Discrete Mathematics

Prerequisites

• High-school mathematics and basic programming experience.
• Willingness to practice formal expression and rigorous proof.
• No advanced mathematics background required.

Learning Outcomes

• Use propositional and predicate logic to express computational properties.
• Write direct, contradiction, induction, and constructive proofs.
• Model system structures with graphs, relations, and automata.
• Solve counting and basic probability problems.
• Connect mathematical models to program correctness, protocols, and cryptographic applications.

Course Format

• Two meetings per week: one for core concepts and one for labs, paper discussion, or project review.
• The course proceeds over 16 weeks, each with a checkable assignment, lab, or project milestone.
• Reproducibility is required: code, configuration, data, lab logs, and reports must be reviewable by staff or peers.

Weekly Plan

Assessment

Course Project

Students model a computing or security topic with discrete structures and provide proof or experimental explanation, such as protocol state machines, access-control relations, control-flow graphs, or cryptographic parameter analysis.

Policies

• AI tools are allowed, but generated code, lab notes, and design suggestions must be reviewed by the student and disclosed in the report.
• Students may not submit code, proofs, configuration, or experimental results they cannot explain; each member must defend their own design, tests, and tradeoffs.
• Late work affects iteration grades, but the course values reproducible, auditable, and maintainable results over last-minute accumulation.