Mathematical Modeling: Math 456-02, Spring 2016

Class Meeting : TuTh 10:00--11:15, LGRC A203

Instructor : Luc Rey-Bellet

Office :  1423 J LGRT
Phone :  545-6020
E-Mail :   luc <at>
Office Hours :   Tu 2:30--3:45,   Th 11:30-12:45   or by appointment.

Teaching Assistant :  Jinchao Feng

Office :  1423 E
E-Mail :   feng <at>
Office Hours :   W 5--6, Th 5--6

Course Web page: Please bookmark The page will be updated regularly. Check it often.

Syllabus: This course is an introduction to mathematical modeling. The main goal of the class is to learn how to translate problems from "real-life" into a mathematical model and how to use mathematics to solve the problem. The domain if applicability of mathematics is huge and covers much of the natural sciences, but mathematics plays a central role in modern economics, and increasingly in social sciences. In this class we will pick a number of topics from games and gambling, economics, social sciences, but also magic (card tricks) and some biology (evolutionary theory) to illustrate how mathematics can be useful to analyze concrete problems. From the mathematical point of view we will use elementary tools from probability, game theory, information theory, and optimization. The prerequisite for this class is a one year sequence of calculus. We will use throughout the class very elementary notions from probability (discrete math), linear algebra, and differential equations. All the necessary mathematics will be introduced from scratch and motivated by examples. Among the problems to be discussed are

Classnotes:: As the class progresses I will post regularly some handouts. You should use as a COMPLEMENT of your class notes, not as a substitute. They will provide a summary of the class and a reference for definitions and main results.

Textbooks and references: We are not following any particular textbook but we are borrowing material from many sources.

General mathematical references: Two references for background material for the class.

References on special mathematical topics: Here we have books on various topics of mathematical modeling which I have found useful in preparing this class. The mathematical level varies enormously.

Popular literature: Here we have a series books, many containing not much mathematics but relating mathematical ideas and concepts to many problems in real life.

Grading and assignments: Your grade will based on your reflective essay (%20), book review (%20) homework (%30), and final project (%30).

Reflective essay (due on February 9):
Each student will write a 5-page, double-spaced, self-reflection essay on their experiences as a mathematics major at UMass. As you farm your essay consider the path that led you to be a mathematics major, your experience taking mathematics classes, Gen Ed. courses, and other research/extracurricular activities. You may choose to comment specifically on some of the questions posed here:

Grading of the paper will be based on organization, clarity of expression, and the personal insights you bring into the paper.

Book review: (pick a book to read by February 4, report due on Friday March 11) You should pick a book (popular literature, non-fiction) which explores the connections between mathematics and real-life applications. Most such books contains little actual mathematics but can be very informative on mathematical ideas shape social and economical ideas. You can either pick a book from the list above or suggest your own book (i will need to approve it then). Write a maximum 10-pages, double-spaced, essay on the books addressing the following points

Homework: Homework will be assigned regularly throughout the class. The homework will be graded. I expect you to do your homework regularly and carefully to assimilate the material. Your homework counts as %30 percent of your grade.

Group project: The class will be divided in groups of three students. Every group will select a subject in consultation with the instructor. I am including here a list of project you could consider. But you have some lot of freedom to choose your subject as long as it is related to mathematical modeling. And I am very much open to suggestions. The references above can be a good starting point to find a project. In particular game theory is used in a very wide variety of contexts and will give you plenty of options, depending on your tastes and backgrounds.

Project suggestions:

The group project as 2 parts:

Project presentation: The group presentations will take place on the last two classes of the semester as well as in the two-hour time slot reserved for the final exam. You should plan for a 15 minutes presentation + a few minutes for questions.