of University Delaware Department of Mathematical Sciences M689-Combinatorics and Graph Theory II Fall 2008 ******************************************************************************* Instructor: Qing Xiang Oce: 508 Ewing Hall Phone: [phone] Email: [e-mail] Oce Hours: 2pm3pm Tue. and Thur. This is the second course in the 688-689 sequence. This sequence is essential for students who want to write a thesis in discrete mathematics. The main emphases of MATH689 will be on designs, codes and nite geometries. We will also cover some topics from graph theory and probabilistic methods in combinatorics. The text is A Course in Combinatorics, by Van Lint and Wilson (Cambridge University Press). Two useful reference books are Combinatorics: Topics, Techniques, Algorithms by Peter J. Cameron (Cambridge University Press) and Combinatorial Theory, by M. Hall, Jr. (Second edition, Wiley, New York, 1986). Syllabus: Week 1 Chap.18, Hadamard matrices Week 2,3 Chap.19, Designs Week 4 Chap.20, Codes and Designs Week 5 More on Codes and Designs Week 6 Chap.21, Strongly regular graphs Week 7 Chap.17, Latin squares Week 8 Chap.22, Orthogonal Latin squares Week Chap.23 9 and 26, Combinatorial designs and projective geometries. Week 10 More on geometries Week 11 Chap.31, algebraic graph theory Week 12 Probabilistic methods in combinatorics Grading: One take-home Midterm: 50 points Comprehensive take-home Final: 100 points Homework: 150 points Total: 300 points Your grade in this course will be based on the total number of points accumulated. Remarks: 1. Make-ups for the exams will be given only in preapproved situations.
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2. I will give one homework set (about 5 problems) almost every week. I will collect the homework on the due date. You must type the solutions to the homework problems by LaTeX. Late homework will not be accepted unless you talk...