Discrete Mathematics Free Books

Algebraic Combinatorics on Words - M. Lothaire
"Algebraic Combinatorics on Words" explains how "combinatorics on words" studies patterns in strings and sequences. Written by "M. Lothaire", the book explores "formal languages" and "algebraic structures" used in advanced mathematics and computer science.

An Introduction to Number Theory - J. J. P. Veerman
This is an easy-to-follow guide to "modular arithmetic", "congruences", and "prime numbers". It combines clear explanations with interactive examples using SageMath, letting students explore number theory concepts hands-on while showing practical applications like cryptography in a simple, engaging way.

An Introduction to the Theory of Numbers - Leo Moser
This is a clear and engaging textbook that introduces the fundamentals of "number theory". It covers key topics like "prime numbers", "congruences", and Diophantine equations, using examples and problems to build understanding. Written for students new to the subject, it makes core number theory concepts accessible and meaningful.

Computational Number Theory & Algebra - Victor Shoup
This textbook covers "number theory", "abstract algebra", and "cryptography". The book explains integers, congruences, finite fields, elliptic curves, and discrete logarithms, emphasizing algorithms and practical computation. It provides clear examples and exercises, making advanced concepts accessible for students and computer science professionals.

Explorations in Algebraic Graph Theory - Chris Godsil
This text introduces how "algebra" helps understand "graphs". Using "matrices" and SageMath software, the book explains graph properties, adjacency, and incidence in a hands-on way. Readers can experiment with calculations, visualizations, and learn practical connections between algebra and graph theory concepts.

Groups as Graphs - Kandasamy & Smarandache
This text explains how "group theory" concepts can be visualized using "graph theory" by representing group elements as vertices and relations as edges. These "identity graphs" help reveal algebraic properties in an intuitive way and extend ideas to other structures like rings and semigroups for better mathematical understanding.

Introductory Elementary Number Theory - Wissam Raji
This is an easy-to-follow guide to "number theory". It teaches "prime numbers", divisibility, and "congruences" with clear explanations and exercises, helping students and beginners understand the basic properties of integers and build a strong foundation in mathematics.

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