7 Best Books on Discrete Math for Beginners in 2021

The word discrete means ‘separate.’ Discrete math is distinct from the continuous math taught in algebra and calculus. Discrete mathematics is important for computer scientists because of computer’s binary nature.

The word discrete means ‘separate.’ Discrete math is distinct from the continuous math taught in algebra and calculus. Discrete mathematics is important for computer scientists because of computer’s binary nature.

The world of mathematical logic is wide open to help with technological advancement. Discrete mathematics forms the mathematical foundation of computer and information science. 

In this article, let’s discuss the best books for learning discrete mathematics for beginners. Each book review highlights the taste of the book, the contents covered, and how it can benefit you.

 

Why Learn Discrete Mathematics?

Let's have a look at top reasons to learn this fascinating subject:

  • Essential for Computer Science: Discrete Mathematics is the backbone of Computer Science. It is the mathematical language of computer science. Modern computer science is built almost entirely on discrete mathematics.

  • Important for Big Data: Discrete math plays a significant role in big data analytics. It produces a collection of powerful methods. It also includes mathematical tools for understanding and managing very high-dimensional data, inference systems for drawing sound conclusions from large and noisy data sets, and algorithms for scaling computations up to very large sizes.

  • Not Too Challenging: Discrete mathematics is simple to understand 

  • Enjoyable to Learn: Discrete math is fun. Most learners find discrete math more fun than algebra or geometry.

With all this in mind, one thing is crystal clear: learning discrete mathematics is valuable for beginners! So, let’s get started!

 

What Makes The Best Discrete Mathematics Books? 

Here are our criteria for the selection of the books:

  • The book should contain a variety of instructional materials, including exercises, examples, questions, learning activities, and other features that promote the reader's engagement and active learning.

  • It uses clear, precise, and easy-to-understand language.

  • Content must be up-to-date and should thoroughly teach and explain the basic concepts of Discrete Mathematics.

  • Contain assignments for practice and hands-on experience.

  • The book should have a clear layout and strictly focus on Discrete Mathematics.

 

Best Books on Discrete Mathematics

Here are some of the best Discrete Mathematics books for beginners:

 

1. Best Book for Active Learners: Discrete Mathematics, 8th Edition

Discrete Mathematics by Richard Johnsonbaugh gives a comprehensive introduction to the topics of Discrete Math. It provides computer science applications in a clear and high-quality format. 

It also includes 4500 exercise sets featuring a large number of applications, especially applications to computer science. They are designed to allow your students to master what they have learned before moving on to more difficult material. 

The topics covered in the book are:

  • Sets and logic

  • Proofs

  • Functions, sequences, and relations

  • Algorithms

  • Introduction to number theory

  • Counting methods and the pigeonhole principle

  • Recurrence relations

  • Graph theory

  • Trees

  • Network models

  • Boolean algebras and combinatorial circuits

  • Automata, grammars, and languages

  • Computational geometry.

By the end of this book, you will be comfortable enough to solve any Discrete Mathematics problem.

 

2. Best Book for Step-by-step Learners: Discrete Mathematics and Its Applications

Discrete Mathematics and its Applications by Kenneth Rosen is a focused introduction to the primary themes in discrete mathematics. This book is flexible and comprehensive and has an experienced pedagogical style.

  • Chapter 1 talks about Foundations, Logic, and Proofs

  • Chapter 2 talks about Basic Structures: Sets, Functions, Sequences, Sums, Matrices

  • Chapter 3 covers Algorithms

  • Chapter 4 covers Number Theory and Cryptography

  • Chapter 5 covers Induction and Recursion

  • Chapter 6 talks about Counting

  • Chapter 7 covers Discrete Probability

  • Chapter 8 covers Advanced Counting Techniques

  • Chapter 9 covers Relations

  • Chapter 10 talks about Graphs

  • Chapter 11 talks about Trees

  • Chapter 12 covers Boolean Algebra

  • Chapter 13 covers Modeling Computation

The book presents a precise, relevant, comprehensive approach to mathematical concepts. The book is recommended not just for beginners but for anyone who wants to polish their Discrete Mathematics concepts.

 

3. Best Book for Completionists: Essential Discrete Mathematics for Computer Science

Essential Discrete Mathematics for Computer Science by Harry Lewis and Rachel Zax is the ideal introductory book for undergraduate courses, high school courses, distance education, and self-study. It gives the reader an essential introduction to discrete mathematics.

This book is filled with practical information and compiled the contents in a well-organized way. This flexible book features thirty-one short chapters that discuss one major topic each. Each chapter is accompanied by a concise summary and a set of exercises.

