Linear Optimization (M765) 2010-2011

Course Information (Fall Semester)

__Teacher__: Siva Sankrithi

__E-mail__: siva dot sankrithi at lakesideschool dot org

__Phone__: (206) 440-2733 (Lakeside), (206) 261-6366 (Cell)

__Website:__ http://teachers.lakesideschool.org/us/math/sankrithi/SivasWebPage.htm

__Textbook__: __Linear Optimization__, Siva Sankrithi

(I will post it online for all of you so you need not spend any money!)

__Period__: 5th (Monday/Friday 11:45-12:30, Wednesday 11:35-12:50)

__Location__: Allen-Gates 201

__What is Linear Optimization? __

Linear Optimization is a very useful and practical field of study that arises in a wide array of different places, including economics, the physical sciences, engineering, and operations research, to name a few. The basic goal of Linear Optimization, also known as linear programming, is to set up and solve real life situations in order to find the "best" solution, whether that might be maximizing profit, minimizing cost, maximizing production, or something else. Once these situations are modeled mathematically, with a linear objective function to maximize or minimize subject to linear constraints, we will learn solving techniques in order to actually find the optimal solutions and optimal values to these linear programs.

__Course Schedule:__

We will follow the textbook very closely, as I wrote it specifically for this course! Our first unit will be a detailed discussion of what linear programs are, 2-variable linear programs, how to model them, and how to solve them graphically. Our second unit will be a discussion of how to solve 2-variable linear programs using the Simplex Method, developed by George Dantzig (1914-2005) in 1947. Our third unit will be solving multi-variable linear programs using the Simplex Method, as well as a discussion of computer techniques to solve linear programs, and duality theory. Our fourth unit, on modeling, is actually one that we will be doing throughout every unit. In particular, you will be given various practical physical situations that you will need to model using linear programming, and your job will be to model them. Naturally early in the semester these models will begin fairly simple and get more and more complex as the semester progresses. Our fifth, and final unit of the course, will be non-linear programming highlights. Here we will discuss some very useful techniques for solving non-linear optimization problems, such as Lagrange's Method. In the last part of the course, you will each pick a problem or optimization topic of interest, research it, write a paper on it, and present your work to the class.

__Materials:__

For this course, you will need a TI-83/83+/84 calculator, some sort of note taking system (e.g. notebook or 3-ring binder), and a laptop so that you can view the textbook and utilize Excel. Most importantly, bring a curiosity and open mind as this will make the course much more enjoyable for all of us.

__Homework:__

Homework will not be assigned daily in this course. Instead what we'll do is have Homework Sets, that are due roughly once every one or two weeks, that will include several problems on the particular unit we are doing as well as some models.

__Grading:__

Your grade will be based on Homework, Quizzes, and Projects. Rather than having any major "tests" in this course, what we'll do is have several quizzes, which like homework sets, will take place every one or two weeks. Homework will count for 40% of your course grade, quizzes will count for 40% of your course grade, and your final project will count for 20% of your course grade. Every assessment will be graded on a 4-point scale, so at any point in time you'll know your grade. If you have any questions on this, be sure to ask Mr. S.

__Attendance:__

Attendance at every class is mandatory. If for some reason you do miss a class, you are responsible for turning in the homework for that day (email is an acceptable means of doing so in the event that you are unable to come to campus).

__Communication:__

The best means to contact me if you have any questions is via email. Also, I will be at my desk most of the time I am not in class so you are certainly welcome to come in and ask questions anytime I am there. Also, I understand that many of you have other time commitments for various club and athletic events, so all I ask is that you let me know of these well ahead of time so that I can work with you individually to get you ahead or catch you up as necessary.

Most importantly, HAVE FUN!!!! If you think of math as a chore, it will be, but if you think of it as fun, you will surely have a great time.