Math470-01   Mathematical  Models and Applications, Spring 2008


Daily Syllabus   Peter Greim's home page    MACS home page   Registrar's page   Citadel home page            

 

Class  Tu, Th   8:00-9:15  in TH 203

Instructor:  P. Greim, Thompson 329, Tel. 953-­5035, E­mail: peter.greim@citadel.edu
http://macs.citadel.edu/~greimp

Office hours are posted at my door and at my class schedule web page. You can read it as long as you are using a Citadel terminal. The class schedule will give you an idea which times might be available if you need to make an appointment.

Text:  There is no required text. Notes are made available electronically; several texts are on reserve in the Daniel Library.

Course description

This is a modeling course. We will apply very simple mathematics (linear equations in one or two unknowns, exponential growth, binomial distributions) to the prices of stocks and options (more generally: derivatives). Then, gradually, the models become more complex and the mathematics more advanced, eventually involving stochastic processes, especially Brownian motion.
The development of the models is a dynamic process: basic features of stock or derivative pricing lead to mathematical equations; the resulting solutions are interpreted in the underlying market situation, and these interpretations may lead to the elimination of some solutions or to the introduction of further conditions in the mathematical model.
Each of the models is applied to stock market data, using spreadsheets for the computations and for market simulations.

Prerequisites

Multi-variable calculus, probability distributions, linear algebra (MATH234 is sufficient). Useful, but not required: linear programming, partial differential equations.

Grades

are based on the final, 2 tests, a project, and homework assignments. The tests combined count 40%, the project 15%, homework 20%, and the final exam counts 25%. You'll receive 0.5 percentage points extra credit for each correctly solved problem of the week. (See Prof. Trautman's web page http://155.225.48.46/potw/potw.htm, and look out for weekly announcements on the MACS bulletin boards.)  I will follow the usual 10% per grade scheme and not grade "on a curve". However, if after grading a test the statistics show a particularly bad performance of the whole class at one problem, I may adjust that problem's weight within the whole test. Tests and final exam may have a closed-book and an open-book part, and I may give a part of a test as a take-home. I’ll give you a list of projects to choose from; most of them have to wait till the last third of the term.  

You can check your standing in the course here. You'll need to know your code number to identify your record. It will be on your first returned homework.

Homework

When you work problems, first try to do them by yourself. After that, whether you succeed or not, you may discuss them with others. You will learn from talking about mathematics. However, do not copy homework from others. I want you to understand a problem solution (either through own research or discussion) and then formulate it in your own words. Discussing a problem solution with a classmate, understanding it, and then formulating it in your own words is allowed. Copying a solution from others is not.

On the take-home part of a test you are completely on your own - almost. I am the only person with whom you may discuss a test problem before turning it in.

Help

is available: you may work with other students, see me after class, during office hours, or make an appointment (or just drop by my office, taking a chance that I may be busy).

One last advice: when you are getting behind (or can't even get started right) - let me know right away. I'll go out of my way to help you if you try. Your grade will be based on your success - not on your effort. However, your effort will determine how much I help.