Discrete mathematics for computer science : an example-based introduction / Jon Pierre Fortney

Includes index.

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.

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.