This is a rigorous introduction to some topics in mathematics that underlie areas in computer science and computer engineering, including: graphs and trees, spanning trees, colorings and matchings, the pigeonhole principle, induction and recursion, generating functions, and applications. The course integrates mathematical theories with applications to concrete problems from other disciplines using discrete modeling techniques. Small student groups will be formed to investigate a modeling problem independently, and each group will report its findings to the class in a final presentation. Satisfies the Integrative Experience for BS-Math and BA-Math majors. Prerequisites: Calculus (MATH 131, 132, 233), Linear Algebra (MATH 235), and Math 300 or COMPSCI 250. For students who have not taken Math 300 or COMPSCI 250, the instructor may permit students with sufficient experience in reading and writing mathematical arguments to enroll.
This is a fully remote course that is synchronous-optional.
Prof. Paul Gunnells, LGRT 1115L, 545–6009, gunnells at math dot 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.
TBA.
Combinatorics and Graph Theory, by Harris, Hirst, and Mossinghoff, Second edition, Springer-Verlag. We will cover material from Chapters 1 and 2, and some additional material not in the textbook.
Please be sure to read the textbook to supplement the lectures. The authors (one of whom I know) have spent a lot of time trying to make the text enjoyable and understandable (unlike a typical math book). Also, not every topic covered in the problems will be explicitly lectured on.
You can get the book in PDF for free through our library, or can purchase a print on-demand softcover edition for about $25.00. Here is a direct link that may or may not work. If it doesn’t, follow these instructions:
Go to the Five Colleges Library Catalog.
Search for “harris hirst mossinghoff”. You will find the book (it’s in various Five College collections). Click on “UM Internet Springer” in the Location and Call Number column.
Click on “UMass: Link to resource”. You will be taken to the publisher’s website for the book, and can get the PDF or can order a printed copy.
Lectures will be given by Zoom live during the scheduled course meeting time. You will be sent an invitation to the lectures as soon as they are set up; the meeting info will not be posted anywhere online. You will need your UMass NetID/Password to log into the meeting. The lectures are only intended for our class.
The format of the lectures will be the instructor (yours truly) writing on sheets of paper under a document camera, to simulate as closely as possible the experience of a normal classroom lecture. This worked well in spring and fall 2020. It has the added benefit that you will not suffer the indignity of having to look at my ugly face or disgusting basement … you will just see the lecture notes.
After the lecture is completed the pages will be scanned and posted to the course website for you to refer to.
The lectures will be recorded during the livestream and will be posted online (details will be given later through your campus email). These lectures will not be available publicly; only the students in our course will have access to them. I know that some students will not want their images captured in a recording and posted online. That is totally understandable and I agree with this sentiment. I also don’t want to violate the privacy of your home. Therefore you will not be required to have your camera on during the lectures; it’s ok to have your camera off and to participate only verbally or via the chat (the chat log will not be posted; verbally asking a question is better because I don’t always catch the questions that come in through the chat, although I try to keep an eye on it).
The recorded lectures and posted lecture notes become part of the course materials that you have access to during the term.
Please attend the lectures live. The live lectures are the main time you have to interact with me and to ask questions. I generally like a lot of feedback during lecture; student feedback and interactions are extremely important. If I say something you don’t understand, you need to ask me right away! I find it difficult to teach without it.
This course will have two take-home midterm exams and a take-home final exam.
Exam I will be distributed Tuesday 2 March and collected Thursday 4 March.
Exam II will be distributed Tuesday 6 April and collected Thursday 8 April.
The final exam will be distributed the first day of finals week 5/6 and collected the last day of finals week 5/12.
The dates of the midterm exams do not have any conflicts with the 2021 New York City Alternate Side Parking Suspension Calendar, which is the most comprehensive list of religious holidays I know.
Sections covered on individual exams will be announced beforehand. The final exam will be cumulative, with some emphasis placed on topics covered since those on the second exam.
The exams will be submitted through our course’s Moodle section. More details will be provided before the exams.
You are expected to take all exams, including the final exam, during their scheduled times. Re-taking of exams is not allowed in this course: once an exam has been taken it cannot be retaken or made up. Reasons for taking an exam at a different time are limited to the following:
For these you must submit a statement from a medical professional. It is your right not to disclose any details, but we must be assured that you are medically incapable of taking the exam. A statement from a medical professional to this effect will suffice (although merely visiting a doctor is not sufficient; the doctor’s note should clearly state that you were unable, for medical reasons, to take the scheduled exam). If advance notice is possible and not given your instructor may refuse your request. If you miss an exam due to illness and advance notice is not possible, your instructor must be notified within 24 hours of the missed exam.
Notify the Dean of Students Office. Someone will then verify the details and notify each of your instructors.
State law and university regulations require that a student be excused from academic pursuits on days of religious observances. Any such claim requires notice from the student, in writing, at the beginning (first two weeks) of the semester.
It is impossible to anticipate all of the possible circumstances that can occur. In case of an exceptional event beyond those covered above, contact the instructor and explain the problem. (You should be prepared to provide a written statement.) Your instructor will evaluate the reasons that you have given and come to a decision.
Students receiving accommodations for exams should have their documented accommodations sent to the instructor as soon as they are available, and arrangements will be made.
Our TA will run a review session before each exam. All such sessions will be announced after they are scheduled.
There are two extra assignments, in addition to the exams and the homeworks.
A paper on a topic related to the material in the course.
A self-reflective personal essay.
UPDATE: You must only complete the self-reflective personal essay; the first writing assignment has been eliminated.
More information about these will be released later in the term. There will be no group presentations since the course is synchronous-optional.
Total scores in our section of Math 455 will be computed as follows:
The homework will be worth 35%.
If your final exam score is less than or equal to the average of your Exam 1 and Exam 2 scores, then each of Exam 1 and 2 counts 17.5%, and the final exam counts 15%.
If your final exam score is greater than the average of your Exam 1 and Exam 2 scores, then your final exam will count 20% (instead of 15%) and each of Exams 1 and 2 will count 15% (instead of 17.5%).
The topical paper will be 10%.
The self-reflective essay will be 5%.
UPDATE: The topical paper has been eliminated, and the self-reflective essay is now worth 15%.
Remarks about grading:
Note that attendance in lecture is not required as part of your grade.
At the end of the term, some of your HW scores will be dropped. This way, if you don’t do as well on an assignment because of extra work in another course or for any reason, it shouldn’t affect your final homework grade. Extensions for HW are not granted except for documented reasons, as described in the Make-Up Exam section above.
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. Rounding up of grades is not allowed by a policy adopted by the 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 best way to get help is to ask your instructor or TA questions during class or in office hours. Unfortunately it is not possible to answer mathematical questions by email. Please bring all such questions to class, recitation, and office hours.
The University of Massachusetts Amherst is committed to providing an equal educational opportunity for all students. If you have a documented physical, psychological, or learning disability on file with Disability Services (DS), you may be eligible for reasonable academic accommodations to help you succeed in this course. If you have a documented disability that requires an accommodation, please notify me within the first two weeks of the semester so that we may make appropriate arrangements.
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, 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 through webassign.
For exams, you will be allowed to use your textbook, your own course notes, the scanned notes from our lectures, and the recordings of our lectures available online. You will not be allowed to discuss the exam with anyone else, except me (I can help with clarifying questions, just like a traditional exam; I can’t help with actual mathematical contributions, of course). I will closely watch my email during exams to see if you have questions. You may not discuss the exam with any other students and may not use any resources other than those indicated above. Use of any unauthorized resources will be considered a violation of academic honesty and will be handled accordingly.