Standard syllabus
Discrete math · Undergraduate · Math
Topics
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)
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