So far, I've tried to make a bunch of long booklists, but I realized that 1) they're often incomplete or lacking; and 2) they're pointless until I reach a sufficient level of competency to make thinking about them worthwhile anyway. I've shortened it quite a bit this time around.
This is my basic list:
>Chapter 1: Introduction to Entry-Level University Mathematics
Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
The Art and Craft of Problem Solving - Paul Zeitz
>Chapter 2: Finishing Entry-Level University Mathematics
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Ordinary Differential Equations – Morris Tenenbaum
Introduction to PDEs with Applications - E. C. Zachmanoglou & D. W. Thoe
>Chapter 3: Introduction to Proofs and Survey of Higher-Level Mathematics
How to Think Like a Mathematician - Kevin Houston
How to Prove It - D. J. Velleman
Mathematics: Its Content, Methods and Meaning - A.D. Aleksandrov, A.N. Kolmogorov, & M.A. Lavrent'ev
>Chapter 4: Bringing It All Together
Calculus Vol. I & II - T. M. Apostol
Analysis I & II - Terrance Tao
<then whatever I want after that, now that I've developed basic proofing skills and mathematical ability>
What do you guys think?
>>8958068
>Pre-Calculus - Carl Stitz & Jeff Zeager
I like this one
I wish modern textbooks still used this kind of layout instead of colors and photographs everywhere.
It's like they're compensating and hope they'll be able to catch the student's attention with pretty colors, only to achieve to exact opposite.
>>8958081
>>Pre-Calculus - Carl Stitz & Jeff Zeager
I'm going through this right now. It's pretty good for a pre-calculus text that tries to be as comprehensive as your general high school pre-calculus text without being dumbed down for brainlets. You'll actually learn what a function is here, among other things.
>>8958081
It's also free, so great for those who are on a /budget/.
>>8958068
Seems like a good list, though I would probably hold back on PDEs unless your book covers them in an entry-level way for science courses (and then in that case, I would try to find a book or a course that covers differential equations for applied purposes and then another book for a more mathematically rigorous study). You're not ready to tackle true PDEs until after doing some analysis IMO.
>>8958771
You just samefagged yourself multiple times, even to accuse yourself of samefagging. What the fuck? You know we can read the amount of posters in the bottom right corner, right? Are you this desperate for advice?
Whatever I did a lot of research on this list. Thanks for nothing faggots. Enjoy your thread about edgy teens getting kicked from Harvard for posting stupid shit in public, I'm sure that's really important right now.
>>8959119
>>8959238
Funny guide. Functional analysis instead of functions, ha ha! Grothendieck as a first course in geometry, LOL! Random signals and noise as "women's studies"... I GET IT!
>>8959677
Yea, those are joked you fucking autistic faggot.
bump thanks for the list OP
>>8959680
I never said they weren't jokes you dense idiot.
>>8958068
Thanks for compiling the list anon. I am going to be starting pre-calculus in the fall so I'll study up to prepare.
>>8959695
No problem. I thought somebody would enjoy it. I tried to cut as much bullshit as possible without getting overly ambitious.
>>8958733
Piggybacking off of this comment, what would be a good book for applied difEQs for the sciences (pre-analysis)? I'd hope to cover ODEs, PDEs, and other differential equations in such a way so that even if I don't feel like continuing onto more rigorous studies, I'm still left with enough math knowledge to handle the sciences. Or is such a goal impossible?
>>8959881
Fuck it, I found a good book that seems to do a great job of balancing breadth, depth, rigor, and application for a year-long treatment of differential equations.
Applied Differential Equations by Vladimir A. Dobrushkin
Final List:
>Chapter 1: Introduction to Entry-Level Mathematics, P. I
Pre-Calculus - Carl Stitz & Jeff Zeager
Calculus: A Modern Approach - Jeff Knisley & Kevin Shirley
The Art and Craft of Problem Solving - Paul Zeitz
>Chapter 2: Introduction to Entry-Level Mathematics, P. II
Linear Algebra and Its Applications - David C. Lay
Calculus of Several Variables - Serge Lang
Applied Differential Equations by Vladimir A. Dobrushkin
>Chapter 3: Introduction to Proofs and Survey of Higher-Level Mathematics
How to Think Like a Mathematician - Kevin Houston
How to Prove It - D. J. Velleman
Mathematics: Its Content, Methods and Meaning - A.D. Aleksandrov, A.N. Kolmogorov, & M.A. Lavrent'ev
>Chapter 4: Bringing It All Together: The First Test of Mathematical Maturity
Calculus Vol. I & II - T. M. Apostol
Analysis I & II - Terrance Tao
Thanks to all who have provided much needed advice and encouragement. I think I'll stick with this list for developing mathematical maturity and applied mathematics ability.