Course Syllabus

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Math 368 - Introduction to Optimization

Northwestern University, Spring Quarter, 2022

 

The content of this syllabus is subject to change.


Textbook information:

Linear Programming, Foundations and Extensions, Fourth Edition, by Robert J. Vanderbei
Free download via SpringerLink using Northwestern login.

You're allowed (but not required) to use a calculator in class and during the exams. The calculator will be needed for performing elementary row operations on matrices and finding inverses of matrices.


Prerequisites:

You will need a good background in multivariable calculus and linear algebra, as well as the ability to understand and write mathematical proofs. The Math 290 and Math 291 sequences each satisfy these prerequisites, as do (taken together) calculus through Math 240 and Math 300. 


Topics to be Covered:

The main focus of this course is the theory of Optimization. This will involve a lot of theorem proving. We will be covering the following topics:

  • Simplex method (Chapters 1-4)
  • Duality theory (Chapters 5-10)
  • Applications of linear programming (Chapters 11-15)
  • Selected topics in non-linear programming

In the past, students have enrolled in this course expecting to learn applications of LP. While we will do some applications in the latter half, they will not be our primary focus and will constitute only a small part of the course. 

 

 

Grades

Your final grade will be composed of your homework, midterm exams, and final project scores according to the following percentages:

  • 35% Homework
  • 25% Midterm 1
  • 25% Midterm 2
  • 15% Final Project

Grade borderlines will be determined at the end of the quarter once all scores have been totaled. Students who obtain at least 90% are guaranteed at least an A–, at least 80% are guaranteed at least a B–, and at least 70% are guaranteed at least a C–.


Exams

There will be two midterms, both during the discussion sections.

  • Midterm 1: Tuesday, May 03, 9:00 - 9:50 am CT in Tech M152
  • Midterm 2: Tuesday, May 31, 9:00 - 9:50 am CT in Tech M152

There are no makeup examinations. If you are absent from exactly one midterm examination for legitimate medical reasons and follow the procedure described in Academic Work Missed for Medical Reasons, then we will waive the missing midterm examination and use the remaining assessments to calculate your grade. You will not receive a passing grade in this course if you miss both the midterms.


Written Homework

Weekly homework assignments will be posted on Canvas. They will be due electronically on Crowdmark on Tuesday at 11:59pm CT. Follow the guidelines for Completing and Submitting a Crowdmark Assigned Assessment. Assignments that fail to conform to the guidelines may not earn credit. Late homework and portions of assignments uploaded after the deadline will not be accepted for credit. Complete and upload your solutions well before the deadline.

You will be allowed to extend the deadline on two of your homework assignments by 24 hours.  This extension is designed to account for all possible reasons why you may need an extension, including illness.  Please contact your instructor to request an extension when you need one. 


Final Project

Throughout the course, you'll be assigned several word problems to model using linear programs and solve using the Solver tool in Excel. You'll have to submit all the solutions in a single Excel spreadsheet at the end of the quarter.

The final submission needs to be well-labelled and easy to follow. Points will be assigned not only for the correctness of the linear program but also for readability and presentation. The final project submissions will be due on Tuesday, Jun 07, 11:59 pm CT. No extensions will be granted for the final submission. 


Missing Academic Work Due to Illness

Review the University's policy on missing academic work due to illness. Your instructor cannot waive an assignment missed due to illness unless he or she can verify your illness with Health Services.


Diversity and Inclusion

We value diversity and inclusion, and are committed to a climate of mutual respect and full participation in and out of the classroom. This class strives to be a learning environment that is equitable, inclusive and welcoming, regardless of backgrounds and identities. Following are some axioms by Federico Ardila that we'll be assuming throughout this course.

  • Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
  • Everyone can have joyful, meaningful, and empowering mathematical experiences.
  • Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
  • Every student deserves to be treated with dignity and respect.

 

 


Policies


Important Dates

  • Tuesday, Mar 29: First class meeting
  • Tuesday, Apr 05: First discussion session
  • Friday, May 06: Last day to drop a class
  • Friday, May 27: Last day to request for withdrawal
  • Monday, May 30: Memorial Day, no classes
  • Wednesday, Jun 01: WCAS Reading Period begins.
  • Wednesday, Jun 05: WCAS Reading Period ends.
  • Monday, Jun 06: Final exam period begins. 


Discussion Sections

You must register for a discussion section as a requirement for this course. Discussion sections meet weekly on Tuesdays.  Discussion sections do not meet during the first week of classes.

During discussion you and your peers will solve problems with the assistance of a teaching assistant. Be prepared to engage in sharing of work and ideas with your peers. 


