Advanced Undergraduate

Applied Combinatorics

At Georgia Tech, applied combinatorics is a junior-level course intended to introduce students to fundamental techniques in enumeration, discrete structions, and algorithms and optimization. In a typical section, about two-thirds of the students are computer science majors. The remaining students are a mixture of computer engineering, industrial and systems engineering, discrete mathematics, and applied mathematics majors. (A very small number of students may be math minors from other science and engineering majors.) I am in the process of writing a textbook for this course with William T. Trotter.

Matrials from the two times I taught the course are below. In Fall 2008, my course enrolled 34 students, while in Spring 2010, I had 65 students.

MATH 3012—Fall 2008

MATH 3012—Spring 2010

Spring 2010 Writing Assignment 2

Assignment: Write an essay that provides an in-depth description of a real-world problem solved using combinatorial techniques. These techniques should hopefully be from this course or built upon the foundation we're building in this course. However, I will approve things that use other topics from combinatorics; consult me before beginning on such an assignment. Preferably, this problem will come from your discipline. However, for some majors (math and economics spring to mind), this may be more of a challenge. I invite you to discuss potential topics with me. Your essay should be written at a level understandable to any student in MATH 3012 (so, for example, computer engineers should remember there are math and economics majors in the class). You must describe the problem, why more traditional methods are insufficient or do not provide an optimal solution, and how combinatorial techniques are used. I expect that you will incorporate information from multiple sources and demonstrate that your understanding of the problem synthesizes information from those sources in an integrated manner. Be sure to cite any references you use (and use quotation marks if quoting verbatim).

Peer feedback: Prior to submitting your final draft of your writing assignment, you must exchange assignments with at least one other member of your group. This offers an opportunity for someone else to review your assignment not only to proofread it but also to evaluate it against the grading rubric in order to suggest areas in which it could be improved. In the text box available at the time you submit your assignment, you must enter (1) the name(s) of the group member(s) on whose assignment(s) you gave feedback, (2) the name(s) of the group member(s) who gave feedback on your assignment, and (3) how you used their feedback to improve your assignment. Peer feedback is mandatory. Failure to engage in and report on the process will result in a deduction of 0.5 from your score on the assignment.

Advance feedback from instructor: (Optional) If you would like feedback from me on a draft, you must email it to me as a PDF file with a request to schedule an appointment (or plans to come to office hours). This email generally must be sent 24 hours prior to the desired appointment and must contain specific questions on which you would like feedback. I will review your essay, prepare comments, and go over them with you at the meeting in my office.

Grading: Your essay will be scored on a scale of 0 to 5 (rounded to one decimal place) according to the attached rubric. Note that the weights for each category are given at the bottom of the rubric. Most of you had very few problems on the first writing assignment with grammar, spelling, etc. However, a good number of you did not provide a conclusion or introduction. (Some got specific comments on this.) These sorts of things will count in the third column of the rubric, so please take this into account while preparing this writing assignment.

Submission: You will submit your writing assignment as  PDF file (any other format will result in a one-point (i.e., one letter grade in most instances) grade reduction) via T-Square. Be sure to see the Peer Feedback section above for instructions on what to put in the text box when you upload your assignment.

Spring 2010 Writing Assignment 1

Write an essay, one to two double-spaced pages in length, describing why you are taking MATH 3012. For most (if not all) of you, this is because your major requires it, so you should write about why your major requires this course. For engineering and computer science majors, you might want to look at the accreditation requirements put forward for your major by ABET, the Accreditation Board for Engineering and Technology.

Be sure to cite any references you use. (Your list of references does not count toward meeting the one-page minimum length requirement.)

Applied Combinatorics

Applied Combinatorics by Mitchel T. Keller and William T. Trotter is now available in some new formats that we hope will be useful.