The mathematics 388 course at Claremont Graduate University goal was the construction, simplification, analysis, interpretation and evaluation of mathematical models that shed light on problems arising in the physical, biological, and social sciences. Furthermore, derivations and methods for solutions of model equations, heat conduction problems, simple random walk processes, simplification of model equations, dimensional analysis and scaling, perturbation theory, and a discussion of self-contained modular units that illustrate the principal modeling ideas were emphasized throughout the class. The major class assignment was to develop a modeling project.
The modeling project that I selected was the predator-prey model. The predator-prey model, also known as Lotka-Volterra, is used to understand the population dynamics involved in a simple system that involves a single predator specie and a single prey specie. By ignoring such things as the variability of individuals of each species, variation in the environment over time, and the effects of other species, the properties of the interactions between the two species are examined and are used to understand the mechanisms involved in the cyclical behavior of their population levels. In my project I examine a modified model that illustrates the fruitful interactions of algebraic and geometric methods, and the classic Lotka-Volterra model.
The class increased my mathematical knowledge in the areas of advance calculus, linear algebra, ordinary and partial differential equations, and numerical methods. Moreover, the project provided me with first hand experience of what mathematical modeling is and of all its elements. Through the class lectures, homework assignments, and project, I was able to increase my experience of mathematical modeling. I was provided with extensive practice of formulating real-world problems in mathematical terms, and to use appropriate analytical and numerical methods to solve simplified equations or approximate the solution for certain parameter regimes. In addition, the course professor emphasized the importance of interpreting solutions or results and to make reasonable predictions on the behavior of different systems as parameters were varied.