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.

• MATLAB (Mathworks, MA). The Student Edition can be purchased and downloaded from mathworks.com or through our bookstore, if you do not already have access. Alternatively, connection through Remote Desktop will allow you access to MATLAB or our ITS lab is open and has Matlab on all their machines.
• A free alternative to MATLAB is Scilab http://www.scilab.org/, however it does not have good compatibility with MATLAB code (i.e, you cannot work with an .m file in Scilab).
• Another free alternative to MATLAB is FreeMat and it can be downloaded from: http://freemat.sourceforge.net/. FreeMat should have good compatibility with MATLAB but it is not as well supported.
• Other options might be available; I’ll let you do some exploring on your own if you are up to the task.
• NOTE: if you have no prior computing experience you should use MATLAB. If you chose to use other software instead of MATLAB to complete your work, you are responsible for resolving any compatibility issues yourself.
• The Claremont Center for Mathematical Sciences has opened the Software Lab located inside the Honnold-Mudd Library. Please stop by the lab for FREE help with Matlab. For more details go to: http://ccms.claremont.edu/CCMS-Software-Lab.

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:

• Title/author Title, author/address lines
• Sec. I. Introduction and Overview of the problem
• Sec. II. Theoretical Background
• Sec. III. Computational or Analytical Results
• Sec. IV. Summary and Conclusions/Recommendations
• Appendix A MATLAB functions/code used and brief implementation explanation
• Appendix B Any algebraically intense calculations

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):

• Use a professional grade word processor (Latex is preferred, this is particularly useful for the senior exercise in mathematics).
• For equations: Latex already does a nice job, but if you must use Word, then use Microsoft Equation Editor.
• Label your graphs. Include brief figure captions. Reference the figure in the text with a more detailed account of the figure.
• Figures should be set flush with the top or bottom of a page.
• Label all equations.
• Provide references where appropriate.
• All coding should be shuffled to Appendix A. Reference it when necessary.
• The homework is being written for YOU! So be clear and concise.
• Spellcheck please!

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:

• Homework 20%
• Exams 50%
• Presentations 15%
• Modeling term project 15%