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[NulledPremium.com] Number Theory Revealed
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Book details Hardcover: 587 pages Format: pdf Size: 9 MB Publisher: American Mathematical Society (November 22, 2019) Language: English ISBN-10: 1470441586 ISBN-13: 978-1470441586
Number Theory Revealed: 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 Revealed: 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.
This book is part of Number Theory Revealed: The Series.
About the Author:
Andrew Granville is the Canada Research Chair in Number Theory at the University of Montreal and professor of mathematics at University College London. He has won several international writing prizes for exposition in mathematics, including the 2008 Chauvenet Prize and the 2019 Halmos-Ford Prize, and is the author of Prime Suspects (Princeton University Press, 2019), a beautifully illustrated graphic novel murder mystery that explores surprising connections between the anatomies of integers and of permutations.
Readership:
Undergraduate and graduate students interested in introductory number theory.
Table of Contents
Preliminary Chapter on Induction The Euclidean algorithm Congruences The basic algebra of number theory Multiplicative functions The distribution of prime numbers Diophantine problems Power residues Quadratic residues Quadratic equations Square roots and factoring Rational approximations to real numbers Binary quadratic forms The anatomy of integers Counting integral and rational points on curves, modulo p Combinatorial number theory The p-adic numbers Rational points on elliptic curves
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