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Elementary number theory / Pio J. Arias.

By: Material type: TextTextPublisher: Burlington, Ontario : Toronto Academic Press, 2024Description: xvii, 241 pages : illustrations ; 25 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 9781774697917
Subject(s): DDC classification:
  • 23 512.72 Ar41e
LOC classification:
  • QA241 .A753 2024
Contents:
1. Introduction to number theory -- 1.1 Definition and brief history of number theory -- 1.2 Applications of number theory in various fields -- 1.3 Fundamentals of number theory -- 1.4 Diophantine equations -- 1.5 Number theory functions -- 1.6 Distribution of primes -- 1.7 Cryptography -- 1.8 Continued fractions -- 1.9 Algebraic number theory -- 1.10 Analytic number theory -- 1.11 Applications of number theory -- 1.12 Theorems in elementary number theory -- 1.13 Future directions in number theory research -- 1.13 Future directions in number theory research -- 2. Congruences -- 2.1 Direction of congruence -- 2.2 Applications of congruence in number theory -- 2.3 Basic properties of congruences -- 2.4 Linear congruence -- 2.5 Quadratic congruences -- 2.6 Systems of congruences -- 2.7 Wilson's theorem and Fermat's little theorem -- 3. Diophantine equations in number theory -- 3.1 Tools to deal with Diophantine equations -- 3.2 Method of infinite descent -- 3.3 Quadratic reciprocity -- 3.4 Factorization -- 4. Multiplicative functions -- 4.1 Definition and historical development -- 4.2 Motivation for studying multiplicative functions -- 4.3 Basic properties of multiplicative functions -- 4.4 Dirichlet convolution -- 4.5 Euler product formula -- 4.6 Mobius inversion formula -- 4.7 Applications of multiplicative functions -- 4.8 Future directions for research -- 5. Quadratic residues -- 5.1 Definition of quadratic residues and nonresidues -- 5.2 Applications of quadratic residues -- 5.3 Basic properties of quadratic residues -- 5.4 Quadratic residues modulo prime numbers -- 5.5 Quadratic residues modulo composite numbers -- 5.6 Quadratic residues and cryptography -- 5.7 Future directions in quadratic -- 6. Number theory and prime numbers -- 6.1 Number theory -- 6.2 Prime basics -- 6.3 Fundamental theorem of arithmetic -- 7. Continued fractions -- 7.1 Basic properties of continued fractions -- 7.2 The Euclidean algorithm and continued fractions -- 7.3 Applications of continued fractions -- 7.4 Continued fractions and quadratic irrationals -- 7.5 Advanced topics in continued fractions -- 8. Applications of elementary number theory -- 8.1 Cryptography -- 8.2 Coding theory -- 8.3 Modular arithmetic -- 8.4 Number sequences.
Summary: "This book serves as a comprehensive guide to Elementary Number Theory, a crucial branch of mathematics focusing on the properties and relationships of integers. The author, Dr. Pio J. Arias, covers a wide range of topics from the fundamentals to advanced theories, including divisibility, prime numbers, congruences, and Diophantine equations. The book explores the application of number theory in various fields such as cryptography, computer science, and physics, making it a valuable resource for students, scholars, and professionals interested in mathematics. Written in an engaging and informative style, it aims to provide a thorough understanding of number theory's essential principles and applications."
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Holdings
Item type Current library Shelving location Call number Copy number Status Date due Barcode
Books Books Main Library Circulation Section CIR 512.72 Ar41e 2024 (Browse shelf(Opens below)) 1-1 Available 030712
Browsing Main Library shelves, Shelving location: Circulation Section Close shelf browser (Hides shelf browser)
CIR 512.7 H550i 2018 Introduction to number theory CIR 512.7 W322n 2014 Number theory : a historical approach / CIR 512.7 W322n 2014 Number theory : a historical approach / CIR 512.72 Ar41e 2024 Elementary number theory / CIR 512.72 Ef44e 2022 Elementary number theory / CIR 512.75 G292 2016 Geometry of numbers. CIR 512.9 C639c 2010 College algebra

Includes bibliographical references and index.

1. Introduction to number theory -- 1.1 Definition and brief history of number theory -- 1.2 Applications of number theory in various fields -- 1.3 Fundamentals of number theory -- 1.4 Diophantine equations -- 1.5 Number theory functions -- 1.6 Distribution of primes -- 1.7 Cryptography -- 1.8 Continued fractions -- 1.9 Algebraic number theory -- 1.10 Analytic number theory -- 1.11 Applications of number theory -- 1.12 Theorems in elementary number theory -- 1.13 Future directions in number theory research -- 1.13 Future directions in number theory research -- 2. Congruences -- 2.1 Direction of congruence -- 2.2 Applications of congruence in number theory -- 2.3 Basic properties of congruences -- 2.4 Linear congruence -- 2.5 Quadratic congruences -- 2.6 Systems of congruences -- 2.7 Wilson's theorem and Fermat's little theorem -- 3. Diophantine equations in number theory -- 3.1 Tools to deal with Diophantine equations -- 3.2 Method of infinite descent -- 3.3 Quadratic reciprocity -- 3.4 Factorization -- 4. Multiplicative functions -- 4.1 Definition and historical development -- 4.2 Motivation for studying multiplicative functions -- 4.3 Basic properties of multiplicative functions -- 4.4 Dirichlet convolution -- 4.5 Euler product formula -- 4.6 Mobius inversion formula -- 4.7 Applications of multiplicative functions -- 4.8 Future directions for research -- 5. Quadratic residues -- 5.1 Definition of quadratic residues and nonresidues -- 5.2 Applications of quadratic residues -- 5.3 Basic properties of quadratic residues -- 5.4 Quadratic residues modulo prime numbers -- 5.5 Quadratic residues modulo composite numbers -- 5.6 Quadratic residues and cryptography -- 5.7 Future directions in quadratic -- 6. Number theory and prime numbers -- 6.1 Number theory -- 6.2 Prime basics -- 6.3 Fundamental theorem of arithmetic -- 7. Continued fractions -- 7.1 Basic properties of continued fractions -- 7.2 The Euclidean algorithm and continued fractions -- 7.3 Applications of continued fractions -- 7.4 Continued fractions and quadratic irrationals -- 7.5 Advanced topics in continued fractions -- 8. Applications of elementary number theory -- 8.1 Cryptography -- 8.2 Coding theory -- 8.3 Modular arithmetic -- 8.4 Number sequences.

"This book serves as a comprehensive guide to Elementary Number Theory, a crucial branch of mathematics focusing on the properties and relationships of integers. The author, Dr. Pio J. Arias, covers a wide range of topics from the fundamentals to advanced theories, including divisibility, prime numbers, congruences, and Diophantine equations. The book explores the application of number theory in various fields such as cryptography, computer science, and physics, making it a valuable resource for students, scholars, and professionals interested in mathematics. Written in an engaging and informative style, it aims to provide a thorough understanding of number theory's essential principles and applications."

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