Prof. Paul Gunnells, LGRT 1115L, 545–6009, gunnells at umass dot edu. The best way to contact me is by email. Please don’t leave a message on my office phone; I almost never listen to messages there.
Combinatorics is the mathematical science of counting. The goal of this course is to study some techniques in combinatorics; one particular emphasis is generating functions. We will study applications to various counting problems, including some from graph theory.
Introduction to Enumerative and Analytic Combinatorics, Third Edition by Miklos Bona. ISBN: 978–1482249095. Table of contents.
Please note that this is the third edition of this book.
The textbook is very readable; the author has put a lot of work into his exposition, and there are many examples given in detail. There is a lot of material in the textbook, way more than we can cover in one semester. We will try to cover all of the Methods and Topics sections, with possibly some extra material.
It will be presumed that you are reading the relevant sections of the textbook outside of class.
We will not follow these sources, but they are excellent and have lots of interesting material. Occasionally we may refer to them.
Analytic Combinatorics by Philippe Flajolet and Robert Sedgewick. ISBN: 978–0521898065. PDF freely available
Combinatorics: The Art of Counting (Graduate Studies in Mathematics) by Bruce E. Sagan. ISBN: 978–1470460327. PDF available free from the homepage of the author.
Enumerative Combinatorics: Volume 1 (Cambridge Studies in Advanced Mathematics, Series Number 49) 2nd Edition by Richard P. Stanley. ISBN: 978–1107602625. Freely available in draft form.
The grading for the course will be as follows. There will be a final exam worth 30%, and two exams during the semester each worth 25%. The remaining 20% will be based on homework exercises.
After being determined by the above algorithm, the total score will be truncated down to the nearest integer less than or equal to the total score. (Note that truncation is not the same as rounding. For example, a score of 89.75 will be truncated to 89, not rounded to 90. This is standard policy in courses offered in the Math and Stat Department.) The letter grade will then be determined by the following scale:
| A | A– | B+ | B | B– | C+ | C | C– | D+ | D | F |
|---|---|---|---|---|---|---|---|---|---|---|
| 90 | 87 | 83 | 79 | 75 | 71 | 67 | 63 | 59 | 55 | <55 |
The final will be cumulative, with some emphasis placed on topics covered after the midterm exam. The date and time will be announced by the University. The final will only be given during the scheduled time.
There will be two midterm exams, given in the evening.
Tuesday, 14 October, 7–9pm, location LGRCA301. Request makeup if necessary by Tuesday, 30 September.
Thursday, 6 November, 7–9pm, location LGRCA301. Request makeup if necessary by Thursday, 23 October.
The exam times are 2 hours to take some of the pressure off. It is not expected that you will need the full 2 hours to complete them.
Sections covered on an exam, as well as other exam policies, will be announced in class some time before the exam date. Some time in the lecture before each exam will be devoted to review.
See below for the academic honesty statement about exams.
Re-taking of exams is not allowed in this course: once an exam has been taken it cannot be retaken or made up.
You are expected to take all exams, including the final exam, during their scheduled times. All students should check your travel plans and exam schedules of your courses carefully. If you have any schedule conflicts, you may log on the Spire page, go to “Student Home” and then to “Evening Exam Conflict”. This will allow you to fill out a conflict form and submit it. Then the registrar will email your instructor who needs to provide a makeup exam. Makeup exams should be requested at least two weeks before the exam.
Which case and where is the official support document for the make-up request?
(1) if you have an exam (or a class) schedule conflicts with the regular exam, you should log on the Spire page, go to “Student Home” and then to “Evening Exam Conflict”. This will allow you to fill out a conflict form and submit it. Then the registrar will email your instructor who needs to provide a makeup exam.
(2) if you have a university trip for university business during the regular exam date, like an athletic competition or academic conference etc., you should ask your supervisor or your coach to write an explanation letter including his/her phone number to your instructor as the official written document. Your instructor may verify the event by phone call.
(3) if you have a religious observance on a regular exam date and can NOT take the exam, you should write an explanation letter yourself and attach the invitation letter or relevant information as the official document.
(4) if you have a medical reason and can not take the regular exam, you should ask a medical professional’s statement including his/her phone number which indicates that you were unable for medical reason to take the scheduled exam. If the medical professional’s statement is not given before the exam, your instructor may refuse your make-up request.
This is not a programming course, and assignments will not require coding. However many computations for examples and problems will benefit from using a computer. For an overview of software you might find useful, see here.
Problem sets will be assigned on the main course page; method of collection will be determined once we have a grader. Late problem sets will not be accepted for any reason. At the end of the term, a few problem set grades will be dropped, so missing one or two problem set submissions shouldn’t affect your grade.
