Description:   The objectives of the class is to learn the basic techniques, theorems, and algorithms of discrete mathematics and graph theory. Discrete mathematics, including graph theory, has numerous applications in network science, design of algorithms, chip layouts, scheduling, management of cell phone networks, to name a few.
Topics to include: pigeon-hole principle, mathematical induction, permutations, binomial theorem, compositions, partitions, Stirling numbers, inclusion-exclusion principle, recurrence relations, generating functions, Catalan numbers, graphs, trees, Eulerian walks, Hamiltionian cycles, matrix-tree theorem, electrical networks, graph colorings, chromatic polynomials, Ramsey theory.
There is no official prerequisite for this course however, it is recommended that you have been exposed to a variety of math and science courses. All topics will be treated in an introductory manner.

Syllabus:     syllabus447.pdf

Lecture notes, and homework:     Please login into sakai at URI

Textbook:     M. Bona, A walk through combinatorics: An Introduction to Enumeration and Graph Theory, 3rd edition, World Scientific Publishing, 2011, ISBN: 978-981-4335-23-2, publisher's website.

Accommodations: Any student with a documented disability is welcome to contact me as early in the semester as possible so that we may arrange reasonable accommodations. As part of this process, please be in touch with Disability Services for Students Office at 330 Memorial Union, 401-874-2098.