Discrete Mathematical Structures (2021, Fall)
Undergraduate course, HNUST, 2021
- Chapter 1. Fundamentals
- 1.1 Sets and Subsets
- 1.2 Operations on Sets
- 1.3 Sequences
- 1.4 Properties of Integers
- 1.5 Matrices
- 1.6 Mathematical Structures*
- Chapter 2. Logic
- 2.1 Propositions and Logical Operations
- 2.2 Conditional Statements
- 2.3 Methods of Proof
- 2.4 Mathematical Induction
- 2.5 Mathematical Statements*
- 2.6 Logic and Problem Solving*
- Chapter 3. Counting
- 3.1 Permutations*
- 3.2 Combinations*
- 3.3 Pigeonhole Principle
- 3.4 Elements of Probability*
- 3.5 Recurrence Relations
- Chapter 4. Relations and Digraphs
- 4.1 Product Sets and Partitions
- 4.2 Relations and Digraphs
- 4.3 Paths in Relations and Digraphs
- 4.4 Properties of Relations
- 4.5 Equivalence Relations
- 4.6 Data Structures for Relations and Digraphs
- 4.7 Operations on Relations
- 4.8 Transitive Closure and Warshall’s Algorithm
- Chapter 5. Functions
- 5.1 Functions
- 5.2 Functions for Computer Science
- 5.3 Growth of Functions*
- 5.4 Permutation Functions*
- Chapter 6. Order Relations and Structures
- 6.1 Partially Ordered Sets
- 6.2 Extremal Elements of Partially Ordered Sets
- 6.3 Lattices
- 6.4 Finite Boolean Algebras*
- 6.5 Functions on Boolean Algebras*
- 6.6 Circuit Design*
- Chapter 7. Trees
- 7.1 Trees
- 7.2 Labeled Trees
- 7.3 Tree Searching*
- 7.4 Undirected Trees*
- 7.5 Minimal Spanning Trees*
- Chapter 8. Topics in Graph Theory
- 8.1 Graphs
- 8.2 Euler Paths and Circuits
- 8.3 Hamiltonian Paths and Circuits
- 8.4 Transport Networks*
- 8.5 Matching Problems*
- 8.6 Coloring Graphs*
- Homework
- Textbook
