Introductory Number Theory Textbook (Cryptology) by Jonathan Poritz
Introductory Number Theory Textbook (Cryptology) - Table of Contents
1. Well-Ordering and Division
2. Congruences
3. Prime Numbers
4. Cryptology
5. Indices = Discrete Logarithms
What You Will Learn in Introductory Number Theory Textbook (Cryptology)
"Yet Another Introductory Number Theory Textbook (Cryptology Emphasis Version)" by "Jonathan A. Poritz" is a comprehensive and accessible guide to "number theory" designed for undergraduate students and beginners in mathematics. The book introduces fundamental concepts such as "congruences", prime numbers, division, and well-ordering in a clear, step-by-step manner. Each topic is explained with precision, providing a solid foundation for understanding the structures and patterns underlying integers. Poritz emphasizes intuitive reasoning alongside formal definitions, making the subject approachable while maintaining mathematical rigor.
The textbook uniquely integrates "cryptology" throughout, showing how abstract number theory principles apply to real-world security problems. Topics like modular arithmetic, Euler’s theorem, and primitive roots are presented not just theoretically but also in the context of building cryptographic systems. Students learn how these mathematical ideas underpin essential digital security protocols, including "RSA" and "Diffie-Hellman" key exchange. This combination of theory and application helps learners see the relevance of mathematics in modern technology and prepares them for advanced studies or practical implementation.
In addition to clear explanations, the book includes examples, exercises, and problem sets designed to reinforce learning. By connecting core number theory concepts with practical cryptographic applications, Poritz provides a text that is both educational and engaging. It is an ideal resource for students, instructors, and self-learners interested in "cryptography", number theory, and mathematical problem solving.
Book Details & Specifications
Title:
Introductory Number Theory Textbook (Cryptology) by Jonathan Poritz
Publisher:
Jonathan Poritz
Year:
2015
Pages:
154
Type:
PDF
Language:
English
ISBN-10 #:
0669627038
ISBN-13 #:
978-0669627039
License:
CC BY-SA 4.0
Amazon:
Amazon
About the Author: Jonathan Poritz
The author
Jonathan Poritz
is an American mathematician and educator at "Colorado State University – Pueblo", known for creating accessible, open educational resources in mathematics. He focuses on making complex concepts clear while connecting theory to real-world applications. His work, "Introductory Number Theory Textbook (Cryptology)", introduces fundamental "number theory" concepts such as "prime numbers", congruences, and well-ordering, with practical applications in "cryptology". Topics like the "RSA cryptosystem" and Diffie-Hellman key exchange are explained clearly for undergraduate students.
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