## Mathematics 315:  Combinatorics Fall 2009Introduction

Professor:        Jeff Johannes                                    Section 1    MWF    12-12:50p   Sturges 103
Office:             South 326A
Telephone:       245-5403
Office Hours:     Monday 9 -  9:50a, 2:30 - 3:30p, Wednesday 3:30 - 4:30p, Thursday 8 - 9p, Friday 11 - 11:50a, sometimes3 - 4p, and by appointment or visit
Web-page:        http://www.geneseo.edu/~johannes

Textbooks
Knots and Surfaces:  A Guide to Discovering Mathematics, David W. Farmer and Theodore B. Stanford (Chapter 1 only, distributed in class)
Combinatorics:  A Problem Oriented Approach, Daniel A. Marcus

Purposes
The purpose of this class is to solve a variety of diverse discrete and counting problems.

Overview
Mathematics is about doing - not about watching.  In this class you will spend most of your time solving problems.  I will help in any way you want, but the mainstay of the work will be done by you.  You will present.  You will work problems.  Combinatorics is much more about solving problems than learning theory.  I expect  this will appeal to all of you - as it's matched well with your earliest experiences in mathematics and probably what draws you the subject in general.

I have carefully two sources for this class.  Both books are designed as guides and problem sources, more than explanation sources.  By answering a series of leading questions you can teach yourself.  There is also some background text in the book.  It is your responsibility to read that on your own.  Our class time will be spent presenting and working on problems.

The entire class is graded out of 126 points

The final grading scale is as follows:
A      118-126
A-     114-117
B+    109-113
B      106-108
B-     101-105
C+    97-100
C      93-96
C-     89-92
D      76-88
E       0-75

Student Presentations
For each part each student must present at least two problems.  Presentations will be scored out of at most 4 points, with no more than 7 points for each pair.

The class presentations will be graded roughly as follows:
4    excellent
3.5 very good - at most minor errors
3    some problems, but the main idea of the solution is clear
2    some correct things
1    attempted
0    no presentation

Priority for presenting problems will be determined based upon prior performance in the class - lower performance leads to higher priority.  Each student who has not yet presented will have priority over students who have presented.  A third (or more) problem may be presented in order to replace a prior presentation.

Written Solutions
Each part will have a problem set.  Students are responsible from choosing their own problems from the associated reading materials.  Class presentation problems are not acceptable choices for problem sets.  Each problem set is graded based entirely on the number of problems clearly completed.  There is no partial credit on any particular problem.  It either counts or it does not.  In order to count it must be clearly written in both mathematics and English.  Each student will receive credit for no more than 11 problems per part.  Writing a problem that no one else submits counts for two problems.  Remember not to count on this, though, because others may submit the same problem at some point.  Please regularly check with me regarding what problems you are choosing.  I reserve the right to deem a selection of problems inadequate and to score them with that limitation.  Please be sure to include a variety of challenges and topics in your problems.  Selecting two problems that are mathematically identical will most likely result in credit for only one of the two problems.

Feedback
Occasionally you will be given anonymous feedback forms.  Please use them to share any thoughts or concerns for how the course is running.  Remember, the sooner you tell me your concerns, the more I can do about them.  I have also created a web-site which accepts anonymous comments.  If we have not yet discussed this in class, please encourage me to create a class code.  This site may also be accessed via our course page on a link entitled anonymous feedback.  Of course, you are always welcome to approach me outside of class to discuss these issues as well.

While working on homework with one another is encouraged, all write-ups of solutions must be your own. You are expected to be able to explain any solution you give me if asked. The Student Academic Dishonesty Policy and Procedures will be followed should incidents of academic dishonesty occur.

Disability Accommodations
SUNY Geneseo will make reasonable accommodations for persons with documented physical, emotional or learning disabilities.  Students should consult with the Director in the Office of Disability Services (Tabitha Buggie-Hunt, 105D Erwin, tbuggieh@geneseo.edu) and their individual faculty regarding any needed accommodations as early as possible in the semester.

Religious Holidays
It is my policy to give students who miss class because of observance of religious holidays the opportunity to make up missed work.  You are responsible for notifying me by September 11 of plans to observe a holiday.

Schedule

August 31                                    Introduction
September 2 - September 16           Part 1:  Graph Theory
September 18 - September 30      Part 2:  Strings and Combinations
October 2 - October 16          Part 3:  Distributions
October 19 - October 30              Part 4:  Partitions
November 2 - November 13            Part 5:  Inclusion and Exclusion
November 16 - December 2      Part 6:  Recurrence Relations
December 4 - December 21       Part 7:  Generating Functions

Monday, December 21           12N-3p    final discussion and presentations