Academic Integrity

Academic Integrity is taken very seriously at Northwestern. Students are responsible for reading and understanding Northwestern's Academic Integrity policies, outlined in the booklet Academic Integrity at Northwestern University: A Basic Guide. All papers submitted for credit in this course must be submitted electronically unless otherwise instructed by the professor. Your written work may be tested for plagiarized content. All suspected violations of academic integrity will be reported to the Weinberg College Dean's Office. These include: cheating, plagiarism, fabrication, unfair advantage, unauthorized collaboration, and aiding and abetting of academic dishonesty. Students found in violation of academic integrity may receive a zero on the assignment or a failing grade for the course, and may be suspended or permanently expelled from the University. See the WCAS website on academic integrity and Northwestern Provost's Academic Integrity webpage for more information.


Supports for Wellness and Mental Health

Northwestern University is committed to supporting the wellness of our students. Student Affairs has multiple resources to support student wellness and mental health.  If you are feeling distressed or overwhelmed, please reach out for help. Students can access confidential resources through the Counseling and Psychological Services (CAPS), Religious and Spiritual Life (RSL) and the Center for Awareness, Response and Education (CARE). Additional information on all of the resources mentioned above can be found at the following links:


Accessibility

Northwestern University is committed to providing the most accessible learning environment as possible for students with disabilities. Should you anticipate or experience disability-related barriers in the academic setting, please contact AccessibleNU to move forward with the university’s established accommodation process (email: accessiblenu@northwestern.edu; phone: 847-467-5530). If you already have established accommodations with AccessibleNU, please let me know as soon as possible, preferably within the first two weeks of the term, so we can work together to implement your disability accommodations. Disability information, including academic accommodations, is confidential under the Family Educational Rights and Privacy Act. See the AccessibleNU website for more information.


Exceptions to Class Modality

Once we transition to in-person instruction, individual students will not be granted permission to attend remotely except as the result of an Americans with Disabilities Act (ADA) accommodation as determined by AccessibleNU. 

Maintaining the health of the community remains our priority.  If you are experiencing any symptoms of COVID do not attend class and update your Symptom Tracker application right away to connect with Northwestern’s Case Management Team for guidance on next steps. Also contact the instructor as soon as possible to arrange to complete coursework.

Students who experience a personal emergency should contact the instructor as soon as possible to arrange to complete coursework.

Should public health recommendations prevent in person class from being held on a given day, the instructor or the university will notify students.


Prohibition of Recording of Class Sessions by Students

Unauthorized student recording of classroom or other academic activities (including advising sessions or office hours) is prohibited. Unauthorized recording is unethical and may also be a violation of University policy and state law. Students requesting the use of assistive technology as an accommodation should contact AccessibleNU. Unauthorized use of classroom recordings – including distributing or posting them – is also prohibited. Under the University’s Copyright Policy, faculty own the copyright to instructional materials – including those resources created specifically for the purposes of instruction, such as syllabi, lectures and lecture notes, and presentations. Students cannot copy, reproduce, display, or distribute these materials. Students who engage in unauthorized recording, unauthorized use of a recording, or unauthorized distribution of instructional materials will be referred to the appropriate University office for follow-up.


Discrimination and Sexual Harassment

Northwestern University’s Policies on Discrimination, Harassment, and Sexual Harassment apply to all members of the University community, including students, staff, faculty, and third parties.  Any student, staff, faculty member, or third party who believes that they have been discriminated against or harassed on the basis of their race, color, religion, national origin, sex, sexual orientation, gender identity, gender expression, pregnancy, parental status, marital status, age, disability, citizenship, veteran status, genetic information or any other classification protected by law, should contact the Office of Equity at (847) 467-6571.  Additional information about the University’s discrimination and harassment policies, including the campus resources available to assist individuals with discrimination or harassment concerns, is available online on the Office of Equity website.

Students, staff, and faculty who report harassment, discrimination, or sexual misconduct are also protected under the University's Policy on Non-Retaliation.


Sexual Misconduct and Reporting

Northwestern University is committed to fostering an environment where students are safe and free from sexual misconduct. Confidential resources are available to those who have experienced sexual misconduct.  Faculty and instructors are not confidential resources and are required to report incidents of sexual misconduct, whether discussed in your assignments or in person, to the Office of Equity, which can provide information about resources and options.  We encourage students who have experienced sexual misconduct to talk with someone to get support.  For more information, including how to request interim protective measures and academic accommodations or file a complaint, see the Get Help page.

Course Summary:

Date Details Due