## MATH501 Introduction to Combinatorial Theory, Fall 2008

### Objectives

This course is an introduction to Combinatorics aimed at first year graduate students. It has three parts (roughly of equal size):
1. Basic Discrete Mathematics and Counting
2. Network Algorithms
3. Applications

### General Information

• Call Number 63396
• Instructor: Anton Betten, room 207, Weber building. Email lastname at math dot colostate dot edu
• Course website: http://www.math.colostate.edu/ betten/courses/MATH501/FA08/501_syllabus.html http://www.math.colostate.edu/~betten/courses/MATH501/FA08/501_syllabus.html
• Credits: 3
• Class: M  W  F     2 - 2:50 pm,     ENGRG E 205
• Prerequisites: none
• Text: Norman L. Biggs: Discrete Mathematics, second edition, Oxford
• Homework: Assigned weekly, due Mondays (there are 3 homework-free weeks, which are the 5th, 10th and 15th week of classes)
• Final Exam: We will have an extended take-home exam.
• Office hours: Monday 3pm, Friday 3pm

### Syllabus:

1. Basic Discrete Mathematics and Counting (Chapters 5, 6, 7, 10, 11, 25, 12, 13)
1. various ways to count (chapters 6, 10)
2. sets, subsets, binomial numbers (chapters 11, 12)
3. functions and bijections (chapters 5, 20)
4. recurrence relations and generating functions (chaper 25)
5. partitions and compositions (chapter 12)
6. optional: inclusion exclusion
7. optional: Euler and Moebius functions
2. Network Algorithms
1. what is a graph / network? (chapter 15)
2. graphical degree sequences (chapter 15)
3. cycles, spanning subgraphs, trees, isomorphism
4. Euler tour, Hamiltionian cycles
5. shortest paths: Dijkstra and Floyd-Warshall (chapter 18)
6. max flow / min cut: Ford-Fulkerson (chapter 18)
7. maximum matchings (chapter 17)
8. optional: strongly regular graphs and eigenvalue techniques
3. Applications
1. Finite fields and finite projective planes (chapter 23)
2. Error correcting codes (chapter 24)
4. Steiner systems and combinatorial designs (chapter 11)