Introduction to Number Theory

Regular price €69.99
A01=Anthony Vazzana
A01=David Garth
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Analytic Number Theory
Arithmetic Functions
Author_Anthony Vazzana
Author_David Garth
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Category1=Non-Fiction
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Category=PBV
Chinese Remainder Theorem
Congruence X2
Congruences
Continued Fraction
Continued Fraction Expansion
Continued Fractions
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Cryptography
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Diophantine Equation
Diophantine Equations
Divisibility
Elliptic Curves
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Euclidean Algorithm
Euler’s Theorem
Form 4k
Gaussian Integers
Greatest Common Divisor
Hilbert’s Tenth Problem
ISBN System
Language_English
Large Primes
Linear Diophantine Equation
Maple
Mathematica
Modular Arithmetic
Number Theory
Odd Prime
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Pell Equation
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Prime
Prime Divisors
Prime Number Theorem
Primes
Primitive Pythagorean Triple
Primitive Root Modulo
Primitive Roots
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Pythagorean Triple
Quadratic Irrational
Quadratic Irrationals
Quadratic Residues
Quadratic Residues Modulo
Residue Class
RSA Encryption
RSA Encryption Scheme
SageMath
Simple Continued Fraction
softlaunch
Special Congruences
Sums of Squares
Tournament Construction
Twin Primes Conjecture

Product details

  • ISBN 9781032920085
  • Weight: 790g
  • Dimensions: 156 x 234mm
  • Publication Date: 14 Oct 2024
  • Publisher: Taylor & Francis Ltd
  • Publication City/Country: GB
  • Product Form: Paperback
  • Language: English
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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 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.

Ideal for a one- or two-semester undergraduate-level course, this Second Edition:

  • Features a more flexible structure that offers a greater range of options for course design
  • Adds new sections on the representations of integers and the Chinese remainder theorem
  • Expands exercise sets to encompass a wider variety of problems, many of which relate number theory to fields outside of mathematics (e.g., music)
  • Provides calculations for computational experimentation using SageMath, a free open-source mathematics software system, as well as Mathematica® and Maple™, online via a robust, author-maintained website
  • Includes a solutions manual with qualifying course adoption

By tackling both fundamental and advanced subjects—and using worked examples, numerous exercises, and popular software packages to ensure a practical understanding—Introduction to Number Theory, Second Edition instills a solid foundation of number theory knowledge.

Martin Erickson (1963-2013) received his Ph.D in mathematics in 1987 from the University of Michigan, Ann Arbor, USA, studying with Thomas Frederick Storer. He joined the faculty in the Mathematics Department of Truman State University, Kirksville, Missouri, USA, when he was twenty-four years old, and remained there for the rest of his life. Professor Erickson authored and coauthored several mathematics books, including the first edition of Introduction to Number Theory (CRC Press, 2007), Pearls of Discrete Mathematics (CRC Press, 2010), and A Student's Guide to the Study, Practice, and Tools of Modern Mathematics (CRC Press, 2010).

Anthony Vazzana received his Ph.D in mathematics in 1998 from the University of Michigan, Ann Arbor, USA. He joined the faculty in the Mathematics Department of Truman State University, Kirksville, Missouri, USA, in 1998. In 2000, he was awarded the Governor's Award for Excellence in Teaching and was selected as the Educator of the Year. In 2002, he was named the Missouri Professor of the Year by the Carnegie Foundation for the Advancement of Teaching and the Council for Advancement and Support of Education.

David Garth received his Ph.D in mathematics in 2000 from Kansas State University, Manhattan, USA. He joined the faculty in the Mathematics Department of Truman State University, Kirksville, Missouri, USA, in 2000. In 2005, he was awarded the Golden Apple Award from Truman State University's Theta Kappa chapter of the Order of Omega. His areas of research include analytic and algebraic number theory, especially Pisot numbers and their generalizations, and Diophantine approximation.