Recommend books for learning math from elementary school?

Question

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

Answer 1

well I don't know about the books but you should try www.khanacademy.com while reading those books, to better grasp all the concepts :)

Answer 2

For precalculus (and trigonometry, since it's included in precalculus) I recommend Precalculus: Graphs and Models A Right Trangle Approch 5th Edition by Bittinger, Beecher, Ellenbogen, Penna. This book includes lots of real life application problems throughout the chapters.

For calculus I recommend Calculus by James Stewart. It's used for mathematics education all over the world, and speaking from my own experience it's a very good book. It includes a lot of problems to practice with, and after each chapter a real life application problem. There are two versions: a single variable version, a multivariable version and a version that includes both. You have to begin with single variable calculus, so make sure you buy the right one.

Answer 3

For a good understanding of basic algebra, I recommend you study the book "College Algebra" (2014) by Paliogiannis.

Answer 4

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:

• Algebra
• Trigonometry
• The Method of Coordinates
• Functions and Graphs
• Sequences, Combinations, and Limits
• Kiselev's Geometry 1 and also 2
• Lines and Curves

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:

• Calculus of One Variable by Kitchen (if you can find it; otherwise, check out Apostol, Hardy, or Spivak)
• Linear Algebra by Berberian
• Advanced Calculus by Loomis and Sternberg (very difficult, but awesome!)
• Set Theory and Metric Spaces by Kaplansky
• Real Analysis by Carothers (Rudin is an easier alternative, but this book is fantastic!)
• Elementary Topology by Viro
• Elements of Abstract Algebra by Clark (Dummit & Foote is good too)

These will get you started. I tried to choose books that are challenging, cheap/free, and have lots of problems.