Generating Functions
Introduction to ordinary generating functions and their utility in solving complex combinatorial problems.
About This Topic
Introduction to ordinary generating functions and their utility in solving complex combinatorial problems.
Key Questions
- What is a generating function and how does it encode a sequence?
- How do generating functions simplify the process of solving recurrence relations?
- How do we extract specific coefficients from a generating function?
Active Learning Ideas
See all activities→Activities & Teaching Strategies
See all activities
Planning templates for Mathematics
5E Model
The 5E Model structures lessons through five phases (Engage, Explore, Explain, Elaborate, and Evaluate), guiding students from curiosity to deep understanding through inquiry-based learning.
Unit PlannerMath Unit
Plan a multi-week math unit with conceptual coherence: from building number sense and procedural fluency to applying skills in context and developing mathematical reasoning across a connected sequence of lessons.
RubricMath Rubric
Build a math rubric that assesses problem-solving, mathematical reasoning, and communication alongside procedural accuracy, giving students feedback on how they think, not just whether they got the right answer.
More in Combinatorics
Advanced Counting Principles
Application of the Pigeonhole Principle, Inclusion-Exclusion Principle, and permutations or combinations with repetitions.
8 methodologies
Recurrence Relations
Formulation and solving of linear recurrence relations with constant coefficients to model discrete sequences.
8 methodologies