Penn State, University Park, Spring 2022

Penn State requires everyone to wear a face mask in all university buildings, including classrooms, regardless of vaccination status. ALL STUDENTS MUST wear a mask appropriately (i.e., covering both your mouth and nose) while you are indoors on campus. This is to protect your health and safety as well as the health and safety of your classmates, instructor, and the university community. Anyone attending class without a mask will be asked to put one on or leave. Instructors may end class if anyone present refuses to appropriately wear a mask for the duration of class. Students who refuse to wear masks appropriately may face disciplinary action for Code of Conduct violations. If you feel you cannot wear a mask during class, please speak with your adviser immediately about your options for altering your schedule.

MATH 484 (Sections 1 and 2) — LINEAR OPTIMIZATION

The instructor reserves the right to make changes to this syllabus during the semester.


Professor Mathieu Stiénon

Information and Communications Technology

All electronic devices must be silenced during lectures. Disrupting class in any way will not be tolerated.

We will use Canvas to share course materials, Gradescope to administer assignments, Teams for instant messaging, and Zoom for virtual office hours.

IT support is available 24/7.

Canvas iOS android
Teams iOS android
Zoom iOS android


Your Gradescope account will be created automatically the first time you click on the “GradeScope” tab in Canvas.

Throughout the semester, remember to always use the links in Canvas to access course assignments in Gradescope.

Using Gradescope with Canvas as a Student

Instant Messaging

We will use Microsoft Teams for text-based communication outside the classroom.

Depending on the issue at hand, we will use either the team channel or the private chat features of Teams. Watch this video to learn how team channels (i.e. public conversations) work. Watch this other video to learn how chats (i.e. private one-on-one or group conversations) work.

Instructions for adding yourself to our team:

  1. Copy the team code you’ll find in the ‘Course Administration’ module in Canvas.
  2. Login to Office 365 with your PSU email address and password.
  3. Click on the Teams application icon.
  4. In the left menu bar of Teams, click on the Teams icon.
  5. Click on ‘Join or Create a Team’ (located in the bottom, left corner of the screen).
  6. In the box for ‘Join a Team with a Code’, paste the Team Code.
  7. Click the ‘Join Team’ button.

For your convenience, I encourage you to install the Teams app on your phone and/or tablet as well.

Please take a moment now to download the app and join the team as I will share important information with the class through Teams rather than through Canvas announcements and your Canvas inbox. Do it now!

Virtual Office Hours

Check the ‘course administration module’ in Canvas for the day and time of virtual office hours.

We will use Zoom in conjunction with a shared online whiteboard. You will find instructions and links for joining the Zoom meeting and the shared online whiteboard in the ‘Course Administration’ module in Canvas. You must be logged into the Zoom app with your PSU credentials to be allowed into the meeting.

Disrupting virtual office hours in any way will not be tolerated. Refusal to comply with University policies is a violation of the Code of Conduct. Students may face disciplinary action for Code of Conduct violations.

Required Textbook

Dimitris Bertsimas and John N. Tsitsiklis, Introduction to Linear Optimization, Athena Scientific / Dynamic Ideas, ISBN 978-1-886529-19-9

Course Description

We will cover at least the first four chapters of the book. We will learn how to solve linear optimization problems, aka linear programs. First, we will learn what they are and how to interpret them geometrically. From the geometry, we will then derive the simplex algorithm, which is probably the most well known and widely used algorithm for solving linear optimization problems — other algorithms have emerged more recently. We will also cover duality theory.


MATH 220 (or any equivalent introductory Linear Algebra course) is an absolute prerequisite for MATH 484. Section 1.5 of our textbook briefly reviews the Linear Algebra material that you should be familiar with and explains the notational conventions adopted in the textbook. Read that section on your own as soon as you get hold of your copy of the textbook.

Weekly Problem Sets

Problem sets will be assigned weekly on Friday and are due one week later. All problem sets will have equal weight.

