Discrete Mathematics for Computer Science: An Example-Based Introduction is intended for a first- or second-year discrete mathematics course for computer science majors. It covers many important mathematical topics essential for future computer science majors, such as algorithms, number representations, logic, set theory, Boolean algebra, functions, combinatorics, algorithmic complexity, graphs, and trees.
Features
• Designed to be especially useful for courses at the community-college level
• Ideal as a first- or second-year textbook for computer science majors, or as a general introduction to discrete mathematics
• Written to be accessible to those with a limited mathematics background, and to aid with the transition to abstract thinking
• Filled with over 200 worked examples, boxed for easy reference, and over 200 practice problems with answers
• Contains approximately 40 simple algorithms to aid students in becoming proficient with algorithm control structures and pseudocode
• Includes an appendix on basic circuit design which provides a real-world motivational example for computer science majors by drawing on multiple topics covered in the book to design a circuit that adds two eight-digit binary numbers
Jon Pierre Fortney graduated from the University of Pennsylvania in 1996 with a BA in Mathematics and Actuarial Science and a BSE in Chemical Engineering. Prior to returning to graduate school, he worked as both an environmental engineer and as an actuarial analyst. He graduated from Arizona State University in 2008 with a PhD in Mathematics, specializing in Geometric Mechanics. Since 2012, he has worked at Zayed University in Dubai. This is his second mathematics textbook.
Author(s): Jon Pierre Fortney
Edition: 1
Publisher: CRC Press
Year: 2020
Language: English
Commentary: Vector PDF
Pages: 270
City: Boca Raton, FL
Tags: Algorithms; Graph Theory; Discrete Mathematics; Set Theory; Boolean Algebra; Mathematical Logic; Combinatorics; Trees; Algorithm Complexity
Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
CHAPTER 1: Introduction to Algorithms
1.1. WHAT ARE ALGORITHMS?
1.2. CONTROL STRUCTURES
1.3. TRACING AN ALGORITHM
1.4. ALGORITHM EXAMPLES
1.5. PROBLEMS
CHAPTER 2: Number Representations
2.1. WHOLE NUMBERS
2.2. FRACTIONAL NUMBERS
2.3. THE RELATIONSHIP BETWEEN BINARY, OCTAL, AND HEXADECIMAL NUMBERS
2.4. CONVERTING FROM DECIMAL NUMBERS
2.5. PROBLEMS
CHAPTER 3: Logic
3.1. PROPOSITIONS AND CONNECTIVES
3.2. CONNECTIVE TRUTH TABLES
3.3. TRUTH VALUE OF COMPOUND STATEMENTS
3.4. TAUTOLOGIES AND CONTRADICTIONS
3.5. LOGICAL EQUIVALENCE AND THE LAWS OF LOGIC
3.6. PROBLEMS
CHAPTER 4: Set Theory
4.1. SET NOTATION
4.2. SET OPERATIONS
4.3. VENN DIAGRAMS
4.4. THE LAWS OF SET THEORY
4.5. BINARY RELATIONS ON SETS
4.6. PROBLEMS
CHAPTER 5: Boolean Algebra
5.1. DEFINITION OF BOOLEAN ALGEBRA
5.2. LOGIC AND SET THEORY AS BOOLEAN ALGEBRAS
5.3. DIGITAL CIRCUITS
5.4. SUMS-OF-PRODUCTS AND PRODUCTS-OF-SUMS
5.5. PROBLEMS
CHAPTER 6: Functions
6.1. INTRODUCTION TO FUNCTIONS
6.2. REAL-VALUED FUNCTIONS
6.3. FUNCTION COMPOSITION AND INVERSES
6.4. PROBLEMS
CHAPTER 7: Counting and Combinatorics
7.1. ADDITION AND MULTIPLICATION PRINCIPLES
7.2. COUNTING ALGORITHM LOOPS
7.3. PERMUTATIONS AND ARRANGEMENTS
7.4. COMBINATIONS AND SUBSETS
7.5. PERMUTATION AND COMBINATION EXAMPLES
7.6. PROBLEMS
CHAPTER 8: Algorithmic Complexity
8.1. OVERVIEW OF ALGORITHMIC COMPLEXITY
8.2. TIME-COMPLEXITY FUNCTIONS
8.3. FINDING TIME-COMPLEXITY FUNCTIONS
8.4. BIG-O NOTATION
8.5. RANKING ALGORITHMS
8.6. PROBLEMS
CHAPTER 9: Graph Theory
9.1. BASIC DEFINITIONS
9.2. EULERIAN AND SEMI-EULERIAN GRAPHS
9.3. MATRIX REPRESENTATIONS OF GRAPHS
9.4. REACHABILITY FOR DIRECTED GRAPHS
9.5. PROBLEMS
CHAPTER 10: Trees
10.1. BASIC DEFINITIONS
10.2. MINIMAL SPANNING TREES OF WEIGHTED GRAPHS
10.3. MINIMAL DISTANCE PATHS
10.4. PROBLEMS
APPENDIX A: Basic Circuit Design
A.1. BINARY ADDITION
A.2. THE HALF-ADDER
A.3. THE FULL-ADDER
A.4. ADDING TWO EIGHT-DIGIT BINARY NUMBERS
APPENDIX B: Answers to Problems
B.1. CHAPTER ONE ANSWERS
B.2. CHAPTER TWO ANSWERS
B.3. CHAPTER THREE ANSWERS
B.4. CHAPTER FOUR ANSWERS
B.5. CHAPTER FIVE ANSWERS
B.6. CHAPTER SIX ANSWERS
B.7. CHAPTER SEVEN ANSWERS
B.8. CHAPTER EIGHT ANSWERS
B.9. CHAPTER NINE ANSWERS
B.10. CHAPTER TEN ANSWERS
Index
