Combinatorics
Explore basic counting; counting structures; partitions and symmetry. Concepts and connections are available independently of video coverage.
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Generating functions
A sequence encoded as series coefficients supports algebraic counting and recurrence calculations.
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Inclusion–exclusion
Alternating intersection counts correct double-counting in unions of finite sets.
Pigeonhole principle
More objects than boxes force at least one box to contain multiple objects.
Recurrence relations
A recurrence specifies sequence terms using earlier terms and initial data.
Algorithmic complexity
Time and space requirements are expressed as functions of input size under a computational model.
Diophantine equations
Diophantine equations seek integer or rational solutions rather than unrestricted real solutions.
Knowledge connections
- Pigeonhole principle · Related · Map context
- Recurrence relations · Related · Map context
- Recurrence relations · Related · Map context
- Inclusion–exclusion · 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.