Two or three years ago I decided to re-learn math from scratch, I did some research on what to read, made a list of books. I started from a Sawyer, it opened my eyes a little bit on the fact that math isn't that cryptic if you study it right, and that in fact it's quite interesting. But, for some reason I dropped it. Now I'm almost finished re-reading "Mathematician's Delight", but I look at the list I made several years ago and it scares and confuses me. I would be grateful if you guys could tell me in what order I should read this books (I own every book but the ones marked "don't have it"), should I buy the ones missing etc.
A little background: my school was math-focused and I kinda did well, but only because I learned by heart formulas and patterns of when to use them. I'm trying to do things right this time. I'd like to go through school program in a year, then spend summer learning Discreete math and Calculus (trying to apply for CS undergrad next year), so I could be month or two ahead of the program. Why I wanna be ahead? Because I found out that I can't at all absorb knowledge in class, mainly because there is always someone who spits answers faster then I get that precious insight on how things work, and why exactly they work this way.
So, here's the list of books with notes to myself:
Basics
- "Mathematician's Delight" by W. W. Sawyer
- "Journey through Genius: The Great Theorems of Mathematics" by William Dunham
Algebra
- "Algebra" by Israel M. Gelfand
- Paul's Notes http://tutorial.math.lamar.edu
Geometry
- "Euclid's Elements"
- "Geometry: Euclid and Beyond" (Undergraduate Texts in Mathematics) by Robin Hartshorne
Trigonometry (prerequisite: geometry)
- "Trigonometry" by I.M. Gelfand
Pre-calculus/Analytical Geometry
- "Functions and Graphs" by I. M. Gelfand
- "Pre-Calculus Demystified" by Rhonda Huettenmueller
Calculus (prerequisite: pre-calculus)
- "Calculus: The Elements" by Comenetz
- "Calculus and Analytic Geometry (9th Edition)" by Thomas, Finney (blue hardcover w/ lighthouse) *don't have it
- "Calculus" by Spivak (read "How to prove it" first)
- Paul's Notes http://tutorial.math.lamar.edu
- Linear algebra is needed for cacl III
Linear Algebra (prerequisite: calculus 1,2)
- "Elementary Linear Algebra, 2nd Edition" by Paul Shields
- "Linear Algebra, 4th Edition" by Friedberg, Insel, Spence *dont have it
- "Linear Algebra Done Right" (Undergraduate Texts in Mathematics) by Sheldon Axler *don't have it
Discrete Math
- "Discrete Mathematics with Applications" by Susanna S. Epp (2nd edition) hardcover
- "Concrete Mathematics: A Foundation for Computer Science" (2nd Edition) by Ronald L. Graham *dont have it
The order is generally right the way you have it more or less: basics, then algebra, then geometry, then calculus and linear algebra, then advanced calculus.
I'd strongly advise against locking yourself in a room with all these books you bought and forcing yourself to read every sentence. That's generally a terrible learning model.
You'd make better progress if you make a friend or two who's as passionate about math as you. Join a community or group. Lots of schools offer free turoring. The best progress you will make is going to be when you are interacting with people and are fully engaged.