I've recently decided to start preparing for uni, so I figured I need to learn logic and some number theory. I picked up Burton's Elementary Number Theory and wasn't quite comfortable with it, seemed very dry throwing out expressions which I couldn't understand since I'm in still in high school.

Could you recommend me any books on subject which are written in a more approachable manner to a highschooler? I need basics: arithmetic, primes, divisibility, Diophantine, some Fermat maybe.

I also plan on taking some logic. Looking through Tarski's book a little it seemed broad, with not enough emphasis on mathematics. I need some recommendations on that one too. Thank you in advance :)

  • $\begingroup$ The book I suggest in this answer will catapult your mathematical maturity two years into the future. $\endgroup$ – Git Gud Apr 21 '14 at 23:25
  • $\begingroup$ For an introduction to logic with an emphasis on mathematical proofs, may I humbly suggest the tutorial that comes with proof-checking freeware. For a list of features, testimonials, a demo video and PC-based download, visit my website at dcproof.com. Also, an introductory book on calculus may be a better choice than number theory. $\endgroup$ – Dan Christensen Apr 25 '14 at 18:03

Peruse these:

  • William Leveque - Elementary Number Theory
  • Underwood Dudley - Elementary Number Theory
  • Oystein Ore - Invitation to Number Theory
  • Mathew Crawford, - Introduction to Number Theory, Art of Problem Solving
  • Joseph H. Silverman, A Friendly Introduction to Number Theory ($$$)

You can also find free notes online and the first three are Dover books with great prices.

For gentle logic books, see Logic and set theory textbook for high school.

Also learn to do proofs (cannot be stressed enough), see how to be good at proving?.

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  • $\begingroup$ found Underwood Dudley's on Gutenberg,seems pretty decent,definitely what was looking for :) $\endgroup$ – bruneleski Apr 21 '14 at 23:56

A great second book : "Computability and Logic" George S. Boolos & Richard C. Jeffrey

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