning some of the first pages, I realized the notation was unknown to me. After some further browsing, I realized some of the notation was found in Set Theory. This led me to infer that Set Theory may be pre-requisite to understanding this book.
Regarding reference materials, I have seen these mentioned:
- Apostal - Calculus Vol.1
- Spivak M. - Calculus
- G. Chartand, A.D. Polimeni and P. Zhang - Mathematical Proofs: A Transition To Advanced Mathematics
My study regimen consists of reading the material, taking copious notes in my own words as well as the authors', asking "why", working through all posed questions, creating questions of my own, then, reviewing the material and organizing said material for input into La/Tex. During my college semesters I devote approximately four hours during the night, weekdays, and 4-6 hours on weekends. During summer periods I adjust the timing of my study periods around my work hours, though if possible, I aim for two 4 hour sessions per day when the time is available.
This may benefit the novice.