← All courses n ! n! n ! Discrete and Data
Discrete mathematics for problem solvers: counting principles, combinations, casework and complements, stars and bars, the binomial theorem, inclusion–exclusion, recursion, and probability through expected value.
Before this: Algebra 1 What you'll be able to do
Count arrangements and selections without double counting Prove combinatorial identities two ways Compute probabilities with conditioning and independence Use linearity of expectation Start the course
Go through each topic step by step — prose, worked examples, quick checks, and a timed practice round after every section.
Every test ends with a score by topic and a list of what to revisit. Test out of a topic with 80% or better to mark it mastered.
Topics 1. Core Ideas in Plain Terms
5 lessons Counting and chance, in everyday language
2. Fundamental Counting: Permutations & Combinations
12 lessons Competition counting & probability, Unit 1
3. Counting Strategies: Casework, Complementary & Overcounting
12 lessons Competition counting & probability, Unit 2
4. Distributions: Stars & Bars and Integer Solutions
12 lessons Competition counting & probability, Unit 3
5. Binomial Theorem, Pascal & Combinatorial Identities
12 lessons Competition counting & probability, Unit 4
6. Inclusion–Exclusion, Derangements & Pigeonhole
12 lessons Competition counting & probability, Unit 5
7. Recursion, Catalan Numbers & Generating Functions
12 lessons Competition counting & probability, Unit 6
8. Probability Fundamentals & Geometric Probability
12 lessons Competition counting & probability, Unit 7
9. Conditional Probability, Independence & Bayes
12 lessons Competition counting & probability, Unit 8
10. Expected Value, Linearity & Advanced Probability
12 lessons Competition counting & probability, Unit 9
11. Identities and Techniques, Proved
9 lessons The hockey stick, Vandermonde, absorption, stars and bars, inclusion–exclusion and linearity — each one proved, not just stated
12. Course Review
13 lessons Every formula, identity, and technique for competition math