Combinatorics
Explore basic counting; counting structures; partitions and symmetry. Concepts and connections are available independently of video coverage.
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Inclusion–exclusion
Alternating intersection counts correct double-counting in unions of finite sets.
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Binomial theorem
Binomial coefficients give the expansion of an integer nonnegative power of a sum.
Combinatorial counting
Count finite outcomes with disjoint-case sums, successive-choice products and equal-fiber division or bijections. Check that cases are disjoint and multiplicities are constant. Multiplication of choice counts is not a probability-independence assumption.
Generating functions
A sequence encoded as series coefficients supports algebraic counting and recurrence calculations.
Graphs
Vertices and edges model connections, with directed and undirected variants.
Integer partitions
A partition writes a positive integer as an unordered sum of positive integers.
Knowledge connections
- Pigeonhole principle · Related · Map context
- Recurrence relations · Related · Map context
- Graphs · Related · Map context
- Prime factorization · Related · Map context
- Binomial theorem · Related · Map context
- Generating functions · Related · Map context
- Combinatorial counting · Related · Map context
- Integer partitions · Related · Map context
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Discrete Mathematics: Counting and Number Theory
Connect functions and counting with elementary number theory, graph structures and algorithmic reasoning. Shared concepts and reviewed map connections organize the path; video explanations are added as resources pass review.