Book published by American Mathematical Society - Primality Testing for Beginners
Professor Lasse Rempe-Gillen and co-author Rebecca Waldecker have had their book entitled "Primality Testing for Beginners" published by the American Mathematical Society.
In 2002, Agrawal, Kayal and Saxena announced the stunning result that there is a deterministic polynomial-time algorithm to test whether a number is prime. Their proof (“Primes is in P”, Annals of Mathematics 160 (2004), 781-793) amazingly requires nothing beyond a Chebyshev-type inequality on the prime number function and some facts from undergraduate commutative algebra.
The goal of their book – an English adaptation of their 2009 edition in German – is to completely present this contemporary mathematical result without requiring any background beyond basic arithmetic and an aptitude for logical thought. They carefully develop the required background in elementary number theory (starting with the induction principle) and the theory of computation before presenting a complete and rigorous proof of the AKS theorem. As such, the book is intended to be accessible to good beginning mathematics undergraduates and motivated high-school students.
The webpage for the book is http://www.ams.org/bookstore-getitem/item=stml-70 .