Introduction to Enumerative Combinatorics
- Acquaintance with the basic notions, methods, and problems of Enumerative Combinatorics.
- Acquiring an idea of the role of Enumerative Combinatorics in other areas of mathematics (algebra, geometry, analysis, etc.)
- Acquiring the skills of applying methods and constructions of Enumerative Combinatorics to scientific research in various areas of mathematics.
- Acquiring the ability for independent study of topical mathematical literature
- Knowledge of the basic notions, methods and problems of Enumerative Combinatorics. Skills of applying methods and construction of Enumerative Combinatorics in other areas of mathematics. Experience in independent study of topical mathematical literature
- Permutations and binomial coefficients
- Binomial coefficients, continued. Inclusion and exclusion formula
- Linear recurrences. The Fibonacci sequence
- A nonlinear recurrence: many faces of Catalan numbers
- Generating functions: a unified approach to combinatorial problems. Solving linear recurrences
- Generating functions, continued. Generating function of the Catalan sequence Partitions.
- Euler’s generating function for partitions and pentagonal formula
- Gaussian binomial coefficients. “Quantum” versions of combinatorial identities
- Interim assessment (4 module)The final grade is the summary of average for 8 quizes (50%) and the final exam (50%).
- Richard P. Stanley. (2013). Topics in algebraic combinatorics. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.21998FFA
- Anders Björner, Kungl Tekniska, & Richard P. Stanley. (2010). A Combinatorial Miscellany by. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.3199213D