Only selected problems (randomly chosen by me) will be graded. The book contains some exercises with complete solutions for self-study. These will be part of the homework, but they will not be graded.
I encourage you to form study groups and to work on the problem sets together. In fact you will learn a lot more about the material through discussing it with your fellow students. However, there are a few guidelines to follow:
Remember that ultimately you’ll be taking exams by yourself, so if you choose to work with others, make sure that you’re understanding what’s going on.
If you do work with other students, you are responsible for writing up the problems yourself in your own words. In other words, your solution must be sunmitted separately; there are no group homework submissions allowed.
If you do work with your students on a problem set, you must indicate this on the first page of your HW submission. Please include the names of the students you worked with. This alerts the grader that some of your solutions may closely resemble other students and that there is nothing amiss.
It is expressly forbidden to use means that do not represent your own work (such as, but not limited to, generative AI and copying solutions from online forums) to complete problem sets. (See the academic honesty statement below for more info.)
Successful completion of the problem sets is essential to help you monitor your progress in the course. The homework problems will be very similar to problems that appear on exams. Please don’t postpone working on the problems; try to take a look at them shortly after the material is covered in class.
I try to answer as many questions as possible during lecture. If you have a question, don’t be afraid to ask. Chances are other students also have the same question. I also usually stick around a few minutes after class to answer quick questions (such as questions about parts of the lecture, a homework problem you’ve tried, etc.). Most students find this to be a good way to clear up confusion.
Outside of class, the best way to get help is through my office hours. Sometimes only a little bit of consultation is all that’s needed to deal with difficulties. One thing to remember is that you will get much more out of office hours if you make a serious effort to do the problem on your own first.
Although I like to get a lot of questions from students, it is not possible to answer mathematical questions by email. Please don’t be offended if you ask me a mathematical question by email and I don’t respond. I’ve found in the past that trying to discuss mathematics by email rarely helps anyone, and usually only causes more confusion. It’s much more effective to ask me such questions during class or office hours.
The University of Massachusetts Amherst is committed to making reasonable, effective and appropriate accommodations to meet the needs of students with disabilities and help create a barrier-free campus. If you have a disability and require accommodations, please register with Disability Services (161 Whitmore Administration building; phone 413–545–0892), meet with an Access Coordinator and send an accommodation letter to your faculty. Information on services and materials for registering are also available on the website www.umass.edu/disability.
Special accommodation request: new disability students should be certified by Umass disability service center (DSC) at first, then you should ask DSC to send the special accommodation documents to your instructor at least two weeks before exam 1 or exam 2, after that you may contact DSC,
Trisha Link
Exam Proctoring Coordinator
examsaccess@admin.umass.edu
413-545-0892
169A Whitmore
directly to schedule an appointment, DSC will notify you when and where to take the exam in a few days before the exam . For the documented disability students, DSC will notify you when you should schedule the final exam in DSC.
Since the integrity of the academic enterprise of any institution of higher education requires honesty in scholarship and research, academic honesty is required of all students at the University of Massachusetts Amherst. Academic dishonesty is prohibited in all programs of the University. Academic dishonesty includes but is not limited to: cheating, fabrication, plagiarism, and facilitating dishonesty. Appropriate sanctions may be imposed on any student who has committed an act of academic dishonesty. Instructors should take reasonable steps to address academic misconduct. Any person who has reason to believe that a student has committed academic dishonesty should bring such information to the attention of the appropriate course instructor as soon as possible. Instances of academic dishonesty not related to a specific course should be brought to the attention of the appropriate department Head or Chair. Since students are expected to be familiar with this policy and the commonly accepted standards of academic integrity, ignorance of such standards is not normally sufficient evidence of lack of intent. For more information see the website of Dean of Students Office.
Expectations for our course as as follows:
For homework, as discussed above, you will be allowed to work with other students collaboratively. In fact, I encourage you to form study groups to work together. However, it is your responsibility to make sure that you are learning the material. You also must submit your own work, indicating if you collaborated with any other students.
The written work you submit must be original. The use of online or other sources for solutions, or the use of generative AI tools such as ChatGPT to produce or write solutions will be considered a violation of academic honesty. Generative AI usage for other means related to the course (like as a study partner, sounding board, etc.) is not considered a violation, but it is the responsibility of the student to verify the accuracy of any content used in that context. (You’re much better off just reading something written by a reputable source, or collaborating with other students in the course, in my opinion.)
All exams will be done in-person and are closed book: no supplemental materials such as the textbook or notes may be used. Devices such as phones, watches, calculators, and computers, are not allowed to be used during exams. Of course no communication between students in any form is allowed during exams. Use of any unauthorized resources will be considered a violation of academic honesty and will be handled accordingly.