Introduction to Discrete Mathematics for Computer Science Specialization Course Syllabus

Overview: This specialization provides a beginner-friendly, puzzle-driven introduction to discrete mathematics essential for computer science. Through five core courses and hands-on Python programming projects, learners develop foundational skills in mathematical reasoning, combinatorics, probability, and graph theory. The program spans approximately 134 hours of content and practical exercises, structured into six modules. Each module combines theory with interactive puzzles and real-world applications, culminating in a final project solving the Travelling Salesman Problem. Lifetime access allows self-paced learning with a certificate upon completion.

Module 1: Mathematical Thinking in Computer Science

Estimated time: 41 hours

• Mathematical induction
• Recursion and recursive thinking
• Logic and logical reasoning
• Invariants and optimality principles

Module 2: Combinatorics and Probability

Estimated time: 23 hours

• Counting techniques and combinatorial analysis
• Permutations and combinations
• Probability distributions and models
• Applications in algorithm design

Module 3: Graph Theory

Estimated time: 25 hours

• Basic graph structures and representations
• Paths, cycles, and connectivity
• Graph algorithms and traversal methods
• Applications in computational problems

Module 4: Computational Logic

Estimated time: 25 hours

• Propositional and predicate logic
• Logical equivalence and inference
• Satisfiability and Boolean reasoning
• Applications in algorithmic decision-making

Module 5: Algorithmic Applications

Estimated time: 20 hours

• Problem modeling using discrete structures
• Understanding the P vs NP problem
• Optimization and complexity analysis
• Designing efficient algorithms

Module 6: Final Project

Estimated time: 30 hours

• Implement the Travelling Salesman Problem in Python
• Apply graph theory and combinatorial optimization
• Submit solution with analysis and performance evaluation

Prerequisites

• Basic understanding of Python programming
• Familiarity with high school level mathematics
• Interest in logical reasoning and problem-solving

What You'll Be Able to Do After

• Apply discrete mathematics to algorithm design and analysis
• Solve complex computational problems using logic and recursion
• Model real-world problems using combinatorics and probability
• Implement graph-based algorithms in Python
• Understand foundational concepts like P vs NP and computational complexity