Discrete math
Undergraduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Discrete Math — scope drawn from LibreTexts Discrete Mathematics and typical US discrete mathematics syllabi (logic, sets, proofs, combinatorics, graphs).
Logic and proof
- Logic: propositions, truth tables, and logical equivalences — Logic: propositions, truth tables, and logical equivalences
- Predicates and quantifiers — Predicates and quantifiers
- Methods of proof (direct, contrapositive, contradiction) — Methods of proof (direct, contrapositive, contradiction)
- Mathematical induction — Mathematical induction
- Strong induction — Strong induction
Sets, functions, and counting
- Sets and set operations — Sets and set operations
- Cartesian products — Cartesian products
- Functions — Functions
- Cardinality (introduction) — Cardinality (introduction)
- Basic counting — Basic counting
- Multiplication principles — Multiplication principles
- Permutations and combinations — Permutations and combinations; binomial coefficients and Pascal's triangle
- The pigeonhole principle — The pigeonhole principle
- Inclusion–exclusion (introduction) — Inclusion–exclusion (introduction)
Relations, recurrences, and graphs
- Recurrence relations — Recurrence relations
- Solving linear recurrences (intro) — Solving linear recurrences (intro)
- Relations — Relations
- Partial orders — Partial orders
- Graphs: paths, cycles, trees, and connectivity — Graphs: paths, cycles, trees, and connectivity
- Euler and Hamilton paths — Euler and Hamilton paths; planarity (introduction)
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Logic and proof
Logic: propositions, truth tables, and logical equivalences
Coming soon - Sets, functions, and counting
Sets and set operations
Coming soon - Relations, recurrences, and graphs
Recurrence relations
Coming soon
Notes
Undergraduate Discrete Math — scope drawn from LibreTexts Discrete Mathematics and typical US discrete mathematics syllabi (logic, sets, proofs, combinatorics, graphs). Topic outline: `content/topics/undergraduate/discrete.json`.