COURSE DESCRIPTION: In
the first N math classes of your career, you are sadly misled as to what the
world is truly like. How? You're given exact problems and told to find exact
solutions. The real world is sadly far more complicated. Frequently we cannot
exactly solve problems; moreover, the problems we try to solve are themselves
merely approximations to the world! We are forced to develop techniques to
approximate not just solutions, but even the statement of the problem! In this
course we discuss some powerful methods from advanced linear algebra and their
applications to the real world, specifically linear programming and random
matrix theory.
Format: Evaluation will be based primarily on homework, presentations and
write-ups, and scholarship.
Prerequisites:
Linear algebra (programming experience and analysis are desirable, but not
necessary)
CONTACTING ME: You can reach me in Bronfman 202 (413 597 TBD; if I'm there it's office hours), email sjm1@williams.edu, or anonymously through ephsmath@gmail.com (password 011235813, the first eight Fibonacci numbers).
OBJECTIVES: The goal is to introduce students to advanced concepts and problems in linear algebra, specifically linear programming and linear algebra, with an emphasis on mathematical modeling. For a fuller statement as to the objectives of this course, please click here. This includes some fascinating videos with some thought provoking comments about what you should get out of your education.
TEXTBOOK: The textbook is a combination of notes for a book I'm writing, and Methods of Mathematical Economics: Linear and Nonlinear Programming, Fixed-Point Theorems by Joel N Franklin (ISBN-10: 0898715091 ISBN-13: 978-0898715095). We will use my lecture notes on linear programming and on random matrix theory.
COURSE DISCLAIMER: I may occasionally say things such as `Probability is one of the most useful courses you can take' or 'If you know probability, stats and a programming language then you'll always be able to find employment'. I really should write `you should always be able to find employment', as nothing is certain. Thus, please consider yourself warned and while you may savor the thought of suing me and/or Williams College, be advised against this! I'm saying this because of the recent lawsuit of a graduate who was upset that she didn't have a job, and sued her school!