09-Discrete Mathematics

Overview

This textbook develops the core language of mathematical reasoning used in computer science and modern mathematics. Topics include logic, proof techniques, sets, combinatorics, number theory, algorithms, and Boolean algebra. Students learn to model discrete systems and construct rigorous proofs.

Table of Contents

1. Chapter 1: What Discrete Mathematics Studies
2. Chapter 2: Logic
3. Chapter 3: Sets
4. Chapter 4: Methods of Proof
5. Chapter 5: Induction and Recursion
6. Chapter 6: Modular Arithmetic
7. Chapter 7: Counting Principles
8. Chapter 8: Permutations, Combinations, and Probability
9. Chapter 9: Advanced Counting
10. Chapter 11: Network Optimization
11. Chapter 12: Algorithms
12. Chapter 13: Boolean Algebra
13. Chapter 14: Capstone and Applications
14. Back Matter

Learning Outcomes

• Use formal logic to analyze and construct mathematical arguments.
• Apply set theory and relations in structured problem solving.
• Construct proofs using direct, contrapositive, contradiction, and induction methods.
• Analyze recursive definitions and sequences.
• Apply modular arithmetic in number theory and computation.
• Solve combinatorial and probability-based counting problems.
• Model networks and optimization problems using graph structures.
• Understand algorithmic thinking and computational processes.
• Work with Boolean algebra in digital logic systems.