GENERAL INFO: In the first N math classes of your career, you can be 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. Additionally, we often need the solutions quickly. Operations Research, which was born as a discipline during the tumultuous events of World War II, deals with efficiently finding optimal solutions. In this course we build analytic and programming techniques to efficiently tackle many problems. We will review many algorithms from earlier in your mathematical or CS career, with special attention now given to analyzing their run-time and seeing how they can be improved. The culmination of the course is a development of linear programming and an exploration of what it can do and what are its limitations. For those wishing to take this as a Stats course, the final project must have a substantial stats component approved by the instructor. Prerequisites: Linear Algebra (Math 250) and one other 200 level or higher CS, Math or Stats course.

COURSE MECHANICS: The semester will start with me lecturing daily, wit the end of the semester reserved for student presentations. There will be weekly problem sets, a midterm and final, and a project. The goal is to introduce students to advanced concepts and problems in optimization theory, 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. Click here for a welcome letter.

OBJECTIVES: The goal is to introduce you to advanced concepts and problems in linear algebra, specifically linear programming, with an emphasis on mathematical modeling. There will be numerous opportunities to work on real world problems for companies. This course has real analysis as a pre-reqs, we will move at a fast pace at times, and you are responsible for doing a significant amount of reading on your own. Note there will be a Board of Trustees composed of recent Williams alumns.

TEXTBOOK/SYLLABUS: The textbook is Mathematics of Optimization: How to do things faster; I also urge you to get Methods of Mathematical Economics: Linear and Nonlinear Programming, Fixed-Point Theorems by Joel N Franklin.

GRADING POLICY: Homework: 15%, Class Presentation: 5%, Midterm 40%, Final or Project: 40%. (Note the grading percentages may change a bit. A large portion of your work and grade in this class will come from a group project or a final, to be determined early in the semester, if a project then it will include a write-up and a class presentation.)

CONTACTING ME: You can reach me in Wachenheim 339 (if I'm there it's office hours), email sjm1@williams.edu

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!

• Article from the NYPost on the lawsuit.
• Another article, which notes that she misspells 'tuition'.
• You can view her motion here.