The course grade will be calculated as follows, out of 660 points total:
You can check your grades via Moodle.
Your grade total will be converted to a letter grade according to the following scale:
|A+||≥ 630||B+||≥ 520||C+||≥ 450||D+||≥ 380|
|A||≥ 570||B||≥ 490||C||≥ 420||D||≥ 350|
|A-||≥ 540||B-||≥ 470||C-||≥ 400||D-||≥ 330|
It is possible to take the course for 4 credits rather than 3, at the cost of extra homework questions and more difficult exams. If you want to do this, you need to register at the math office in Altgeld Hall soon after the start of the course.
There will be 10 homework assignments, to be turned in at the beginning of class the day they are due. Of these homework assignments, the top 8 homework scores will determine your grade. Each assignment is graded out of 20 points, for a total of 160.
If you cannot attend class, you can submit a scanned copy or a photo of your homework as a PDF file by e-mail before class begins. Please avoid doing this unless it's necessary, since it is more work for the grader.
If the homework assignment is received after class on the due date, but before the next class, it will be accepted as late, for a 2-point penalty. Homework will not be accepted after the next class for any reason.
There will be three evening midterm exams: Wednesday 2/13, Wednesday 3/13, and Wednesday 4/17 from 7pm to 8:30pm in 341 Altgeld Hall. Correspondingly, three lectures will be canceled, not necessarily in the same week as the midterm exams. The first of these is already marked in the syllabus below.
The final exam will be on Monday 5/6 from 7pm to 10pm in 311 Gregory Hall (our usual classroom).
This course is based on several textbooks with a lot of overlap; read whichever ones help. In the syllabus, I will refer you to sections of the textbooks below that cover the relevant material.
The syllabus below will initially describe a tentative plan for what topics will be covered when. As the semester progresses, I will update the syllabus with information about what actually happened in class, adjustments to my plans for the future, and links to homework assignments.
|Mon January 14||Background
PS Chapter 1
|Intro to linear programs||GM 1.1|
|Wed January 16||LPs in different forms||GM 4.1; PS 2.1|
|Fri January 18||No class|
|Mon January 21||MLK Day: no class|
|Wed January 23||Convex geometry||GM 4.3-4.4; PS 1.5, 2.3|
|Fri January 25||The Simplex Method
PS Chapter 2
|Basic solutions; pivoting||GM 4.2; PS 2.2, 2.4||HW 1 due|
|Mon January 28||Objective functions||GM 5.1; PS 2.5, 2.6|
|Wed January 30||Extreme (temperature) point day: no class|
|Fri February 1||Simplex method example||GM 5.2, 5.3; PS 2.9||HW 2 due|
|Mon February 4||Two-phase simplex method||GM 5.4, 5.6; PS 2.8|
|Wed February 6||Pivot rules and cycling||GM 5.7, 5.8; PS 2.7|
|Fri February 8||Proofs and notation||GM 4.2, 5.5; PS 2.2||HW 3 due|
|Mon February 11||Revised simplex method||GM 5.6; PS 4.1, 4.2|
|Wed February 13||Simplex method review||Exam: 7pm in 341 AH (Topics)|
|Fri February 15||Counting pivot steps||GM 5.9; PS 8.6|
|Mon February 18||Duality
PS Chapter 3
|Intro to duality||PS 3.1, GM 6.1-6.2, V 5.1-5.4|
|Wed February 20||Complementary slackness||PS 3.2, GM 6.4, V 5.5|
|Fri February 22||Duality in the tableau||PS 3.5, GM 6.3||HW 4 due|
|Mon February 25||Dual simplex method||PS 3.6-3.7, V 5.6|
|Wed February 27||Shadow costs|
|Fri March 1||Sensitivity analysis||V 7.1.1||HW 5 due|
|Mon March 4||Zero-sum games||GM 8.1|
|Wed March 6||Zero-sum games||GM 8.1|
|Fri March 8||No class|
|Mon March 11||Other topics||Fourier-Motzkin elimination||GM 6.7||HW 6 due|
|Wed March 13||Exam review||Exam: 7pm in 341 AH (Topics)|
|Fri March 15||Applications||GM 2.4, 2.6|
|Mon March 18||Spring break: no class|
|Wed March 20|
|Fri March 22|
|Mon March 25||Graph Theory||Totally unimodular matrices||GM 8.2|
|Wed March 27||Matchings and vertex covers||GM 8.2, PS 10.1|
|Fri March 29||Network flows||V 15.5||HW 7 due|
|Mon April 1||Max-flow min-cut thorem||V 15.5|
|Wed April 3||Augmenting paths||PS 5.6??|
|Fri April 5||Ford-Fulkerson||PS 6.1-6.2||HW 8 due|
|Mon April 8||Extensions of max-flow||external slides|
|Wed April 10||Push-relabel||external notes|
|Fri April 12||More push-relabel||HW 9 due|
|Mon April 15||Integer Programming
PS Chapter 13
|The power of integer programs||PS 13.1, CCZ 1.1|
|Wed April 17||Exam review||Exam: 7pm in 341 AH (Topics)|
|Fri April 19||The branch-and-bound method||PS 18.1, V 23.5, CCZ 1.2.1|
|Mon April 22||The cutting plane method||CCZ 1.2.2|
|Wed April 24||Primal-Dual Method
PS Chapter 5
|The primal-dual method||PS 5.1, 5.2|
|Fri April 26||More primal-dual method||PS 5.3, example|
|Mon April 29||Solving the restricted primal||PS 5.2||HW 10 due|
|Wed May 1||Exam review (optional)|
|Mon May 6||Final Exam (Topics)|