Graphs and Networks

Selected topics about the mathematics of graphs and networks with an emphasis on random graph models and the dynamics of processes operating on these graphs. Topics include: empirical properties of biological, social, and technological networks (small-world effects, scale-free properties, transitivity, community structure); mathematical and statistical models of random graphs and their properties (Bernoulli random graphs, preferential attachment models, stochastic block models, phase transitions); dynamical processes on graphs and networks (percolation, cascades, epidemics, queuing, synchronization). Prerequisites: Multivariable calculus; Linear algebra; APMA 0355 or equivalent; APMA 1655 or equivalent; programming experience. APMA 1200 or APMA 1690 or similar courses recommended.