num_pages: 587
description: Number Theory A Masterclass acquaints enthusiastic students with the Queen of Mathematics . The text offers a fresh take on congruences power residues quadratic residues primes and Diophantine equations and presents hot topics like cryptography factoring and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod p and modern twists on traditional questions like the values represented by binary quadratic forms the anatomy of integers and elliptic curves. This Masterclass edition contains many additional chapters and appendices not found in Number Theory An Introduction highlighting beautiful developments and inspiring other subjects in mathematics (like algebra). This allows instructors to tailor a course suited to their own (and their students') interests. There are new yet accessible topics like the curvature of circles in a tiling of a circle by circles the latest discoveries on gaps between primes a new proof of Mordell's Theorem for congruent elliptic curves and a discussion of the abc-conjecture including its proof for polynomials.
language: English
title: Number Theory Revealed: A Masterclass
publisher: American Mathematical Society