Discrete Mathematics: A Brief Introduction 1st edition

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• Chapter 0: What is Discrete Mathematics with Examples
  • 0.0: What is Discrete Mathematics?
  • 0.1: Logistic Population Models and the Interplay between Discrete and Continuous Systems and Models
  • 0.2: The Königsburg Bridge Problem and the Party Problem
  • 0.3: Some Useful Definitions
  
  
• Chapter 1: Preliminaries 1: Sets
  • 1.0: Sets, subsets and set operations: Unions, Intersections, Complements
  • 1.1: Set Equality: Truth Tables, Venn Diagrams and Element Chasing
  • 1.2: Set Identities: Associate, Commutative, Absorptive; Identity Laws; DeMorgan's Laws
  • 1.3: Functions and Relations
  • 1.4: Relations on a set A and their properties
  • 1.5: Equivalence Relations and modular arithmetic
  • 1.6: Partial Orderings and Hasse Diagrams
  • 1: Chapter 1 Review
  
  
• Chapter 2: Preliminaries 2: Logic and Proof
  • 2.0: What is Proof; Conditional Connectives, Converses and Contrapositives
  • 2.1: Mathematical Induction
  • 2.2: More Mathematical Induction and Strong Induction
  • 2.3: Universal and Existential Quantifiers
  • 2.4: Recurrence Relations
  • 2: Chapter 2 Review
  
  
• Chapter 3: Counting (with Discussions of Discrete Probability)
  • 3.0: Introduction: What is counting?
  • 3.1: Ordered Samples with and without Repetition, Permutations
  • 3.2: Unordered Samples without Repetition: Subsets, Pascal's Triangle and the Binomial Theorem
  • 3.3: Unordered Samples with Repetition: Multisets (Optional)
  • 3.4: The Principle of Inclusion and Exclusion
  • 3.5: Wrap up on Discrete Probability
  • 3: Chapter 3 Review
  
  
• Chapter 4: Trees and Other Graphs
  • 4.0: Some Definitions and Uses: Graphs, Multigraphs, Network Problems, Transportation Problems
  • 4.1: Graphs and Cycles: Adjacency Matrices, the Königsburg Bridge Problem and Euler Cycles
  • 4.2: Trees and Spanning Trees: Spanning Tree Algorithm and the Daisy Chain Theorem
  • 4.3: Greedy Algorithms: Minimal spanning trees, shortest paths, Prim's Algorithm, and Dijkstra's Algorithm
  • 4.4: Binary Trees: Search Algorithms, Reverse Polish Notation
  • 4.5: Planar Graphs and Euler's Theorem
  • 4: Chapter 4 Review
  
  
• Chapter 5: Introduction to Propositional Calculus, Boolean Algebra and Digital Logic Gates
  • 5.0: Set Theory, Propositional Calculus and Boolean Algebra, what's the difference?
  • 5.1: Propositional Calculus
  • 5.2: Boolean Algebra
  • 5.3: Digital Logic Gates
  • 5.4: Karnaugh Maps: Simplifying Boolean Expressions
  • 5: Chapter 5 Review