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Penn State, University Park, Fall 2024

MATH 220H — MATRICES

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

Space-Time Coordinates

Mon Wed Fri from 09:05 to 09:55 in Willard Building 369

Classes begin on Monday August 26, 2024 and end on Friday December 13, 2024.

Thanksgiving break: November 25-29, 2024.

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

Instructor

Professor Mathieu Stiénon

Information and Communications Technology

We will not use Canvas.

We will use Gradescope (iOS) (android) to administer assignments and record scores and Teams (iOS) (android) for instant messaging, course materials distribution, and virtual office hours.

IT support is available 24/7.

Gradescope

Gradescope is a website designed to streamline the process of submitting, grading, and providing feedback on assignments. It allows students to submit their work online. Gradescope is widely used in higher education to improve the grading process.

Instructions for adding yourself to the course on Gradescope:

  1. If you don’t already have a Gradescope account, please create one using your abc123@psu.edu email address as your username.
  2. Use the code provided by your instructor to add MATH 484 to your account. See ‘joining a course using a course code’.
  3. Install the Gradescope mobile app (iOS) (android) on your phone and/or tablet. You will use it to scan your homework and submit it for credit.

Once an assignment is graded, the scores are available in Gradescope.

How to submit homework on the Gradescope mobile app

How to submit homework on the Gradescope website

Using Gradescope as a Student

Teams

Microsoft Teams is a versatile collaboration platform that integrates chat, video meetings, file storage, and more. It simplifies real-time communication and collaboration between students and instructors outside the classroom. In this course, we will use Teams for distributing course materials, making announcements, holding group discussions, conducting private one-on-one chats, and hosting virtual office hours.

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. Log in to Teams with your PSU email address and password.
  2. In the left menu bar of Teams, click on the Teams icon.
  3. Click on ‘Join or Create a Team’ (located in the bottom, left corner of the screen).
  4. In the box for ‘Join a Team with a Code’, type in the team code provided by your instructor.
  5. Click the ‘Join Team’ button.

For your convenience, I encourage you to install the Teams mobile app (iOS) (android) on your phone and/or tablet. Please take a moment now to download the app and join the team as I will share important information with the class through Teams exclusively. Do it now!

Quick Start Guide

How to message your class and other students in Microsoft Teams

Virtual Office Hours

Tentatively scheduled on Wednesdays from 16:00 to 17:00.

You will find the meeting link for virtual office hours in Teams (calendar).

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

David Lay, Linear Algebra and Its Applications, Pearson

The content is virtually the same in all editions. The only difference is that the exercises change from one edition to the next. Most problems are exactly the same, but the numerical values in each problem are different. Thus, no matter which edition you get, you will be solving the same problems but with different numbers. If I were you, I’d buy the cheapest used copy I could find that is still in good physical shape.

Be smart: buy a previous edition of the textbook and save money.

Course Description

This honors course provides an introduction to linear algebra with a focus on solving systems of linear equations. Topics covered include:

Compared to the non-honors version, this course is typically more theoretical and includes more sophisticated problems. Additionally, certain topics are discussed in greater depth and may include applications not covered in the non-honors version.

Prerequisites

MATH 110, MATH 140, or MATH 140H

Tentative Course Outline

geometry in $\mathbb{R}^3$

matrix algebra (Lay 2.1)

systems of linear equations and their solution sets

spanning sets and linearly independent sets

linear transformations (Lay 1.8 and 1.9)

invertible linear transformations

linear subspaces, bases, dimension, rank of a matrix

orthogonal projections

square matrices

matrix factorizations

Key Learning Objectives

  1. Systems of Linear Equations: Analyze and solve systems of linear equations using various methods.
  2. Matrix Algebra: Perform matrix operations and understand their properties, including inverses and factorizations.
  3. Determinants: Calculate determinants and understand their significance in linear algebra.
  4. Vector Spaces: Grasp the concepts of vector spaces, subspaces, bases, and dimensions.
  5. Eigenvalues and Eigenvectors: Compute eigenvalues and eigenvectors and apply them to problems involving diagonalization.
  6. Orthogonality: Understand orthogonality, orthogonal sets, and projections, and apply these concepts to least-squares problems.
  7. Linear Transformations: Explore linear transformations and their matrix representations.
  8. Applications: Apply linear algebra concepts to real-world problems in various fields such as computer graphics, engineering, and science.