Discussion of problem sets with others is allowed, but each student should write his or her own solutions independently. You should definitely never share work you are submitting for credit with other students.

Once you have completed the assignment for the week, you will scan your work and submit the resulting PDF file through Gradescope.

Submit your work well ahead of the deadline. Assignments submitted late will automatically be marked as such in Gradescope and the Canvas grade-book. If you submit too many assignments late, I reserve the right to apply a penalty to your grade.

Problem Sets will lock 48 hours after their respective due dates and late submission will be disabled at that time.

Students who have a valid and documented reason for not submitting problem solutions on time may request to be excused for that assignment. However, there will be no makeup assignments.

Scanning Apps for Your Phones and Tablets

The mobile apps for Microsoft OneDrive and Google Drive allow you to scan your completed assignments, convert them into PDF files, and store them in the cloud. As a PSU student, you have virtually unlimited cloud storage on OneDrive and Google Drive — you must be logged into the app with your PSU credentials.

Should you prefer to save your work locally on your device, you might want to use either Microsoft Lens or SwiftScan.

OneDrive iOS android
Google Drive iOS android
Microsoft Lens iOS android
SwiftScan iOS android

Instructions for Assignment Submission

  1. Download the PDF of the assignment from Gradescope.
  2. Solve the problems using a black pen either on the printout or on blank sheets of white letter-size printer paper. Show all your work and explain your work briefly in full sentences. Final answers without supporting work and explanations will not receive credit. Write cleanly! If your work is not easily readable and intelligible, you will loose points!
  3. Write your name on every page you turn in. If you use both sides of a sheet, write your name on both sides. No name, no grade, no exceptions.
  4. Scan your work, and submit it as one single PDF file in Gradescope. If you’d rather work directly on your pen-enabled tablet, make sure to submit all layers of the PDF document.
  5. Check that your submission is complete and that you have submitted all pages. Unreadable work will result in a zero score.
  6. Assignments dropped in the instructor’s mailbox, sent to his email address, slipped under his office door, or submitted in Teams chat are not acceptable, will not be acknowledged, will be ignored, and will not be graded. You must submit your work through Gradescope.


Students in this class are expected to complete the examinations on their own, and to write their answers in their own words. Students are not to obtain exam answers from any other person and present them as their own. Students who present other people’s work as their own may receive a zero score on the examination and an F or XF grade for the course.

Should I have any reason to believe that you may have submitted work which is not your own, I will request that you meet with me through videoconferencing, I will have you explain your work to me and I will ask you follow-up questions to test your understanding of the material. If you are not able to answer satisfactorily, I reserve the right to reduce your score on the examination, possibly down to zero. Academic integrity matters!

Warning: All University and College policies regarding academic integrity/academic dishonesty apply to this course and to the students enrolled in this course. Academic dishonesty could result in a transcript notation indicating failure due to academic misconduct.

Midterm Examination

A midterm examinations will be given in class on Friday March 4, 2022.

No books, notes, or calculators may be used on the mid-term examination.

If there is a valid and documented reason for not being available during the regular mid-term examination time-window, such as classes or other official university activities or illness, a student may arrange with the instructor to take a makeup exam.

You need to IM (Teams) your instructor 48 hours prior to the exam regarding conflicts, and within 24 hours of missing the exam due to illness. If you miss the mid-term exam without an official excuse (such as illness or official university business), you may be allowed to take a makeup exam, but with an automatic 15% deduction from the grade. To avoid this deduction, you must notify your instructor via IM (Teams) with your official excuse, within 24 hours of the missed exam.

Forgetting the date or time of an examination is not a valid excuse.

Final Examination

A comprehensive final examination will be given during the final examination period (May 2-6, 2022).

The final examination will start at 09:00 (Eastern) on Thursday May 5th and will end at 14:00 (Eastern) on Friday May 6th.

