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Introduction to Number Theory: A Computational Approach

Lusine Sukiasyan and Charles Pooh

This book offers a friendly introduction to number theory from a computational perspective. It starts with the basics, such as divisibility, prime numbers and congruences, and then gradually progresses to more advanced topics like continued fractions, Diophantine equations and cryptography. Abstract ideas are presented in a way that makes them concrete and approachable, with examples that can be explored computationally.

Each chapter is thoughtfully structured to build on the previous ones, and the book is organized into seven key parts, each accompanied by exercises (with solutions) that encourage independent problem solving and verification of results. Readers can download the free interactive ebook version to engage directly with live Wolfram Language code. This book is ideal for students, self-learners and anyone curious about the underlying arithmetic of modern mathematics.

Notebooks can be opened in Mathematica or the free Wolfram Player.

Information & Media Inquiries

  • Title: Introduction to Number Theory: A Computational Approach
  • Authors: Lusine Sukiasyan and Charles Pooh
  • Paperback: $29.95  202 pages
  • Kindle: $9.95  202 pages
  • Wolfram Notebooks: download free
  • Publisher: Wolfram Media, Inc.
  • Publication Date: May 19, 2026
  • ISBN-13: 978-1-57955-115-5 (paperback)
  • ISBN-13: 978-1-57955-116-2 (Kindle)
  • ISBN-13: 978-1-57955-114-8 (Wolfram Notebooks)

Publicity and Interviews: publishing@wolfram.com

Trim Size: 7" x 10"

Non-fiction

Distribution by Ingram

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Contents

  • Preface
Introduction
  • What Is Number Theory?
  • Integers: The Basics
  • Primes and Composites
  • Part 1 Exercises
Primes and Divisibility
  • Prime Factorization
  • Multiples and Divisors
  • Greatest Common Divisor
  • Part 2 Exercises
Modular Arithmetic
  • Congruences
  • Modular Arithmetic
  • Chinese Remainder Theorem
  • Part 3 Exercises
Continued Fractions
  • Real Number Representations
  • Continued Fractions
  • Best Rational Approximations
  • Part 4 Exercises
Diophantine Equations
  • Diophantine Equations
  • Linear Diophantine Equations
  • Diophantine Equations of Degree 2
  • Part 5 Exercises
Cryptography
  • Cryptography
  • The RSA Algorithm
  • Part 6 Exercises
Additional Topics
  • Primality Testing: Miller–Rabin
  • Factorization: Pollard's Rho
  • Diophantine Equations: Hilbert's Tenth Problem
  • The Riemann Zeta Function
  • Special Numbers
  • Numeral Systems
  • Part 7 Exercises

About the Authors

Lusine Sukiasyan is a Kernel Developer in discrete computation at Wolfram. She holds a BSc in informatics and applied mathematics and an MSc in numerical analysis and mathematical modeling, both from Yerevan State University. Her work spans number theory, computational geometry and calculus, and she also contributes to the development of educational content for Wolfram that helps make advanced mathematics more accessible and engaging.

Charles Pooh is the Manager of Discrete Computation at Wolfram, where he works in research and development, focusing on algorithms for Wolfram Language. He holds a postgraduate diploma in mathematics from the International Centre for Theoretical Physics and a PhD in mathematics from the University of Georgia.