Discrete math
Undergraduate · Math
Syllabus focus
Standard syllabus · STEM / applied
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Topics typically covered
Standard syllabus
Logic and proof
- Logic: propositions, truth tables, and logical equivalences
- Predicates, quantifiers, and methods of proof (direct, contrapositive, contradiction)
- Mathematical induction and strong induction
Sets, functions, and counting
- Sets, set operations, and Cartesian products
- Functions: injections, surjections, bijections, and cardinality (introduction)
- Basic counting: addition and multiplication principles
- Permutations and combinations; binomial coefficients and Pascal's triangle
- The pigeonhole principle and inclusion–exclusion (introduction)
Relations, recurrences, and graphs
- Recurrence relations and solving linear recurrences (intro)
- Relations: equivalence relations and partial orders
- Graphs: paths, cycles, trees, and connectivity
- Euler and Hamilton paths; planarity (introduction)
STEM / applied
Computer science connections
- Boolean algebra and logic gates (CS orientation)
- Algorithmic complexity: big-O notation (introduction)
- Graph algorithms: shortest paths, spanning trees, and traversals
- Finite-state machines and regular languages (overview)
Applications
- Cryptography basics: modular arithmetic and RSA (overview)
- Coding theory and error detection (optional)
- Combinatorial probability tied to counting problems
- Recurrence relations in divide-and-conquer algorithms
Notes
Topics reflect common discrete mathematics syllabi at US colleges and universities. CS-heavy programs emphasize graphs, algorithms, and logic; math-heavy programs emphasize proof and combinatorics.