Important theorems will include the Law of Large Numbers, and the Central Limit Theorem. Probability has rich and varied applications to many fields, including gambling theory, computer networks, queueing theory, probabilistic algorithms, option-pricing, and genetics, and is thus basic to advanced study in these areas. As far as possible, this course will emphasize both these fun and interesting problems as well as the applications of probability. MATH128A or 142 or 179 or instructor consent. Open to advanced undergraduates and graduate students.
Graph theory is an interesting area of mathematics that has many applications in computer science.
Topics to be covered will include graphs, digraphs, paths and cycles, planarity and graph embeddings, connectivity, networks and flows, hamiltonian cycles, orientations and tournaments, matchings and factorizations, as well as graph coloring.