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.
Prof. Paul Gunnells, LGRT 1115L, 545-6009, gunnells at math dot umass dot edu. The best way to contact me is by email, but please read this before trying to send me email.
Emma Dowling, LGRT 1325, 545-1801, dowling at math dot umass dot edu. Her office hours for Math 455 are 10:15-11:15 Mondays, Wednesdays, and Fridays.
Combinatorics and Graph Theory, by Harris, Hirst, and Mossinghoff, Second edition, Springer-Verlag. We will cover material from Chapters 1 and 2, and possibly 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 purchase your copy of the text however you like, but the best way is through our library. The library has a subscription to some electronic resources of Springer-Verlag (a large mathematics publisher). Our subscription means you can either download the pdf of the book (yes, free), or you can order a print-on-demand copy for substantially cheaper than retail. In fact, the book is listed in Spire as costing about $50 retail; ordering a copy via our library costs about $25.
Here's how you can get it:
I bought my own copy this way. The quality is very good, and I actually like having a printed copy to complement the downloaded pdf. It takes a few days to receive your copy after purchase.
The grading for the course will be as follows. There will be a final exam worth 40%, and two exams during the semester, each worth 20%. Of the remaining 20%, half will be based on homework exercises, and half on the final project.
The final will be cumulative, with some emphasis placed on topics covered after the second exam.
The date and time of the final exam will be scheduled by the university. The final will only be given at that time, and not at any other time for any reason, with the exception of the reasons outlined in the academic regulations (see below for more information). In particular, adjust your travel plans accordingly; planning to leave for vacation before the final exam is a bad idea.
The University has a byzantine final examination policy for resolving conflicts. The details are contained in the academic regulations, specifically Section X.C (on p.29). Please read it carefully and make sure that you have no final exam conflicts when the schedule becomes available. It is your responsibility to understand and follow this policy (note that part of the process is getting proof of a conflict from the Registrar's office, since no faculty member can parse the text of the academic regulations).
The dates of the exams during the semester are the following:
These exam dates do not conflict with any religious observances, as determined by the 2014 NYC Alternate Side Parking Rules Suspension Calendar, which is the most complete list of holidays I know.
Please be aware of these exam dates and record them. Exams will not be given at any other time. Sections covered on an exam will be announced before the exam date.
Make-up exams will only be given in the case of family or medical emergency. Both situations will require a note from your advisor, and the latter will require a note from your physician. No make-up exams will be given for any other reason.
Problem sets will be assigned on the main course page and will be collected in-class. Late problem sets will not be accepted for any reason, and will simply be marked late and returned ungraded. 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.
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, 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.
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.
As part of the course, you will complete a group project. The details will come later in the term. My plan now is to assign you into small groups, each of which will pick a topic from a prepared list of projects. I expect that most of the projects will involve some kind of programming. Programming experience is not a prerequisite for the course, but many of you will have it. I will prepare some kind of questionnaire during the term for you to let me know your experience, and will try to form groups with this in mind. Group project=teamwork. You will work on these projects with your team outside of class. At the end of the term we will have presentations in class so you can show off what you've done.
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 and the teaching assistant's 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 calculus 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.