This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated...

Covers classical modular forms. This book is suitable to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations.

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated...

This is a tutorial explaining how to use the free and open source mathematical software package Sage (version 6.1.1). Sage and this can be downloaded free from the website: http: //www.sagemath.org/. Copyright: (c) 2014 Creative Commons Attribution-ShareAlike 3.0. Royalties go directly to the Sage Foundation.

This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.