1CHAPTER 1 Introduction to Discrete Mathematics
327.2 Graph Representations
21.1 What is Discrete Mathematics?
337.3 Graph Connectivity
31.2 Historical Overview
347.4 Trees and Forests
41.3 Importance and Applications
35CHAPTER 8 Discrete Probability
5CHAPTER 2 Set Theory
368.1 Sample Spaces and Events
62.1 Basics of Sets
378.2 Probability Laws and Axioms
72.2 Set Operations
388.3 Conditional Probability and Independence
82.3 Set Identities
398.4 Random Variables and Expected Value
92.4 Cardinality of Sets
40CHAPTER 9 Algebraic Structures
10CHAPTER 3 Logic
419.1 Groups: Definitions and Properties
113.1 Propositional Logic
429.2 Rings and Fields
123.2 Predicate Logic
439.3 Lattices and Boolean Algebras
133.3 Logical Equivalence and Normal Forms
449.4 Applications of Algebraic Structures
143.4 Inference and Proofs
45CHAPTER 10 Cryptography
15CHAPTER 4 Proof Techniques
4610.1 Basic Concepts and Terminology
164.1 Direct Proof
4710.2 Cryptographic Techniques
174.2 Proof by Contradiction
4810.3 Public Key Cryptography
184.3 Proof by Induction
4910.4 Cryptanalysis
194.4 Disproof Techniques
50CHAPTER 11 Complexity Theory
20CHAPTER 5 Combinatorics
5111.1 Time and Space Complexity
215.1 Basic Counting Principles
5211.2 NP-Completeness
225.2 Permutations and Combinations
5311.3 P vs NP Problem
235.3 Binomial Coefficients
5411.4 Approximation Algorithms
245.4 Pigeonhole Principle
55CHAPTER 12 Automata Theory
25CHAPTER 6 Relations and Functions
5612.1 Finite Automata
266.1 Relations: Definitions and Properties
5712.2 Regular Languages
276.2 Equivalence Relations and Partial Orders
5812.3 Pushdown Automata
286.3 Functions: Definitions and Properties
5912.4 Turing Machines
296.4 Composition and Inverse Functions
60Glossaries
30CHAPTER 7 Graph Theory
61Index
317.1 Basic Concepts: Graphs and Digraphs
