Number Theory Revealed: A Masterclass

by Andrew Granville

Number Theory A Masterclass presents 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, Fermat's Last Theorem for polynomials, and modern twists on traditional questions. This Masterclass edition contains many additional chapters and appendices not found in Number Theory An Introduction. It is ideal for instructors who wish to tailor a class to their own interests and gives well-prepared students further opportunities to challenge themselves and push beyond core number theory concepts, serving as a springboard to many current themes in mathematics. Additional topics in A Masterclass include the curvature of circles in a tiling of a circle by circles, the latest discoveries on gaps between primes, magic squares of primes, a new proof of Mordell's Theorem for congruent elliptic curves, as well as links with algebra, analysis, cryptography, and dynamics.

Genres: Mathematics

587 pages, Paperback

Published September 23, 2020

Reviews

[TH Williamson · Rating 3 out of 5]

I honestly don’t recommend this one unless you really can’t find anything else, not because it’s terrible, but because there has to be a better, more readable option than this book. While Granville presents some sections clearly and lucidly, other sections seem to have dubious motivation and logical lines of thought that can be quite difficult to follow. That being said, I believe that if this book were better organized, color coded, and if more thought were given to the visual presentation, it could be much more readable. All in all, many sections can be quite illuminating, but those are sometimes overshadowed by confusing and obscure chapters, often on unfortunately fundamental results and theorems. I may give it another try some day and properly review it again, but until then, try to find a more visually compelling and clearer option.