  • Chapter 1 talks about the Pigeonhole Principle

  • Chapter 2 covers Basic Proof Techniques

  • Chapter 3 talks about Proof by Mathematical Induction

  • Chapter 4 covers Strong Induction

  • Chapter 5 covers Sets

  • Chapter 6 talks about Relations and Functions

  • Chapter 7 covers Countable and Uncountable Sets

  • Chapter 8 talks about Structural Induction

  • Chapter 9 covers Propositional Logic

  • Chapter 10 covers Normal Forms

  • Chapter 11 talks about Logic and Computers

  • Chapter 12 covers Quantificational Logic

  • Chapter 13 talks about Directed Graphs

  • Chapter 14 covers Digraphs and Relations

  • Chapter 15 covers States and Invariants

  • Chapter 16 talks about Undirected Graphs

  • Chapter 17 covers Connectivity

  • Chapter 18 covers Coloring

  • Chapter 19 talks about Finite Automata

  • Chapter 20 covers Regular Languages

  • Chapter 21 covers Order Notation

  • Chapter 22 talks about Counting

  • Chapter 23 covers Counting Subsets

  • Chapter 24 covers Series

  • Chapter 25 talks about Recurrence Relations

  • Chapter 26 covers Probability

  • Chapter 27 covers Conditional Probability

  • Chapter 28 talks about Bayes’ Theorem

  • Chapter 29 covers Random Variables and Expectation

  • Chapter 30 talks about Modular Arithmetic

  • Chapter 31 covers Public Key Cryptography

The book aims to teach mathematical reasoning as well as concepts and skills. It includes more than 300 exercises. The book will simply polish your discrete mathematics concepts from good to outstanding!

 

4. Best Book for Serious Learners: Journey into Discrete Mathematics

Journey into Discrete Mathematics by Owen D. Byer, Deirdre L. Smeltzer, and Kenneth L. Wants is a clear and self-contained introduction to discrete mathematics. It promotes the development of a mathematical mindset and prepares readers for further study.

The book is divided into thirteen chapters and the main topics covered are:

  • Mini-Theories

  • Logic and Sets

  • Logic and Proof

  • Relations and Functions

  • Induction

  • Number Theory

  • Counting

  • Graph Theory

  • Invariants and Monovariants

Many of the core topics, including counting, number theory, and graph theory are discussed twice in a deeper perspective. 

The topics are explained attractively and engagingly. The book helps the reader to think like a mathematician through the exposition and the problems provided.

 

5. Best Book for Hands-on Learners: Discrete Mathematics for Computer Science

Discrete Mathematics for Computer Science by David Liben-Nowell provides a comprehensive introduction to discrete mathematics. The book gives a strong emphasis on the relationship between the discrete mathematics concepts and their application to computer science.

The book is divided into twelve chapters and includes the following contents:

  • Chapter 1 gives an introduction to the book 

  • Chapter 2 talks about Basic Data Types 

  • Chapter 3 covers Logic

  • Chapter 4 talks about Proofs and error-correcting codes

  • Chapter 5 covers Mathematical Induction

  • Chapter 6 talks about the Analysis of Algorithms

  • Chapter 7 covers Number Theory and Cryptography 

  • Chapter 8 covers Relations

  • Chapter 9 talks about Counting, Combinations, and Permutations

  • Chapter 10 talks about Probability

  • Chapter 11 covers Graphs and Trees

  • Chapter 12 is the index

The book includes a wide selection of exercises and detailed exploration problems. This hands-on book contains over 450 examples, thorough chapter summaries, simple quizzes, and approximately 1600 homework exercises of widely varying difficulty. It's a great book for computer science students.

 

6. Best Book for Perfectionists: Discrete Mathematics and Applications

Discrete Mathematics and Applications by Kevin Ferland combines a balance of theory and applications with mathematical rigor. It is written in an accessible writing style.

The author uses a range of examples to teach core concepts. The corresponding exercises allow readers to apply what they learn. The book is divided into two parts:

Part 1 focuses on:

  • How to write proofs

  • Then moves on to topics in number theory

  • employing set theory in the process.

Part 2 focuses on:

  • Computations

  • Combinatorics

  • Graph theory

  • Trees, and algorithms

The book includes engaging anecdotes and topics of interest to inform as well as motivate learners.

 

7. Best Book for Absolute Beginners: Essentials of Discrete Mathematics

Essentials of Discrete Mathematics by David J. Hunter is organized around five types of thinking: logical, relational, recursive, quantitative, and analytical.

The book is divided into six chapters 

  • Chapter 1 talks about Logical Thinking

  • Chapter 2 covers Relational Thinking

  • Chapter 3 talks about Recursive Thinking

  • Chapter 4 covers Quantitative Thinking

  • Chapter 5 talks about Analytical Thinking

  • Chapter 6 emphasizes the multidisciplinary approach and contains case studies

The book gives careful attention to mathematical logic and proof techniques. The coverage of algorithms is appropriate for computer science majors, as well as students with no previous programming experience.

 

More Ways to Learn Discrete Mathematics 

So these are the 7 best Discrete Mathematics books for beginners. They serve as a great resource for those who want to learn best through reading.

There are also a few online courses on the list that let you learn Discrete Mathematics.

  • Coursera: Learn the math that defines computer science by Introduction to Discrete Mathematics for Computer Science specialization. There are five courses in this specialization including

    • Mathematical Thinking in Computer Science

    • Combinatorics and Probability

    • Introduction to Graph Theory

    • Number Theory and Cryptography

    • Delivery Problem

If you want to learn to code on a budget, I have compiled over 70 free coding resources, which I hand-picked for quality. I wish you the best of luck learning discrete math and hope to see you in other articles!

 
Miranda Limonczenko

Miranda is the founder of Books on Code, with a mission to bring book-lover culture to programmers. Learn more by checking out Miranda on LinkedIn.

http://booksoncode.com
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