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I am looking for books for the full high school maths curriculum, just to refresh myself (it's been years). it must have questions & solutions.

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I think you posted this question earlier today and I had about a three paragraph response with a ton of advice but then you deleted the post (apologies if that wasn't you). So... here is the abbreviated version. Read the following books,

If you are interested in getting access to higher mathematics afterwards I recommend the following book by Chartrand, Polimeni, and Zhang. It is an incredible introduction to proofs and various areas of mathematics.

"Mathematical Proofs: A Transition to Advanced Mathematics" by Gary Chartrand, Albert D. Polimeni, and Ping Zhang. [Amazon Link]

There is an entire chapter devoted to each of the following:

  • Communicating Mathematics
  • Naive Set Theory
  • Logic
  • Direct Proof
  • Proof by Contrapositive
  • Existence and Proof by Contradiction
  • Mathematical Induction (and Strong Induction)
  • Equivalence Relations (Equivalence Classes, Congruence Modulo n, Modular arithmetic)
  • Functions (Bijective, Inverse, Permutations)
  • Set Theory (up to Schroder-Bernstein Theorem and the Continuum Hypothesis)
  • Number Theory
  • Calculus (Limits, Infinite Series, Continuity, Differentiability)
  • Group Theory (up to Isomorphic Groups)

With Three Additional Chapters online covering:

  • Ring Theory
  • Linear Algebra
  • Topology

That should keep you busy for a while, and after reading through Chartrand/Polimeni/Zhang, you will know what area of mathematics you are more interested in or if you still want to learn more!

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  • $\begingroup$ No problem! Hopefully you actually get through this material. I really encourage you to try and do it. If you have any conceptual troubles or questions about a specific exercise remember that you can always ask for help this site! $\endgroup$ – Samuel Reid Jan 13 '12 at 6:41
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    $\begingroup$ It should be fine, I used to be an "ace", but its just been sooooo long, planning to get a mathematical degree and dont want to look like a complete fool :) heheh $\endgroup$ – cstruter Jan 13 '12 at 6:49

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