Math 4080/6080
Spring 2026
Western Michigan University
Spring 2026
Western Michigan University
Instructor:
Office:
My office is 5524 Everett Tower. I will be in my office for students MF at 1:00 to 1:50 p.m. No appointment is necessary during those times. I will usually have my Webex room open during those times, https://wmich.webex.com/meet/jay.treiman. You can also make an appointment at another time.
Textbook:
Linear Programming: Foundations and Extensions: Fifth Edition, by Robert J. Vanderbei. You should be able to download this book through the WMU library website. I may use other texts that can be downloaded.
You will need a to use Maple for this class. It is the mathematics tool that I use. A link to purchase it from Maplesoft will be in the elearning content section for this class.
Catalog descriptions:
MATH 4080 - Linear Programming
Linear programming and its applications. This course will cover basic theory and applications of linear programming. The topics will include convex geometry, the simplex algorithm, and duality. The applications may include problems in the areas of network optimization, the transportation problem, the assignment problem, the diet problem, cluster analysis, L1 fits, game theory, and scheduling.
Prerequisites & Corequisites: Prerequisite: MATH 2300 or MATH 3740. A grade of “C” or better is required to satisfy any course prerequisite.
Credits: 3 hours
MATH 6080 - Linear Programming
This course covers the general types of optimization problems and how linear programming fits into optimization, the geometry of linear programming (linear inequalities, convex sets, the geometry of optimality for linear programs, sensitivity, and duality), applications of linear programming (may include game theory, resource allocation, robust regression, the diet problem, and other applications), the simplex algorithm, the general paradigm of descent algorithms for optimization, penalization for optimization problems, and interior methods for solving linear programming problems.
Note: Open to graduate students only.
Prerequisites/Corequisites: Prerequisite: An introductory course in linear algebra and a course in multivariate calculus.
Credits: 4 hours
Course objectives:
General:
This class is an in-person class from from 2:00 to 3:15 pm on MW in 3307 Rood Hall for Math 4080. Math 6080 is scheduled for 2:00 to 3:40 pm on MW in 3307 Rood Hall for the extra credit hour. I expect we will need to change the ending time to allow the extra 50 minutes for the graduate students. Even though roll will not be taken, all students should be in class every day.
The prerequisite for the Math 4080 class is linear algebra and the prerequisite for the Math 6080 class is linear algebra and multivariate calculus. I will try to include enough multivariate calculus material in the class so that the 4080 students can follow the geometry of descent in optimization.
You are responsible for all material in the text and all material presented in class. This includes any material not in the text and all material in the text that was not presented in class. A list of topics may be available.
It is expected that you will spend enough time outside of class to learn the material in the lectures, text, and homework problems. A list of expectations is available.
The sessions will be recorded and the recordings should be linked to the content section in elearning. The written work done in class sessions will also be posted to the content section of e-learning. The files containing the writing will be in the format for Xournal++. If you want to read those notes you will need to download Xournal++. It is available for Windows, MacOS, Linux,iOS, and android. All of this material is only for students in this class and cannot be shared without permission of the instructor.
You are expected to follow all university conduct policies. This includes giving credit on any assignment you turn in for any help you receive and referencing any resources you use that are not the text or the lectures.
There are some other university policies you should be aware of.
The last day to withdraw is March 23, 2026.
Electronic Devices:
All cell phones, cameras, wireless devices, mp3/mp4 type media players, and similar devices are to be turned off and put away while you are in the classroom. If you ask, you may get an exception for note taking. This means taking written notes, not recording the class. Since the lectures will be posted, you should not be taking a picture of the screen during class. Use of one of these devices during a quiz/exam will be considered an academic violation.
Homework:
A portion of your grade will come from homework. A list of problems to work will be on this web site. Assignments to be turned in will be posted in the dropbox section of elearning. Not all of this homework will be collected, you are responsible for all of the problems on the list. If you have any questions about homework problems, please ask them in class, in office hours, via e-mail, or by making an appointment for an on-line personal session.
All written homework will be submitted as a PDF file through a dropbox in e-learning. Submit all written assignments as a single PDF file containing the solutions to all of the assigned problems. The problems must be legible and in order of section and the numerical order, e.g. section 2.1 problem 1, section 2.1 problem 5, section 2.2 problem 2,... All pages in your PDF must be the same size. If a signed statement is required for the assignment, it is to be the first page of your submission with a written, not typed, signature. Do not submit a zip file. Your name must be in the name of the file. Make certain that you have clicked the submit button for the dropbox in e-learning. If you do not follow these instructions you may be allowed to resubmit the assignment or you may get a zero for the assignment.
If you get help from a tutor or someone else on a written assignment, that must be noted on your submission. You will not lose points for getting help, but I want to know if a tutor is using methods or notation that are not appropriate. Failure to tell me who gave you help is an academic violation.
Project:
A portion of your grade will come from a project. For this project you will choose an application of linear programming from an article/paper and change the given problem in a way that is not done in the article. You will then formulate you problem as a linear program and solve the problem. When you have solved the problem you must compare your results to those in the paper you are using and discuss the validity of your solution. You must have your references listed in a proper format. The writing style should be for technical writing.
You must submit a proposed topic by February 13, 2026. A draft version of you paper is due on March 20, 2026. Your paper should be ready for submission on April 10, 2026.
Your results will be submitted as a paper in PDF format in the dropboxes along with the corresponding Maple worksheet used to solve the problem. Your Maple code must be commented. You will present your paper and results to the class in a 15 minute presentation in the last two weeks of the semester. Your submission will be due on the day of your presentation.
If you get help from anyone on a this assignment, that must be noted in your submission. This includes any help with your writing. Failure to tell me how or where you got help is an academic violation.
AI:
Although artificial intelligence can do many things for people, the goal of this class is not to teach you how to use AI. The goal is for you to learn how linear programming works, for you to be able to translate problems in linear programs, and for you to be able to use linear programming. Since that is the goal of this class and I have seen students using inappropriate tools on assignments without giving appropriate references, most of your grade is from proctored exams. For those portions of your grade that are not proctored, you should not use an AI unless you have no other resources. In other words, the text, other students, tutors, other texts, web videos, and your professor must always come before an AI. If you use any resource besides the class text or your professor, it is an academic violation to not include the information of where you got help for the assignment. Waiting until the last few hours before an assignment is due is not a reason to use an AI.
Exams:
Three exams will be given during the term. The dates are on the tentative schedule. Information about the format of the exams will come later.
Final Exam:
A final exam will be given. The final exam will be given on Wednesday, April 29,2026 at 2:45 to 4:45 p.m. in the regular classroom. It will be comprehensive.
Grading policy:
All exams will follow the following outline: 50% of the questions are things you must be able to do, 25-30% of the problems are things you should be able to do, and 20-25% of the questions are more difficult. If you expect to finish every question on a test you may be disappointed when you have actually done very well.
To pass this class with a "C" (a "B" for graduate students) you must demonstrate that you can do all the required material. A starting scale is: A 85%+; BA 78+; B 72+; CB 66+; C 58+; DC 52+; and D 46+. This scale will probably change as the term progresses and will be different for undergraduate and graduate students.
The distribution of points for calculating grades is as follows. The final exam is worth 30%, the other exams are worth 30%, the project counts for 20% of your grade and the homework, computer assignments, and other assignments are worth the final 20% of your grade.
Jay Treiman: jay dot treiman at wmich dot edu