This summer (2014) will feature two mini-courses: Introduction to Hodge Theory, June 5 through June 30, taught by Jie Wang Mathematical Models of the Environment, July 7- Tuesday July 29, taught by Caner Kazanci Course Descriptions Instructor: Jie Wang Title: Introduction to Hodge Theory Schedule: The course will meet June 5 through June 30, Tue, Thu 9:15-11:30, room TBD Course Content Instructor: Caner Kazanci Title: Mathematical models of the environment. Schedule: The course will meet MWF starting July 9, ending on June 28. Classes will run for 75 minutes, except for a 2-hour field trip on July 16 (12 hours total). The tentative schedule is MWF from 2:30pm-3:45pm, in Driftmier 312 Course Content: The course will cover several mathematical approaches to model, simulate and analyze the environment to address relevant questions. The most common approaches start by compartmentalizing the ecosystem into essential living and non-living compartments, and building a network of biomass or energy flows among these compartments. The result is weighted digraph with some interesting graph theoretical properties. The flow rates among compartments are actually functions of time, often determined by a differential equation system. Tentative outline of topics to be covered: Mathematical methods for modeling the environment Graph Theoretical Models Differential Equation Models Stochastic Models Ecological Network Analysis Network Environ Analysis Formulation and properties of environmental health indicators Centrality indices and keystone species Outcome: Gain a decent understanding of how ecological and environmental systems are modeled and analyzed using interesting mathematics. Prerequisites: Basic linear algebra and differential equations knowledge is required. Although we'll discuss some graph theoretical issues, no advanced knowledge is necessary. Field trip: I'll arrange a van for a 2-hour field trip to Lake Herrick for an exercise on the mathematical modeling of terrestrial and aquatic systems. Dr. Whipple or Dr. Patten from Ecology will be joining us. Text book: No text book is required. I will bring notes in class from 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 some lectures.