Spring 2014: Mathematical Modeling
MW 2:45 pm – 4:00 pm
Textbook: Mathematical Models in Biology by L. Edelstein-Keshet, SIAM (Applied Mathematics Texts, 2005). ISBN: 9780898715545. The textbook is highly recommended but not required for this class. Notes will be distributed in class or posted in Sakai along with primary research literature readings, as needed.
Software: We will use numerical computation software in this class. Here are some options.
Course Description. The main goal of this course is to provide opportunities for students to construct and analyze mathematical models that arise in the biological, physical, and social sciences. Mathematical models are usually created in order to obtain understanding of problems and situations arising in the real world; other times, the main goal is to make predictions or to control certain processes; finally, some models are created in order to aid in decision making.
Construction of a mathematical model consists of translating a real world problem into a mathematical problem involving parameters, variables, functions, equations and/or inequalities. Analysis of the model involves the solution (if possible) of the mathematical problem through logical, algebraic, analytical or computational means, and assessing what the solutions imply about the real situation under study. If an analytical or computational solution is not possible, computer simulations can sometimes be used in order to study various scenarios implied or predicted by the model.
Analysis techniques can be drawn from many areas of mathematics. In this course, it is assumed that students have a good working knowledge of Calculus, Linear Algebra and Ordinary Differential Equations. These areas are adequate for the analysis of some models. However, many modeling situations require the use of some probability theory and simulation techniques. These mathematical topics will be covered in the course. In calculus and differential equations courses, students have been exposed to some continuous models. In this course, we will also introduce students to discrete models as well.
Course Structure and Requirements. The course will be structured around a series of case studies that will provide ample opportunity for students to learn about (and to practice) the development and analysis of models raging from the discrete to the continuous, and from the deterministic to the stochastic (or probabilistic), and in many cases involving mixed-type modeling. An important goal for this course is to also train you to read primary research literature critically. This requires that you learn to read literature, which will be achieved with assigned reading. Another important goal is to learn how to talk to non-mathematicians in order to set up a model and calibrate your results and their relevance; we will have some guest lectures and trips to facilitate your learning.
Assignments. The assignments in this course will be as follows.
Homework. During the semester, you will receive roughly weekly homework that you will turn in via the class Sakai DROPBOX. The homework assignments should be written as if it were an article/tutorial being prepared for submission. The following is the expected format for homework submission:
I will grade based upon how completely you solved the homework, as well as clarity and overall legibility and organization. Homework is worth 10 points each. Five points will be given for the overall layout, correctness and neatness of the assignment, and five additional points will be for specific things that I will look for in the homework itself, depending on assignment instructions.
A few things should be kept in mind when preparing your assignments (please refer to this frequently):
Exam. There will be two (2) midterms in this course.
Project. Students will be required to work in teams of two or three on a modeling project in the last part of the course. The project consists of a term paper describing the construction and analysis of the model. In addition, students will be required to give a formal presentation on the modeling project at the end of the semester. The presentation will be a celebration of your learning and will be open to the community (this is one of the CP components in this course).
Grading Policy. Grades will be based solutions to assigned problems, a midterm, the term paper and the modeling project presentation. The overall score will be computed according to the following distribution: