10 Best Books on Discrete Math for Beginners in 2024
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, 4th Edition
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
Each section in Chapters 1 through 5 now include new activities designed to be completed in class using inquiry-based learning. 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.
8. Best Book for Analytical Thinkers: Discrete Mathematics with Applications
Discrete Mathematics with Applications by Susanna S. Epp provides a strong foundation of discrete mathematics for computer science and upper-level mathematics courses. The book introduces discrete mathematics with clarity and precision, and helps you learn to think abstractly as you study the ideas of logic and proof.
The includes lots of real-world examples and applications, and exercises. The contents covers in the book are:
Chapter 1 covers Variables, Sets, Relations and Functions, and Graphs.
Chapter 2 talks about the Logic of Compound Statements. Topics include Logical Form and Logical Equivalence, Conditional Statements, Valid and Invalid Arguments.
Chapter 3 talks about the Logic of Quantified statements. Predicates and Quantified Statements, Statements with Multiple Quantifiers, and Arguments with Quantified Statements.
Chapter 4 covers Elementary Number Theory and Methods of Proof .
Chapter 5 covers Sequences, Mathematical Induction, and Recursion
Chapter 6 covers the Set Theory
Chapter 7 talks about Properties of Functions, Composition of Functions, and Cardinality with Applications to Computability.
Chapter 8 covers Properties of Relations
Chapter 9 talks about Counting and Probability
Chapter 10. Theory of Graphs and Trees
Chapter 11 covers Algorithm Efficiency
Chapter 12 covers Regular Expressions and Finite-State Automata
The book is great for self-taught programmers without formal mathematical or computer science education.
9. Best Book for Basics: Schaum's Outline of Discrete Mathematics
Schaum's Outline of Discrete Mathematics by Seymour Lipschutz and Marc Lipson helps you understand basic concepts and get the extra practice you need to excel in computer science courses. The book provides clear, concise explanations of discrete mathematics concepts. There are 467 solved problems, and hundreds of additional practice problems.
You’ll get expanded coverage of logic, the rules of inference, and basic types of proofs in mathematical reasoning. The book focuses on discrete probability, aspects of probability theory, and greater accessibility to counting techniques. Topics include
Set theory
Relations
Functions and algorithms
Logic and propositional calculus
Techniques of counting
Advanced counting techniques, recursion
Probability
Graph theory
Directed graphs
Binary trees
Properties of the integers
Languages, automata, machines
Finite state machines and Turning machines
Ordered sets and lattices, and Boolean algebra
The Logic chapter emphasizes the IF-THEN and IF-THEN-ELSE sequencing that occurs in computer programming. Moreover, the Cryptology chapter includes substitution and RSA method. This edition comes with new Schaum’s app and website!
10. Best Book for Computer Scientists: Practical Discrete Mathematics
Practical Discrete Mathematics by Ryan T White and Archana Tikayat Ray is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level.
This book is well-organized, allowing the reader to quickly grasp key concepts and test them out using the provided Python examples. The book also gives a good introduction to machine learning.
Here’s what you’ll get from the book:
Understand the terminology and methods in discrete math and their usage in algorithms and data problems
Use Boolean algebra in formal logic and elementary control structures
Implement combinatorics to measure computational complexity and manage memory allocation
Use random variables, calculate descriptive statistics, and find average-case computational complexity
Solve graph problems involved in routing, pathfinding, and graph searches, such as depth-first search
Perform ML tasks such as data visualization, regression, and dimensionality reduction
By the end of this book, you'll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning.
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
Udemy:
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
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