Introduction to Combinatorics

MATH 474 (Spring 2004) course policies

Instructor: Dr. André Kündgen
Email: akundgen@csusm.edu
Office: Science Hall 2, 339
Office phone: (760) 750-8070
Office hours: Tuesdays 10:00-11:00, 16:00-17:00 (when classes are in session), or by appointment.

The easiest way to arrange an appointment, or to get a hold of me in general, is by email.

CRN: 21403
Lectures: Tuesday, Thursday 14:30-15:45 (SCI2 Room 306).
Webpage: http://courses.csusm.edu/math474ak

The webpage contains useful information, like the homework assignments, general announcements, and clarifications regarding the homework. You should check it at least once a week.

Textbook

R.A. Brualdi, Introductory Combinatorics (3rd edition), Prentice Hall (1999), ISBN 0-13-181488-5 (hardcover).

Prerequisites

A certain amount of mathematical maturity is necessary for this course. MATH 350, MATH 370 or a similar discrete mathematics course that stresses the ability to understand and write proofs is required.

Grading Policies

The numerical scores of all exams and assignments will be used in computing a final score that will determine your final letter grade:

Homework 15%
Midterms 3 x 20%
Final Exam 25%
Letter grade Numerical grade
A 85-100
B 70-84
C 60-69
D 50-59
F 00-49
There will be around 12 homework assignments, which you need to submit on the announced due dates. Doing the assigned work regularly, seriously, and carefully is vital to your success in this course. Although your homework is lightly weighted, you should keep in mind that you can only learn combinatorics by doing problems. This will be crucial for your exam performance.

Late homeworks will not be accepted.

Important Dates

TR>
January 5: First day of classes
February 17: Midterm 1
March 23: Midterm 2
March 27-April 3: Spring break (no classes)
April 27: Midterm 3
May 6: Last day of classes
May 13: Final Exam, 1:45-3:45PM

Policy concerning collaboration on assignments

Students often learn a lot from working with one another and you are encouraged to meet with other students from class for this purpose. For example, you might work through exercises in the text together or discuss any material you found confusing in lecture or in the textbook.

It is also legitimate to discuss assignment problems with other students in the class or consult other texts. Assignments must be written up completely by yourself using only the text and your own notes as aids. The point is that your written report should be your own work. Do not let other students even look at your completed assignment solutions, since this can lead to copying. These rules are meant to ensure that all students understand their solutions to the problems well enough to write up solutions by themselves. If challenged you must be able to reproduce and explain your work.

Failure to comply with these guidelines is a serious academic offense. Penalties for such violations range from receiving a zero on the homework to suspension from the university.

On the first page of each homework assignment you must explicitly list all students with whom you have discussed assignment problems (even briefly) and which problems you discussed with each student. If you have discussed the homework with no one except me, write ``NO OUTSIDE DISCUSSION''. You must also list all other texts and aids that you have consulted. If you have consulted no text except the textbook and course notes, write ``NO EXTRA TEXT CONSULTED''. Without these statements, your assignment may not be graded and you will be penalized.

Course content

"In how many ways can you ..." is the key question in Combinatorics, aka "The art of counting". The goal of this course is to tackle many problems of this type.

The core material consists of the pigeonhole principle, combinations (binomial coefficients) and permutations (factorials), recurrence relations (and how to solve them), generating functions, and the principle of Inclusion/Exclusion. We will also encounter some assorted topics, like partially ordered sets, derangements, Fibonacci numbers, Catalan numbers, Stirling numbers, and a bit on design theory.