Professor: Jeff Johannes
Section 1
MWF 12:30-1:45p South 328

Office: South
326A

Telephone: 245-5403

Office Hours: Monday 3:30 - 4:30p South 328, Tuesday
8:00 - 9:00p South 336, Wednesday 10:30 - 11:20a South 328, Thursday
4:00 - 5:00p Welles 121, Friday 1:00 - 2:00p South 338, and by
appointment or visit.

Email Address: Johannes@Geneseo.edu

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)

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 it is probably what draws you the
subject in general.

#### Learning Outcomes

Upon successful completion of Math 315 - Combinatorics, a student
will be able to:

- Apply diverse counting strategies to solve varied problems
involving strings, combinations, distributions, and partitions,
- Write and analyze combinatorial, algebraic, inductive, and
formal proofs of combinatoric identities, and
- Recognize properties of graphs such as distinctive circuits or
trees.

#### Reading

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.

#### Grading

The entire class is graded out of 126 points

The final grading scale is as follows:

A 118-126

A- 113.5-117.5

B+ 109-113

B 105.5-108.5

B- 101-105

C+ 96.5-100.5

C 93-96

C- 88.5-92.5

D 76-88

E 0-75.5

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

I will determine priority for presenting
problems. 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. 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.

#### Solutions and Plagiarism

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. There
are plenty of places that one can find all kinds of solutions to
problems in this class. Reading them and not referencing them
in your work is plagiarism, and will be reported as an academic
integrity violation. Reading them and referencing them is not
quite plagiarism, but does undermine the intent of the
problems. Therefore, if you reference solutions you will
receive 0 points, but you will *not* be reported for an academic
integrity violation. Simply - please do not read any solutions
for problems in this class.

#### 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.

#### Accommodations

SUNY Geneseo is dedicated to providing an
equitable and inclusive educational experience for all students. The
Office of Accessibility will coordinate accommodations, auxiliary
aids, and/or services designed to ensure full participation and
equal access to all academic programs, activities, and services at
SUNY Geneseo. Students with letters of accommodation should submit a
letter and discuss needs at the beginning of the semester. Please
contact the Office of Accessibility Services for questions related
to access and accommodations. Erwin Hall 22 (585) 245-5112 access@geneseo.edu
www.geneseo.edu/accessibility-office.

#### 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 no later
than September 12 of plans to observe the holiday.

#### Military Obligations

Federal and New York State law requires
institutions of higher education to provide an excused leave of
absence from classes without penalty to students enrolled in the
National Guard or armed forces reserves who are called to active
duty. If you are called to active military duty and need to miss
classes, please let me know and consult as soon as possible with the
Dean of Students.

####

####

#### Schedule

August 30
Introduction

August 30 - September 8
Part 1: Graph
Theory

September 13 - September 22 Part 2: Strings and
Combinations

September 27 - October 6 Part
3: Distributions

October 13 - October 25
Part 4: Partitions

October 27 - November 8 Part
5: Inclusion and Exclusion

November 10 - November 22 Part 6:
Recurrence Relations

November 29 - December 8 Part 7:
Generating Functions

December 8 - December 19 (12N-2:30p) More?