You must submit your answers as a single PDF file through the Gradescope assignment created for the final examination. Submit your work well ahead of the deadline. Late submissions will not be accepted.

Students who miss or cannot take the final examination due to a valid and documented reason, such as illness, may be allowed to take a makeup final examination at the beginning of the next semester. Personal business, such as travel, employment, weddings, graduations, or attendance at public events such as concerts and sporting events is not a valid excuse. Forgetting the date or time of the examination is not a valid excuse. All such makeup examinations must be arranged through the instructor, and students in such a situation should contact their instructors within 24 hours of the scheduled final examination.

Students who miss the final exam without a valid reason might be allowed to take a makeup exam but a 15% penalty will be imposed. Students who have taken the original final examination are not permitted to take a makeup examination.

Final Project

Information about the final project will appear in Canvas and Gradescope on Week 13.

The deadline for submission of your final project is Monday May 2nd at 09:00.


Assignments will be weighted as follows:

Type of Assignment Weight
Weekly Problem Sets 50%
Midterm Examination 15%
Final Examination 15%
Final Project 20%

Course letter grades will be assigned as follows:

100% ⩾ A ⩾ 93% > A- ⩾ 90% > B+ ⩾ 87% > B ⩾ 83% > B- ⩾ 80% > C+ ⩾ 77% > C ⩾ 70% > D ⩾ 60% > F ⩾ 0%

The unavoidable consequence is that some students will be ‘just a point’ away from the next higher or lower grade. For reasons of fairness, the policy in this course is to NOT adjust individual grades in such circumstances.

Your grade will be based exclusively on the problem sets, the midterm examination, the final examination, and the final project. There is no ‘extra-credit’ work.

Deferred Grades

Students who are currently passing a course but are unable to complete the course because of illness or emergency may be granted a deferred grade which will allow the student to complete the course within the first several weeks of the following semester. Note that deferred grades are limited to those students who can verify and document a valid reason for not being able to take the final examination. For more information see Deferred Grades.


Students may add/drop a course without academic penalty within the first six calendar days of the semester. A student may late drop a course within the first twelve weeks of the semester but accrues late drop credits equal to the number of credits in the dropped course. A baccalaureate student is limited to 16 late drop credits. The late drop deadline for Spring 2022 is April 8, 2022 at 23:59 (Eastern Time).


Free mathematics tutoring is available at Penn State Learning. They offer both online and in-person options.

For more help, the Department of Mathematics maintains a list of private tutors.

Counseling and Psychological Services

Many students at Penn State face personal challenges or have psychological needs that may interfere with their academic progress, social development, or emotional well-being. The university offers a variety of confidential services to help you through difficult times, including individual and group counseling, crisis intervention, consultations, online chats, and mental health screenings. These services are provided by staff who welcome all students and embrace a philosophy respectful of students’ cultural and religious backgrounds, and sensitive to differences in race, ability, gender identity and sexual orientation.

The National Suicide Prevention Lifeline provides 24/7, free and confidential support for people in distress, prevention and crisis resources for you or your loved ones, and best practices for professionals.

Academic Integrity

Academic integrity is the pursuit of scholarly activity in an open, honest and responsible manner. Academic integrity is a basic guiding principle for all academic activity at The Pennsylvania State University, and all members of the University community are expected to act in accordance with this principle. Consistent with this expectation, the University’s Code of Conduct states that all students should act with personal integrity, respect other students’ dignity, rights and property, and help create and maintain an environment in which all can succeed through the fruits of their efforts. Academic integrity includes a commitment not to engage in or tolerate acts of falsification, misrepresentation or deception. Such acts of dishonesty violate the fundamental ethical principles of the University community and compromise the worth of work completed by others. In order to ensure all students have a fair and equal opportunity to succeed in this course, the Mathematics Department is committed to enforcing the University’s academic integrity policy. Below is a description of academic misconduct and the department’s responsibilities when misconduct is suspected.

