Summer 2019 will feature two mini-courses: Mini-Course #1 Math 8950 - Inequalities Instructor: Jason Cantarella Ten Lectures on June 10-14 (MTWRF) Course Webpage Mini-Course #2 Math 8970 - Stochastic processes in life sciences Instructor: Caner Kazanci 8 Lectures on June 5-7 (WRF) and 10-14 (MTWRF) A course on stochastic processes in general, focusing on methods applicable to modeling living systems (neural networks, biochemical reactions, and ecosystem modeling.) Tentative outline of topics to be covered: - Review of basics of probability - Mathematical modeling of living systems, a broad overview - Markov Chains, branching processes - Basic introduction to stochastic processes - Gillespie's stochastic algorithm - Brownian motion and diffusion - Basic introduction to Stochastic Differential Equations - Master Equation - Langevin Equation - Cellular Automata Outcome: Gain a decent understanding mathematics used to model and simulate the probabilistic behavior observed in living systems. Prerequisites: Basic linear algebra and differential equations knowledge should be enough to understand the topic. Text book: No text book is required. I will provide class notes based on two books: "A first course in Stochastic processes" by Karlin & Taylor, and "Handbook of Stochastic Methods" by Gardiner. I will use powerpoint style slide shows for most lectures.