Class Attendance

Regular class attendance is one of the most important ways that students learn and understand course materials. It is a critical element of student success. Accordingly, it is the policy of the University that class attendance is expected. Students should attend every scheduled class and should be held responsible for all work covered in the course. Class attendance is expected regardless of the format of the course and this expectation applies equally to students in face-to-face, online, and hybrid courses.

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. 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.

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. 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.
  4. In Gradescope, once you have uploaded your PDF file, you must match the pages of your document to the questions of the assignment. Otherwise, your submission will be considered incomplete and will receive a zero score.
  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.

Examinations

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 Examinations

Two 45-minutes midterm examinations will be given in class on Wednesday October 2, 2024 and Wednesday November 13, 2024.

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

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, December 16-20, 2024. The final examination may be scheduled on any day of finals week. Do not plan to leave University Park until after Friday, December 20, 2024. Students may access their final exam schedules on Monday, September 30, 2024, through their LionPATH account. Notification of conflicts is given on the student’s final exam schedule. Final exam conflicts must be submitted through Lionpath by Sunday, October 20, 2024.

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.

Grades

Assignments will be weighted as follows:

Type of Assignment Weight
Weekly Problem Sets 40%
First Midterm Examination 15%
Second Midterm Examination 15%
Final Examination 30%

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 weekly problem sets, the two midterm examinations, and the final examination. 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. A deferred grade which is not changed to a letter grade by the instructor by 10 weeks after the course ends will automatically become an F. For more information see Deferred Grades.

Late-Drop

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 is Friday November 15, 2024 at 23:59 (Eastern Time).

Tutoring

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.

988 Suicide & Crisis Lifeline

The 988 Lifeline is a national network of local crisis centers that provides free and confidential emotional support to people in suicidal crisis or emotional distress 24 hours a day, 7 days a week in the United States.

There is hope. Providing 24/7, free and confidential support to people in suicidal crisis or emotional distress works. The Lifeline helps thousands of people overcome crisis situations every day.

Need Support Now? If you or someone you know is struggling or in crisis, help is available. Call or text 988 or chat 988lifeline.org.

Academic Integrity

According to Penn State policy G-9: Academic Integrity, an academic integrity violation is “an intentional, unintentional, or attempted violation of course or assessment policies to gain an academic advantage or to advantage or disadvantage another student academically.” Unless your instructor tells you otherwise, you must complete all course work entirely on your own, using only sources that have been permitted by your instructor, and you may not assist other students with exams or other assessments.

Using ideas, images, or word phrases created by another person (e.g., from Course Hero or Chegg) or by generative technology, such as ChatGPT, is prohibited in this course. You may not submit false or fabricated information, use the same academic work for credit in multiple courses, or share instructional content. Students with questions about academic integrity should ask their instructor before submitting work.

Students facing allegations of academic misconduct may not drop/withdraw from the affected course unless they are cleared of wrongdoing (see G-9: Academic Integrity). Attempted drops will be prevented or reversed, and students will be expected to complete course work and meet course deadlines. Students who are found responsible for academic integrity violations face academic outcomes, which can be severe, and put themselves at jeopardy for other outcomes which may include ineligibility for Dean’s List, pass/fail elections, and grade forgiveness. Students may also face consequences from their home/major program and/or The Schreyer Honors College.

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.

Sanctions

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.

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: 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.

Calendar

Week Mon Wed Fri
1 Aug 26 Aug 28 Aug 30
2   Sep 4 Sep 6
3 Sep 9 Sep 11 Sep 13
4 Sep 16 Sep 18 Sep 20
5 Sep 23 Sep 25 Sep 27
6 Sep 30 Oct 2 Oct 4
7 Oct 7 Oct 9 Oct 11
8 Oct 14 Oct 16 Oct 18
9 Oct 21 Oct 23 Oct 25
10 Oct 28 Oct 30 Nov 1
11 Nov 4 Nov 6 Nov 8
12 Nov 11 Nov 13 Nov 15
13 Nov 18 Nov 20 Nov 22
14 Dec 2 Dec 4 Dec 6
15 Dec 9 Dec 11 Dec 13