One of the goals of scientific inquiry is to understand the processes of nature on a quantitative basis. In pursuit of this goal theorists create models to represent the order they observe, and in turn devise mathematical methods for interpreting and solving these models. This program will provide a thorough yet engaging introduction to such mathematical methods and the associated techniques of model building. Differential equations, ordinary, partial and non-linear, will be an important component of the program. We will study both the derivation of these equations from physical and biological models and their solution using analytical and numerical methods. In addition we will study the methods and applications of linear algebra, Fourier and Laplace transforms, the calculus of variations, and chaotic dynamics. In Spring quarter we will focus on continuous and discrete mathematical models in Biology – examining models of population dynamics, competition, evolution, and the origins of life. In addition to the theoretical work we will also discuss questions of a more philosophical and historical nature such as: Is mathematics discovered or created? Can mathematical models represent reality? What makes a model good?
Students will attend weekly lectures, seminars and computer labs. Students will also be expected to give presentations each quarter and in Spring quarter students will have the opportunity to apply the tools they have learned to complete an independent project. Up to 44 credits of upper division science credit will be awarded, contingent on upper division performance.