Discrete math for CS
Undergraduate · CS / Programming
Syllabus focus
Standard syllabus · Theoretical / proof-based
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$60.00 · 60 min · Undergraduate · Online ($60/hr)
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Topics typically covered
Standard syllabus
Logic and proof
- Propositional logic and truth tables
- Predicates, quantifiers, and inference rules
- Direct proof, contrapositive, and contradiction
- Mathematical induction and strong induction
- Sets, functions, and cardinality (intro)
Combinatorics and graphs
- Counting: permutations, combinations, binomial theorem
- Pigeonhole principle and inclusion–exclusion (intro)
- Recurrence relations and generating functions (intro)
- Graphs: paths, cycles, trees, connectivity
- Euler/Hamilton paths; planarity (intro)
Theoretical / proof-based
Proof depth
- Proof by cases and constructive vs existential proofs
- Well-ordering and structural induction
- Bijections and counting proofs
- Graph isomorphism and coloring arguments
- Intro to Ramsey theory (optional)
CS theory connections
- Big-O notation tied to counting arguments
- Boolean algebra and logic circuits
- Regular languages preview (automata intro)
- Pigeonhole arguments in hashing and compression
- Problem sets mirroring qualifying-exam discrete topics
Notes
Gateway course for algorithms and theory. Overlap with math department discrete courses varies.