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 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:
- 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 Floyd-Warshall (chapter 18)
-
max flow / min cut: Ford-Fulkerson (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
File translated from
TEX
by
TTH,
version 3.81.
On 9 Dec 2008, 11:01.