Mathematics 315:  Combinatorics
Fall 2022

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:


    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


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


    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:


    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-     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

Student Presentations

    For each part each student must present at least two problemsPresentations 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. 


    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. 


    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

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.


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?