I've learned math long time ago, but I hardly remember anything.
I really want to relearn by reading good books, from the ground up.
Workbooks didn't really help.
Other posts recommend different books. So a list of best books feels helpful from Pre-algebra to calculus and beyond. Would you be so kind to add which others you recommend. English is not my native language; please excuse typing errors.
Children
- The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger
- Alice in Puzzle-Land by Raymond M. Smullyan
- The Phantom Tollbooth by Norton Juster
- …
Beginner
- What Is Mathematics? An Elementary Approach to Ideas and Methods by Richard Courant
- Mathematics: Its Content, Methods and Meaning (Dover Books on Mathematics) by A. D. Aleksandrov
- Mathematics: A very short introduction by Timothy Gowers
- …
Basic Math
- Basic Mathematics by Serge Lang 1998 (high school or college students.)
- …
Pre-Algebra
- Pre-Algebra DeMYSTiFieD by Allan Bluman
- …
Algebra
- Algebra by Israel M. Gelfand 2013
- A book of Abstract Algebra by Charles Pinter?
- …
Algebra II
- …
Trigonometry
- Trigonometry by I.M. Gelfand 2013
- …
Pre-Calculus
- …
Calculus
- Calculus by Michael Spivak
- …
Problem Solving
- https://en.wikipedia.org/wiki/Yakov_Perelman#Books
- How to Solve it by Polya's
- Techniques in Problem Solving by Steven George Krantz
- The Art and Craft of Problem Solving by Paul Zeitz
- How to Prove It: A Structured Approach by Daniel J. Velleman 2006
- Problem-Solving Strategies (Problem Books in Mathematics) by Arthur Engel
- Number Theory (Dover Books on Mathematics) by George E. Andrews
- Some of the books in the Art of Problem Solving series at www.ArtofProblemSolving.com
Best Answer
For "highschool level" you might try the Art of Problem Solving books (they have materials for students in elementary school now as well if those are too advanced). I also recommend the following books:
If you're interested in more advanced problem solving/olympiad material, check out this page, and this page. You needn't read all of this stuff, but pick what looks good and what you have time for.
For more advanced stuff (what most consider undergraduate studies), you might check out the following to get started:
These will get you started. I tried to choose books that are challenging, cheap/free, and have lots of problems.