An Introduction to Number Theory by J. J. P. Veerman
An Introduction to Number Theory - Table of Contents
PART-I INTRODUCTION TO NUMBER THEORY
1. A Quick Tour of Number Theory
2. The Fundamental Theorem of Arithmetic
3. Linear Diophantine Equations
4. Number Theoretic Functions
5. Modular Arithmetic and Primes
6. Continued Fractions
PART-II CURRENTS IN NUMBER THEORY: ALGEBRAIC, PROBABILISTIC, AND ANALYTIC
7. Fields, Rings, and Ideals
8. Factorization in Rings
9. Ergodic Theory
10. Three Maps and the Real Numbers
11. The Cauchy Integral Formula
12. The Prime Number Theorem
PART-III TOPICS IN NUMBER THEORY
13. Primes in Arithmetic Progressions
14. The Birkhoff Ergodic Theorem
What You Will Learn in An Introduction to Number Theory
"An Introduction to Number Theory" by "J. J. P. Veerman" is a concise and accessible textbook that introduces the fundamentals of "number theory" for undergraduate students and self-learners. The book begins with basic concepts such as "divisibility", greatest common divisors, and prime numbers, establishing a strong foundation for more advanced topics. Veerman emphasizes clarity and logical progression, making it easier for readers to understand abstract mathematical concepts while providing a rigorous introduction to the subject.
The text covers essential topics such as "congruences", modular arithmetic, and basic Diophantine equations, blending theory with practical examples to reinforce understanding. Each chapter includes exercises designed to develop problem-solving skills and deepen comprehension of key principles. The presentation is structured to gradually guide learners from simple arithmetic properties to more complex number theory ideas, ensuring a smooth learning curve.
Veerman also highlights historical context and real-world applications, showing how number theory underpins fields such as "cryptography" and computer science. By integrating examples, exercises, and accessible explanations, the book serves both as a classroom resource and a self-study guide. With its focus on clarity, engagement, and practical relevance, Veerman’s textbook provides students with a solid grasp of the central ideas of number theory, preparing them for more advanced mathematical study.
Book Details & Specifications
Title:
An Introduction to Number Theory by J. J. P. Veerman
Publisher:
Portland State University
Year:
2022
Pages:
340
Type:
PDF
Language:
English
ISBN-10 #:
0321816196
ISBN-13 #:
978-0321816191
License:
CC BY-NC 4.0
Amazon:
Amazon
About the Author: J. J. P. Veerman
The author J. J. P. Veerman
is a mathematician and educator at "Radboud University Nijmegen", known for his work in "number theory" and teaching. He focuses on making abstract concepts clear and accessible, helping students build a strong understanding of fundamental mathematics. His work, "An Introduction to Number Theory", covers essential topics such as "primes", "divisibility", "modular arithmetic", and "congruences". The text provides a solid foundation for students and self-learners interested in exploring the theory and applications of number theory.
Read or Downloadable An Introduction to Number Theory
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