7 Best Books on Discrete Math for Beginners in 2021
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
Functions, sequences, and relations
Introduction to number theory
Counting methods and the pigeonhole principle
Boolean algebras and combinatorial circuits
Automata, grammars, and languages
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:
Logic and Sets
Logic and Proof
Relations and Functions
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:
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
Discrete Mathematics by Miran Fattah is a 19-hour high-rated course. This course helps to master Discrete Math for Computer Science and Mathematics Students.
Master Discrete Mathematics by Grant Hall is a 7-hour high rated course that helps you to learn and master all of Discrete Math - Logic, Set Theory, Combinatorics, Graph Theory, etc
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!