Math 475 - Introduction to Combinatorics

• Prerequisites: Math 320 or 340, or consent of instructor.
• Frequency: Fall (I), Spring (II)
• Student Body: Math, statistic and comp science majors
• Credits: 3. (N-A)
• Recent Texts: Introduction to Combinatorics, 4th ed, Richard A. Brualdi
• Course Coordinator: Richard A. Brualdi
• Background and Goals: As the title Introduction to Combinatorics suggests, Math 475 is a first course with emphasis on the basics of combinatorial counting techniques, number sequences, and patterns, with some graph theory thrown in. It is not however a course on what is traditionally called discrete mathematics. We will discuss algorithms for some of the combinatorial problems considered.
• Alternatives: N/A
• Subsequent Courses: N/A

Content coverage:

• Pigeon-hole principle and applications
• Permutations and combinations
• Generating permutations and combinations
• Properties of binomial coefficients (combination numbers)
• Partial orders, equivalence relations, and Dilworth's theorem
• Inclusion-exclusion principle
• Recurrence relations and generating functions
• Difference sequences, Catalan numbers, Stirling numbers, partition numbers, and other counting sequences
• Marriage Theorem and Stable Marriages
• Graph theory (paths, cycles, trees, graph coloring, etc.)
• Polya counting (counting in the presence of symmetries)