Summer 2019 will feature two mini-courses:
Math 8950 - Inequalities
Instructor: Jason Cantarella
Ten Lectures on June 10-14 (MTWRF)
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.