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):
 Basic Discrete Mathematics and Counting

Network Algorithms

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 homeworkfree weeks, which are the 5th, 10th and 15th week of classes)

Final Exam: We will have an extended takehome exam.

Office hours:
Monday 3pm, Friday 3pm
Syllabus:
 Basic Discrete Mathematics and Counting (Chapters 5, 6, 7, 10, 11, 25, 12, 13)
 various ways to count (chapters 6, 10)

sets, subsets, binomial numbers (chapters 11, 12)

functions and bijections (chapters 5, 20)

recurrence relations and generating functions (chaper 25)

partitions and compositions (chapter 12)

optional: inclusion exclusion

optional: Euler and Moebius functions

Network Algorithms
 what is a graph / network? (chapter 15)

graphical degree sequences (chapter 15)

cycles, spanning subgraphs, trees, isomorphism

Euler tour, Hamiltionian cycles

shortest paths: Dijkstra and FloydWarshall (chapter 18)

max flow / min cut: FordFulkerson (chapter 18)

maximum matchings (chapter 17)

optional: strongly regular graphs and eigenvalue techniques

Applications
 Finite fields and finite projective planes (chapter 23)

Error correcting codes (chapter 24)

Hadamard matrices

Steiner systems and combinatorial designs (chapter 11)
Grading:
Your final grade will be determined from a score of 500.
The homework counts 200, the final is valued at 200 points the remaining 100 are obtained
from a short presentation.
Homework and Take Home Final:
homework and take home final
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On 9 Dec 2008, 11:01.