Counting Principles Course
What will I learn?
This course covers the full spectrum of counting principles, starting with set theory, Venn diagrams, and the addition and multiplication rules. You will develop fluency with factorials, permutations, and combinations before advancing to the binomial theorem and Pascal's triangle. The inclusion-exclusion principle and the Pigeonhole Principle are treated in depth with rigorous proofs and applied problems. Advanced topics include stars-and-bars, generating functions, recurrence relations, Burnside's Lemma, and Catalan numbers. Supplementary chapters connect combinatorics to probability, graph theory, cryptography, and algorithm analysis. You will also build proof-writing skills through double counting, bijective arguments, and complementary counting strategies.
Elevify advantages
Develop skills
- Permutation and Combination Identification: Recognise and solve ordered versus unordered selection problems accurately.
- Inclusion-Exclusion Principle: Apply multi-set overlap formulas to eliminate overcounting in complex problems.
- Binomial Theorem Fluency: Expand binomial expressions and extract specific terms using combinatorial coefficients.
- Advanced Enumeration Methods: Use stars-and-bars, recurrence relations, and generating functions for non-routine problems.
Suggested summary
Before starting, you can change the chapters and the workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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