Standard syllabus
Discrete math · Undergraduate · Math
Learning objectives from the Discrete math syllabus, grouped by unit. Click an objective for study materials.
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)
Learning objectives
Click an objective for study materials.
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
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)
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
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
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$1,162 · Discrete math · 18 tutoring hrs
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