A more intuitive approach to the mathematical foundation of computer science
Discrete mathematics is the basis of much of computer science, from algorithms and automata theory to combinatorics and graph theory. This textbook covers the discrete mathematics that every computer science student needs to learn. Guiding students quickly through thirty-one short chapters that discuss one major topic each, this flexible book can be tailored to fit the syllabi for a variety of courses.
Proven in the classroom, Essential Discrete Mathematics for Computer Science aims to teach mathematical reasoning as well as concepts and skills by stressing the art of proof. It is fully illustrated in color, and each chapter includes a concise summary as well as a set of exercises. The text requires only precalculus, and where calculus is needed, a quick summary of the basic facts is provided.
Essential Discrete Mathematics for Computer Science is the ideal introductory textbook for standard undergraduate courses, and is also suitable for high school courses, distance education for adult learners, and self-study.
- The essential introduction to discrete mathematics
- Features thirty-one short chapters, each suitable for a single class lesson
- Includes more than 300 exercises
- Almost every formula and theorem proved in full
- Breadth of content makes the book adaptable to a variety of courses
- Each chapter includes a concise summary
- Solutions manual available to instructors
Author(s): Harry Lewis, Rachel Zax
Edition: 1
Publisher: Princeton University Press
Year: 2019
Language: English
Pages: 408
City: New Jersey
Tags: Computer Science; Discrete Mathematics; Informatics; Pigeonhole Principle; Proof Techniques; Induction; Sets; Relations; Functions; Countable Sets; Uncountable Sets; Propositional Logic; Graphs; States; Invariants: Finite Automata; Counting; Series; Probability; Bayes' Theorem; Random Variables; Modular Arithmetic; Public Key Cryptography
Cover
Title
Copyright
Contents
Preface
1 The Pigeonhole Principle
Chapter Summary
Problems
2 Basic Proof Techniques
Chapter Summary
Problems
3 Proof by Mathematical Induction
Chapter Summary
Problems
4 Strong Induction
Chapter Summary
Problems
5 Sets
Chapter Summary
Problems
6 Relations and Functions
Chapter Summary
Problems
7 Countable and Uncountable Sets
Chapter Summary
Problems
8 Structural Induction
Chapter Summary
Problems
9 Propositional Logic
Chapter Summary
Problems
10 Normal Forms
Chapter Summary
Problems
11 Logic and Computers
Chapter Summary
Problems
12 Quantificational Logic
Chapter Summary
Problems
13 Directed Graphs
Chapter Summary
Problems
14 Digraphs and Relations
Chapter Summary
Problems
15 States and Invariants
Chapter Summary
Problems
16 Undirected Graphs
Chapter Summary
Problems
17 Connectivity
Chapter Summary
Problems
18 Coloring
Chapter Summary
Problems
19 Finite Automata
Chapter Summary
Problems
20 Regular Languages
Chapter Summary
Problems
21 Order Notation
Chapter Summary
Problems
22 Counting
Chapter Summary
Problems
23 Counting Subsets
Chapter Summary
Problems
24 Series
Chapter Summary
Problems
25 Recurrence Relations
Chapter Summary
Problems
26 Probability
Chapter Summary
Problems
27 Conditional Probability
Chapter Summary
Problems
28 Bayes’ Theorem
Chapter Summary
Problems
29 Random Variables and Expectation
Chapter Summary
Problems
30 Modular Arithmetic
Chapter Summary
Problems
31 Public Key Cryptography
Chapter Summary
Problems
Index
