Mathematical Thinking in Computer Science Course Syllabus
Full curriculum breakdown — modules, lessons, estimated time, and outcomes.
Overview: This course introduces the foundational role of mathematical thinking in computer science, guiding beginners through logical reasoning, problem-solving techniques, and the application of discrete mathematics to real computational challenges. Designed by the University of California San Diego, it emphasizes hands-on learning and conceptual understanding over advanced prerequisites. The course spans approximately 24 hours of content, divided into six structured modules, each building critical thinking skills essential for computer science. Learners engage with interactive exercises, peer-reviewed assignments, and practical applications to develop confidence in using mathematical reasoning for algorithmic and computational thinking. Lifetime access ensures flexibility for self-paced study, culminating in a certificate of completion.
Module 1: Solving Problems with Logic and Proofs
Estimated time: 4 hours
- Introduction to logical reasoning and truth tables
- Writing basic mathematical proofs
- Applying logic to computational problems
- Understanding implications and quantifiers
Module 2: Recursion and Induction in Problem Solving
Estimated time: 4 hours
- Principles of mathematical induction
- Recursive thinking and definitions
- Solving recurrence relations
- Applications in algorithm analysis
Module 3: Counting and Combinatorics
Estimated time: 4 hours
- Basic counting principles
- Permutations and combinations
- Combinatorial problem-solving techniques
- Applications in probability and algorithms
Module 4: Graph Theory and Applications
Estimated time: 4 hours
- Introduction to graphs and representations
- Paths, cycles, and connectivity
- Graph algorithms and real-world applications
- Modeling problems using graphs
Module 5: Number Theory and Cryptography
Estimated time: 4 hours
- Modular arithmetic fundamentals
- Prime numbers and divisibility
- Introduction to encryption principles
- Applications in computer security
Module 6: Final Project
Estimated time: 4 hours
- Design a computational problem using logic or proofs
- Apply combinatorics or graph theory to a real-world scenario
- Submit solution with peer-reviewed justification
Prerequisites
- Basic high school algebra
- Familiarity with logical thinking
- No prior programming required
What You'll Be Able to Do After
- Apply mathematical logic to solve computer science problems
- Construct and understand mathematical proofs
- Use recursion and induction in algorithm design
- Analyze problems using combinatorics and graph theory
- Understand foundational concepts in cryptography and number theory