MAT 378 - Discrete Mathematics - Spring 2007
Week 1: 1/23
- Chapter 1: What is Combinatorics?
Week 2: 1/28 -- 1/30
- 2.1 & 2.2: The pigeonhole principle
- 2.3: Ramsey's theorem
Week 3: 2/4 -- 2/6
- 3.1 Four basic counting principles
- 3.2 Permutations of sets
- 3.3 Combinations of sets
Week 4: 2/11 -- 2/13
- 3.4 Permutations of multisets
- 3.5 Combinations of multisets
- 4.1 Generating permutations
Week 5: 2/18 -- 2/20
- 4.2 Inversions in permutations
- 4.3 Generating combinations
- 4.4 Generating r-combinations
Week 6: 2/25 -- 2/27
- 4.5 Partial orders and equivalence relations
- 5.1 Pascal's formula
- 5.2 The binomial theorem
Week 7: 3/3 -- 3/5
- 5.3 Binomial identities
- Review
- Exam I
Week 8: 3/10 -- 3/12 (Midterm grades on Wednesday)
- 5.5 The multinomial theorem
- 5.6 Newton's binomial theorem
- 6.1 The inclusion/exclusion principle
Week 9: 3/17 -- 3/19
Week 10: 3/24 -- 3/26
- 6.2 Combinations with repetition
- 6.3 Derangements
- 7.1 Some number sequences
Week 11: 3/31 -- 4/2
- 7.2 Linear Homogeneous Recurrence Relations
- 7.3 Nonhomogeneous recurrence relations
- 7.4 Generating functions
Week 12: 4/7 -- 4/9
- 11.1 Introduction to graph theory
- Review for exam II
- Exam II
Week 13: 4/14 -- 4/16
- 11.2 Eulerian trails
- 11.3 Hamiltonian chains and cycles
- 11.4 Bipartite multigraphs
Week 14: 4/21 -- 4/23
- 11.5 Trees
- 11.7 More on trees
- 13.1 Chromatic number
Week 15: 4/28 -- 4/30
- 13.2 Plane and planar graphs
- 13.3 The 5-color theorem
- 13.4 Independence and Clique numbers
Week 16: 5/5 -- 5/7
- 13.5 Connectivity
- Review for final.
Week 17: 5/12 -- 5/14
- Final Exams
(Our exam is scheduled for Wednesday, May 14th at 12:45 PM.)