Spring 2023 Syllabus
The main theme of this course will be graph theory. We will discuss a wide range of topics, including spanning trees, eulerian trails, matching theory, connectivity, hamiltonian cycles, coloring, planarity, integer flows, surface embeddings, and graph minors. The prerequisites for the course are very modest—all graduate students of mathematics should be able to follow the lectures. There are many books on graph theory. I recommend for the course Graph Theory by Reinhard Diestel, Fifth Edition, Springer, 2016, which is available as a paperback (for about $50 from various online stores), as a free preview, or, best yet, free e-book from LSU Libraries (LSU login required). Another good book on the subject is Introduction to Graph Theory by Douglas B. West, Prentice Hall, 1996. Having these books, especially the first one listed, will be very helpful, but not absolutely necessary. I plan to present the lectures with my own notes, which will be available for download, both as slides, and as a handout, and which should make good study material. Beware, both of these files are subject to change as the course progresses—check for updates regularly. The files include assignments given last time the course was given, which are also subject to change. Also, the amount of detail in my lecture notes cannot compare with that of either of the mentioned books. If your interest in the subject is anything more than superficial, you would be well advised to get at least one of those books.
The grade for the course will be based 70% on homework and 30% on the final exam. The grading scale will follow 97-100: A+, 93-97: A, 90-93: A-, 87-90: B+, etc. Decisions in borderline cases will be made on the basis of class participation. There will be the total of over twenty problems given as homework, and the two lowest problem scores will be discarded. Homework will be graded not only on mathematical correctness, but also on the clarity of exposition. If you have any questions about the course, do not hesitate to contact me.
- Name:
- Bogdan Oporowski
- Class time:
- MWF 10:30–11:20
- Email:
- bogdan@math.lsu.edu
- Office hours:
- Zoom appointments (email me for Zoom ID)