Advanced topics in discrete mathematics and combinatorics including setting up and solving recurrence relations, finite calculus, manipulation and evaluation of sums, Möbius inversion, binomial coefficients, Fibonacci numbers, Stirling numbers, and generating functions.
- Use recurrence relations to formulate and solve combinatorial problems.
- Manipulate and evaluate complicated sums.
- Prove and use identities involving binomial coefficients.
- Prove and use identities involving special numbers such as Fibonacci numbers and Stirling numbers.
- Find and use generating functions to solve combinatorial problems.