Recommend books for learning math from elementary school?

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.


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 :)