Academic Misconduct

In this course, academic misconduct includes, but is not limited to:

When Academic Misconduct is Suspected

If a student is suspected of academic misconduct, the instructor’s duties are to:

Note that a student’s refusal to meet with the instructor or respond to the charges within a reasonable period of time is construed as acceptance of the allegation and proposed sanctions.

Once the Academic Integrity form has been accepted or contested by the student, it is sent to the College’s Academic Integrity Committee for adjudication. A student cannot drop or withdraw from the course during the adjudication process.


If a student accepts an academic misconduct allegation, or if (s)he is found guilty during adjudication, probable sanctions include:

Additional sanctions might include:

In addition, the student will be unable to drop or withdraw from the course.

Please see the Eberly College of Science Academic Integrity homepage for additional information and procedures. Also see the Code of Ethics for Engineers published by the National Society of Professional Engineers.

Students with Disabilities

Penn State welcomes students with disabilities into the University’s educational programs. If you have a disability-related need for reasonable academic adjustments in this course, contact Student Disability Resources at 814-863-1807 (V/TTY). For further information, please visit the Student Disability Resources web site. In order to receive consideration for accommodations, you must contact SDR and provide documentation (see the documentation guidelines at the Student Disability Resources web site). If the documentation supports your request for reasonable accommodations, SDR will provide you with an accommodation letter identifying appropriate academic adjustments. Please share this letter with your instructors and discuss the accommodations with them as early in your courses as possible. You must follow this process for every semester that you request accommodations.

Code of Mutual Respect and Cooperation

The Eberly College of Science Code of Mutual Respect and Cooperation pertains to all members of the college community; faculty, staff, and students. The Code of Mutual Respect and Cooperation was developed to embody the values that we hope our faculty, staff, and students possess, consistent with the aspirational goals expressed in the Penn State Principles. The University is strongly committed to freedom of expression, and consequently, the Code does not constitute University or College policy, and is not intended to interfere in any way with an individual’s academic or personal freedoms. We hope, however, that individuals will voluntarily endorse the 12 principles set forth in the Code, thereby helping us make the Eberly College of Science a place where every individual feels respected and valued, as well as challenged and rewarded.

Educational Equity

The Office of the Vice Provost for Educational Equity serves as a catalyst and advocate for Penn State’s diversity and inclusion initiatives. Educational Equity’s vision is a Penn State community that is an inclusive and welcoming environment for all. If you wish to learn more or if you wish to report bias, please visit the Educational Equity website.

All course materials students receive or to which students have online access are protected by copyright laws. Students may use course materials and make copies for their own use as needed, but unauthorized distribution and/or uploading of materials without the instructor’s express permission is strictly prohibited. University Policy AD 40, the University Policy on Recording of Classroom Activities and Note Taking Services, addresses this issue. Students who engage in the unauthorized distribution of copyrighted materials may be held in violation of the University’s Code of Conduct and/or liable under Federal and State laws.

A rising trend across the University is the posting and/or retrieval of material from course-share sites. Generally speaking, the uploading of materials to a course-share site is viewed as an Intellectual Property violation, and the downloading and use of materials from a course-share site could be a violation of academic integrity. If you have questions regarding the specific use of such a site, seek clarification directly from your instructor.

Student Class Recordings

Students are not allowed to record class sessions without permission.

According to University Policy, students must get express permission from their instructor to record class sessions. Screenshots showing instructors and students are considered recordings. Even if permission is granted, student-initiated recordings must be used only for educational purposes for the students enrolled in the initiating student’s class. Recordings may be used only during the period in which the student is enrolled in the class. Authorized student-initiated recordings may not be posted or shared in any fashion outside of the class, including online or through other media, without the express written consent of the course instructor or appropriate University administrator. Students who engage in the unauthorized distribution of class recordings may be held in violation of the University’s Code of Conduct, and/or liable under Federal and State laws.