COMPSCI 575/MATH 513: Combinatorics and Graph Theory

David Mix Barrington

Fall, 2016

This is the home page for CMPSCI 575 and MATH 513, a single course cross-listed in both computer science and mathematics. COMPSCI 575 has a section for undergraduates and a section for graduates, but all students in the course will be treated and graded equally.

The subject matter will be (1) graph theory, including fundamental graph algorithms, (2) combinatorics, including basic counting, generating functions, and recurrences, and (3) a bit of combinatorial game theory.

Instructor Contact Info: David Mix Barrington, 210 CMPSCI building, 545-4329, office hours Monday 2-3, Tuesday 11-12, Thursday 2-3. I generally answer my email fairly reliably.

TA Contact Info:

myphan@cs.umass.edu

Grader Contact Info:

djsaunde@umass.edu

The course is intended for advanced undergraduates or masters' students in either mathematics or computer science. The prerequisite is COMPSCI 250 or MATH 455, both courses in discrete mathematics emphasizing the mathematical method of definition and proof. A grade of B or better is normally required in this prequisite course, but override applications will be considered, particularly from students with later courses such as COMPSCI 311 or MATH 411 that demonstrate the kind of reasoning that will be needed here. Applications should be made via the on-line CICS override form linked from this page.

The course meets for three lecture meetings a week, Monday, Wednesday, and Friday 10:10-11:00 in Integrated Sciences Building room 221.

The textbook is Applied Combinatorics by Alan Tucker, available through the UMass Amazon virtual bookstore and elsewhere. Most homework assignments will be taken from the text.

The course is using the Moodle course management system. Basic information about the course will be on this site, and specifics of the course will be off of the Moodle main page.

Announcements (11 January 2017):

(11 Jan) The final exam and its solution are posted. Grades for the exam and for the course have been posted to Moodle. The scale on the final was A = 105, C = 70. The top was 123 (followed by 122, 116, 115, 114), the median was 94 (a B+), and there were only five scores below 70.

For the course overall, there were 5 A+, 9 ordinary A, 15 A-, 7 B+, 8 B, 4 B-, 3 C+, 3 C, and a D+, so that the median was actually a low A-. Generally I was pleased by the performance in the course, and I thank you all for an interesting and enjoyable semester.

(20 Dec) The solutions to the practice final are posted. Note that the final exam will be in ELAB II 119 (the silver curved building just south of the CICS building) rather than in our classroom as the syllabus said until just now.

(17 Dec) The practice final is up.

(1 Dec) I have now posted the second midterm and its solution. As I said in class, I made the scale more generous at the C level, with A = 90, B = 72, C = 54, D = 36. Of the 56 people who took the exam, the high was 100 (followed by two 98's), the median was 76, and the low was 41 (with second-lowest at 49). There was one in the 100's, 10 in the 90's, 11 in the 80's, 12 in the 70's, 12 in the 60's, 8 in the 50's, and two in the 40's.

On Moodle, your exam score is shown on the same 0-400 scale used for each component of the course. Your final numerical grade will be a weighted average of these 0-400 scores, using the weights given on the requirements and grading page. That grade will be converted to a letter grade by rounding to the nearest standard value (A = 400, A- = 367, B+ = 333, B = 300, etc.) with a five-point bonus. (So the minimum score for an A is 379.) Numerical scores above 417 will be eligible for course citations.

(14 Nov) Solutions to the practice second midterm are now posted.

(11 Nov) I have posted the practice second midterm. Solutions will probably be posted on Monday.

(22 Oct) I have posted the first midterm and its solution. The high score was 100, the median 81, and the low 51. The scale was A+ = 98, A = 93, A- = 88, B+ = 83, B = 78, B- = 73, C+ = 68, C = 63, C- = 58, and D+ = 53. Along with the 100 there were 11 scores in the 90's, 22 in the 80's, 17 in the 70's, 4 in the 60's, and 3 in the 50's.

(6 Oct) I have posted solutions to the practice first midterm. We expect to have solutions to HW#3 and grades for HW#2 on the Moodle site sometime on Saturday.
(4 Oct) As I announced by email, I have canceled this Friday's lecture. The first midterm is posted. I will post solutions before I leave on Friday morning.
(28 Sept) Apologies for the Moodle issues this morning, which have now allegedly been fixed. I promised the HW#3 assignment here, so I will put it here in case it is needed: 3.3 questions 1, 2, 4, 9, 10; 3.4 questions 2, 3, 9 plus two more below related to #2; 4.1 questions 3, 5, 7, 9, 11; 4.2 questions 1, 4, 6, 10, 14.
Question DAMB-1 is to show using decision trees that any comparison based algorithm to merge two sorted lists of size n requires 2n - O(log n) comparisons in the worst case. Question DAMB-2 is to show using an adversary argument that such an algorithm requires 2n - 1 comparisons in the worst case. Note that since different proof methods are specified, you will need different proofs. Also be sure to document any sources of help.
(9 Sept) My's office hours are now posted here and on the Moodle site.
(7 Sept) For the benefit of those students not yet on the Moodle site, here is the first homework assignment: Prelude Question 16; Section 1.1 Questions 13, 14, 20, 27; Section 1.2 Questions 2, 6, 7, 12, 14; Section 1.3 Questions 1, 10, 16; Section 1.4 Questions 5, 7, 13, 24; and Chapter 1 Supplemental Questions 10, 22, and 28.
(12 Aug) This section of the main page will serve as a blog for some announcements, though most announcements will be made on Moodle. Today I am establishing this web site with the main page, course requirements and grading page, and syllabus/schedule.

Last modified 11 January 2017