Advanced Number Theory with Applications

Richard A. Mollin

ISBN 10: 1138113255 / ISBN 13: 9781138113251

Published by Chapman And Hall/CRC, 2017

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - By covering a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory, this text provides the most up-to-date and comprehensive material for a second course in this field. With numerous examples and exercises, it begins with coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density, and primes. The author then applies these tools to Diophantine equations, before developing elliptic curves and modular forms. He also presents Fermat's Last Theorem, the ABC conjecture, and sieve methods.

Seller Inventory # 9781138113251

Bibliographic Details

• Title: Advanced Number Theory with Applications
• Publisher: Chapman And Hall/CRC
• Publication Date: 2017
• Language: English
• ISBN 10: 1138113255
• ISBN 13: 9781138113251
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 234W x 156H x 26D millimeters 234 millimeters width by 156 millimeters height by 26 millimeters depth
• Weight: 726 grams

About this title

Synopsis

Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and more than 1,500 entries in the index so that students can easily cross-reference and find the appropriate data.

With numerous examples throughout, the text begins with coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density, and primes in arithmetic progression. It then applies these tools to Diophantine equations, before developing elliptic curves and modular forms. The text also presents an overview of Fermat’s Last Theorem (FLT) and numerous consequences of the ABC conjecture, including Thue–Siegel–Roth theorem, Hall’s conjecture, the Erdös–Mollin-–Walsh conjecture, and the Granville–Langevin Conjecture. In the appendix, the author reviews sieve methods, such as Eratothesenes’, Selberg’s, Linnik’s, and Bombieri’s sieves. He also discusses recent results on gaps between primes and the use of sieves in factoring.

By focusing on salient techniques in number theory, this textbook provides the most up-to-date and comprehensive material for a second course in this field. It prepares students for future study at the graduate level.

About the Author

Richard A. Mollin is a professor in the Department of Mathematics and Statistics at the University of Calgary. In the past twenty-three years, Dr. Mollin has founded the Canadian Number Theory Association and has been awarded six Killam Resident Fellowships. Over the past thirty-three years, he has written more than 190 publications.