Math 482: Linear Programming (Fall 2019)

Mikhail Lavrov


Location

Grading

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.

Homework

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 should submit a scanned copy or a photo of your homework as a single 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.

Exams

There will be three evening midterm exams: Wednesday 9/18, Wednesday 10/16, and Wednesday 11/13 from 7pm to 8:30pm in Noyes 161. Correspondingly, three lectures will be canceled, not necessarily in the same week as the midterm exams. I will mark these in the syllabus below as we get closer to the date.

I'll post details of the final exam once they're ready, too.

Detailed syllabus

This course is based on several textbooks with a lot of overlap; read whichever ones help, or read my lecture notes (or both). 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 lecture notes, adjustments to my plans for the future, and links to homework assignments.

Date Chapter Details References Homework/Exams
Mon August 26 Background Intro to linear programs GM 1.1; V 1.1, 1.2
Wed August 28 Constraints in LPs GM 4.1, 4.3; PS 1.5, 2.1
Fri August 30 The Simplex Method
PS Chapter 2
Basic solutions; pivoting GM 4.2; PS 2.2, 2.4; V 2.1
Mon September 2 Labor Day: no class
Wed September 4 Objective functions GM 5.1; PS 2.5, 2.6; V 2.1
Fri September 6 Simplex method example GM 5.2, 5.3; PS 2.9; V 2.2 HW 1 due
Mon September 9 Two-phase simplex method GM 5.4, 5.6; PS 2.8, V 2.3
Wed September 11 Pivoting rules GM 5.7, 5.8; PS 2.7, V 3.1-3.4
Fri September 13 No class
Mon September 16 Corner points GM 4.2, 4.4, 5.5; PS 2.2 HW 2 due
Wed September 18 Exam review (Exam topics) Exam: 7pm in Noyes 161
Fri September 20 Revised simplex method
Mon September 23 Worst cases
Wed September 25 Duality
PS Chapter 3
Fri September 27 HW 3 due
Mon September 30
Wed October 2
Fri October 4 HW 4 due
Mon October 7
Wed October 9
Fri October 11 HW 5 due
Mon October 14 Other topics
Wed October 16 Exam review Exam: 7pm in Noyes 161
Fri October 18
Mon October 21 Graph Theory
Wed October 23
Fri October 25 HW 6 due
Mon October 28
Wed October 30
Fri November 1 HW 7 due
Mon November 4
Wed November 6
Fri November 8 HW 8 due
Mon November 11 Integer Programming
PS Chapter 13
Wed November 13 Exam review Exam: 7pm in Noyes 161
Fri November 15
Mon November 18
Wed November 20
Fri November 22 HW 9 due
Mon November 25 Fall break: no class
Wed November 27
Fri November 29
Mon December 2 Primal-Dual Method
PS Chapter 5
Wed December 4
Fri December 6
Mon December 9 HW 10 due
Wed December 11 Exam review
TBA Final Exam

Last updated September 16, 2019. Mikhail Lavrov <mlavrov@illinois.edu>