Math 407 Sections A-D Autumn 2020
LINEAR OPTIMIZATION
Instructor: E-Mail: James Burke jvburke(at)uw(dot)edu MW 9:30-10:20am (Zoom) Math 308

#### URL for the course website:

• http://www.math.washington.edu/~burke/crs/407/

### Text:

Online course notes: http://www.math.washington.edu/~burke/crs/407/notes/

### Course Content:

Math 407 is an introductory course in linear optimization with a focus on linear programming (or LP). The four basic components of the course are modeling, solution methodology, duality theory, and sensitivity analysis. Modeling concerns the question of how problems posed in the real world can be formulated in terms of the mathematical framework called linear programming. Solution methodologies concern practical techniques for computing the solution of an LP. We focus on the simplex algorithm due to George Dantzig since it offers a complete framework for discussing both the geometry and duality theory for linear programs. Duality theory illustrates the rich underlying mathematical structure of linear programming and its extensions. We will interpret the duality theory in a number of ways. In particular, we show how it can be used to explain pricing systems in market economies. Sensitivity analysis concerns the behavior of the optimal solution subject to changes in the initial data describing the problem.

Quizzes: There are 7 fifteen minute quizzes each worth 70 points. The quizzes are given each Friday except Friday November 13 and 27, and December 11. There also a quiz on Friday October 2, but it is practice quiz. The quizzes cover the homework of the previous week. The potential content of the quiz will be announced the Wednesday before the quiz. Each quiz will typically contain two questions. The first question will either be of a theoretical nature (definitions, theorems, proofs) or to model a problem as an LP. The second question will be computational in nature. Your top 5 quiz scores count toward your grade. The design of the quizzes and how they are formated may change as the quarter proceeds in order to adjust to the new remote learning format.

Midterms: There is one midterm: Monday, November 9. The content of the midterm will be discussed in advance and a sample midterm will be distributed before the exam. The midterm is worth 300 points. The format of the midterm has yet to be determined.

Final Exam: The final exam for 407A&C is to be given on Wednesday, December 16, 2:30-4:20pm, and that for 407B&D on Thursday, December 17, 8:30-10:20am. The details and format of the final exam has yet to be determined. The final exam is comprehensive. A sample final exam will be distributed. The final exam is worth 350 points.

Final Grade: The total number of possible points is 1000:

 350 quiz points $+$ 300 midterm points $+$ 350 final exam points $=$ 1000 points.
• 0.7 = 400 points
• 2.0 = 550 points
• 3.0 = 750 points
• 4.0 = 900 points.
Grades are linearly interpolated between these values.

### Time Conflicts with an Exam and Religeous Accommodation:

There will be no make-up quizzes or exams except in the following cases.
1. A documented emergency (medical, family, University, ...).
2. A religious accommodation (see below).
3. A documented unavoidable conflict whose validity is pre-authorized by the instructor.
For unavoidable pre-approved conflicts, the instructor requires at least two weeks notice prior to the exam or quiz so that it can arrange for you to take the exam or quiz BEFORE the actual exam date.

### Student Conduct Code:

The University of Washington Student Conduct Code (WAC 478-121) defines prohibited academic and behavioral conduct and describes how the University holds students accountable as they pursue their academic goals. Allegations of misconduct by students may be referred to the appropriate campus office for investigation and resolution. More information can be found online at https://www.washington.edu/studentconduct/.

### Religious Accommodation:

Washington state law requires that UW develop a policy for accommodation of student absences or significant hardship due to reasons of faith or conscience, or for organized religious activities. The UW policy, including more information about how to request an accommodation, is available at Faculty Syllabus Guidelines and Resources . Accommodations must be requested within the first two weeks of this course using the Religious Accommodations Request form available at https://registrar.washington.edu/students/religious-accommodations-request/ .

### Disability Resources for Students:

Your experience in this class is important to me. If you have already established accommodations with Disability Resources for Students (DRS), please communicate your approved accommodations to me at your earliest convenience so we can discuss your needs in this course.

If you have not yet established services through DRS, but have a temporary health condition or permanent disability that requires accommodations (conditions include but not limited to; mental health, attention-related, learning, vision, hearing, physical or health impacts), you are welcome to contact DRS at 206-543-8924 or uwdrs@uw.edu or disability.uw.edu. DRS offers resources and coordinates reasonable accommodations for students with disabilities and/or temporary health conditions.

### Incomplete:

A grade of Incomplete will be given only if a student is doing satisfactory work up until the end of the quarter, and then misses the final exam due to a documented medical or family emergency.

### Important Dates:

Holidays: Veterans Day, Wednesday, November 11: Thanksgiving, Thursday-Friday, November 26-27.

Midterm Date: Monday, November 9.

Final Exam: The final exam for 407A&C is to be given on Wednesday, December 16, 2:30-4:20pm, and that for 407B&D on Thursday, December 17, 8:30-10:20am.