MATA1420 Introduction to combinatorics (4 cr)

Introduction to combinatorics and linear recurrence relations.

The contents correspond to Anderson: "A First Course in Combinatorial Mathematics" and Bogart: "Discrete Mathematics", chapters 5-7.

After completing the course, the student

• can apply the basic principles of combinatorics (addition principle, multiplication principle and inclusion-exclusion principle) and knows some of their applications.
• knows the the basic definitions of combinatorics, such as permutations and combinations.
  
• knows how to calculate the number of partitions of a set and knows Stirling's numbers.
  
• knows the basic properties of recurrence equations and knows some solution methods.
  
• can model and solve combinatoric problems using linear recurrence equations.
  
• can apply induction in proving results in combinatorics.
• is familiar with the generating functions.  
  

Good command of the long mathematics curriculum of high school. Courses "How to prove it?" and "Introduction to mathematics" are useful.

Lecture notes,

Anderson: A First Course in Combinatorial Mathematics,

Bogart: Discrete mathematics.

Erickson: Introduction to Combinatorics,

Berman & Fryer: Introduction to Combinatorics.