Table of Contents
Preface To the Student 1 The Foundations: Logic, Sets, and Functions 1.1 Logic 1.2 Propositional Equivalences 1.3 Predicates and Quantifiers 1.4 Sets 1.5 Set Operations 1.6 Functions 1.7 Sequences and Summations 1.8 The Growth Functions 2 The Fundamentals: Algorithms, the Integers, and Matrices 2.1 Algorithms 2.2 Complexity of Algorithms 2.3 The Integers and Division 2.4 Integers and Algorithms 2.5 Applications of Number Theory 2.6 Matrice 3 Mathematical Reasoning 3.1 Methods of Proof 3.2 Mathematical Induction 3.3 Recursive Definitions 3.4 Recursive Algorithms 3.5 Program Correctness 4 Counting 4.1 The Basics of Counting 4.2 The Pigeonhole Principle 4.3 Permutations and Combinations 4.4 Discrete Probability 4.5 Probability Theory 4.6 Generalized Permutations and Combinations 4.7 Generating Permutations and Combinations 5 Advanced Counting Techniques 5.1 Recurrence Relations 5.2 Solving Recurrence Relations 5.3 Divide-and-Conquer Relations 5.4 Generating Functions (and more...)