# Introduction to Number Theory

The book interweaves the theoretical development of the material with Mathematica® and MapleTM calculations while giving brief tutorials on the software in the appendices. ## Introduction to Number Theory

One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topics. This classroom-tested, student-friendly text covers a wide range of subjects, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments that include cryptography, the theory of elliptic curves, and the negative solution of Hilbert’s tenth problem. The authors illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems, such as congruences in the ISBN system, modular arithmetic and Euler’s theorem in RSA encryption, and quadratic residues in the construction of tournaments. The book interweaves the theoretical development of the material with Mathematica® and MapleTM calculations while giving brief tutorials on the software in the appendices. Highlighting both fundamental and advanced topics, this introduction provides all of the tools to achieve a solid foundation in number theory.

### More Books: Language: en
Pages: 536
Authors: Anthony Vazzana, Martin Erickson, David Garth
Categories: Mathematics
Type: BOOK - Published: 2007-10-30 - Publisher: CRC Press

One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array Language: en
Pages: 264
Authors: Richard Michael Hill
Categories: Mathematics
Type: BOOK - Published: 2017-12-04 - Publisher: World Scientific Publishing Company

Introduction to Number Theory is dedicated to concrete questions about integers, to place an emphasis on problem solving by students. When undertaking a first course in number theory, students enjoy actively engaging with the properties and relationships of numbers. The book begins with introductory material, including uniqueness of factorization of Language: en
Pages: 297
Authors: G. Everest, Thomas Ward
Categories: Mathematics
Type: BOOK - Published: 2007-05-21 - Publisher: Springer Science & Business Media

Includes up-to-date material on recent developments and topics of significant interest, such as elliptic functions and the new primality test Selects material from both the algebraic and analytic disciplines, presenting several different proofs of a single result to illustrate the differing viewpoints and give good insight Language: en
Pages: 212
Authors: Daniel E. Flath
Categories: Number theory
Type: BOOK - Published: 2018-09-27 - Publisher: American Mathematical Soc.

Growing out of a course designed to teach Gauss's Disquisitiones Arithmeticae to honors-level undergraduates, Flath's Introduction to Number Theory focuses on Gauss's theory of binary quadratic forms. It is suitable for use as a textbook in a course or self-study by advanced undergraduates or graduate students who possess a basic Language: en
Pages: 426
Authors: Anthony Vazzana, David Garth
Categories: Mathematics
Type: BOOK - Published: 2015-11-18 - Publisher: CRC Press

Introduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves, and the negative solution of Hilbert's tenth