Discrete Mathematics

Index

• 1. Logic and Proofs
  • 1.1 Propositional Logic
  • 1.2 Predicate Logic
  • 1.3 Rules of Inference
  • 1.4 Proof Techniques
• 2. Sets, Functions, and Relations
  • 2.1 Set Theory
  • 2.2 Functions
  • 2.3 Cardinality
  • 2.4 Relations
  • 2.5 Equivalence Relations and Orders
• 3. Induction and Recursion
  • 3.1 Sequences and Summations
  • 3.2 Mathematical Induction
  • 3.3 Recursive Definitions
• 4. Number Theory
  • 4.1 Divisibility
  • 4.2 GCD and LCM
  • 4.3 Modular Arithmetic
  • 4.4 Applications of Number Theory
• 5. Combinatorics
  • 5.1 Counting Principles
  • 5.2 Permutations and Combinations
  • 5.3 Binomial Coefficients
  • 5.4 Pigeonhole Principle
  • 5.5 Inclusion–Exclusion
  • 5.6 Special Counting Sequences
• 6. Recurrence Relations and Generating Functions
  • 6.1 Recurrence Relations
  • 6.2 Divide-and-Conquer Recurrences
  • 6.3 Generating Functions
• 7. Discrete Probability
  • 7.1 Probability Fundamentals
  • 7.2 Bayes and Applications
  • 7.3 Random Variables
  • 7.4 Distributions and Bounds
• 8. Graph Theory
  • 8.1 Graph Fundamentals
  • 8.2 Graph Representation and Isomorphism
  • 8.3 Connectivity
  • 8.4 Traversals and Paths
  • 8.5 Planarity and Coloring
  • 8.6 Matchings and Flows
• 9. Trees
  • 9.1 Tree Fundamentals
  • 9.2 Applications of Trees
  • 9.3 Tree Traversal
  • 9.4 Spanning Trees
• 10. Algorithms and Complexity
  • 10.1 Algorithm Basics
  • 10.2 Growth of Functions
  • 10.3 Complexity Analysis
• 11. Boolean Algebra
  • 11.1 Boolean Functions
  • 11.2 Logic Circuits
  • 11.3 Circuit Minimization
• 12. Algebraic Structures
  • 12.1 Groups
  • 12.2 Rings and Fields
  • 12.3 Applications
• 13. Formal Languages and Automata
  • 13.1 Languages and Grammars
  • 13.2 Finite-State Machines
  • 13.3 Regular Languages
  • 13.4 Computability

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