Penn State, University Park, Fall 2019

# MATH 220H

PreRequisite: MATH 110 , MATH 140 , or MATH 140H

This syllabus and all other information pertaining to this course is available on canvas.psu.edu.

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

### Log of changes to the syllabus:

• September 25: The times of the midterm examinations have been modified. All three exams (regular, conflict, and makeup) are affected. See below for the correct times.
• September 25: Quizzes submitted by email to the instructor are not acceptable and will be ignored. You must submit your work through canvas.psu.edu.

## Course Description

Honors course in systems of linear equations; matrix algebra; eigenvalues and eigenvectors.

This course is intended as an introduction to linear algebra with a focus on solving systems for linear equations. Topics include systems of linear equations, row reduction and echelon forms, linear independence, introduction to linear transformations, matrix operations, inverse matrices, dimension and rank, determinants, eigenvalues, eigenvectors, diagonalization, and orthogonality.

In contrast to the non-honors version of this course, the honors version is typically more theoretical and will often include more sophisticated problems. Moreover, certain topics are often discussed in more depth and are sometimes expanded to include applications which are not visited in the non-honors version of the course.

## Learning Objectives

Upon successful completion of MATH 220, the student should be able to:

1. Know what is meant by a system of linear equations (or linear system) and its solution set.
2. Know how to write down the coefficient matrix and augmented matrix of a linear system.
3. Use elementary row operations to reduce matrices to echelon forms.
4. Make use of echelon forms in finding the solution sets of linear systems.
5. Know how to manipulate with vectors in Euclidean space.
6. Understand the meaning of linear independence/dependence and span.
7. Interpret linear systems as vector equations.
8. Define matrix vector product and be able to interpret linear systems as matrix equations.
9. Write the general solution of linear systems in parametric vector form.
10. Understand the relation between the solution set of a consistent inhomogeneous linear system and its associated homogeneous equation.
11. Determine whether sets of vectors are linearly independent or dependent.
12. Know what is meant by a linear transformation between Euclidean spaces.
13. Determine the standard matrix of a linear transformation.
14. Give the geometric description of some matrices.
15. Understand the notion of one-to-one mapping and onto mapping.
16. Know how to scale a matrix, take the transpose of a matrix, and how to add and multiply matrices.
17. Know what is meant by an invertible matrix.
18. Know how to compute the inverse of a matrix, if it exists.
19. Understand the various characterizations of an invertible matrix.
20. Determine if a given subset of a Euclidean space is a subspace.
21. Know what is the column space and nullspace of a matrix and how to determine these spaces.
22. Find a basis of a subspace of a Euclidean space.
23. Define the concept of dimension and how to use the rank plus nullity theorem.
24. Know the recursive definition of determinants.
25. Make use of the properties of determinants in their calculations.
26. Find eigenvalues and eigenvectors of square matrices.
27. Diagonalize square matrices, whenever possible.
28. Compute the matrix of a linear transformation relative to given bases.
29. Compute the inner product of vectors, lengths of vectors, and determine if vectors are orthogonal.
30. Know what is meant by an orthogonal set, orthogonal basis and orthogonal matrix.
31. Find the orthogonal projection of a vector onto a subspace.
32. Find an orthogonal basis using the Gram-Schmidt process.
33. Determine the least-squares solutions of linear systems.
34. Orthogonally diagonalize symmetric matrices.
35. Know how to eliminate cross-product terms in quadratic forms.

## Schedule

Course Days Time Room
MATH 220H Tue Thu 09:05 — 09:55 Huck Life Sciences 005
office hours Tue 15:40 — 16:40 McAllister 325

Arriving late to class, leaving class early, or disrupting class in any way will not be tolerated.

All electronic devices must be silenced during lectures.

## Instructor

Professor Mathieu Stiénon (stienon@psu.edu)

You can expect to get an answer by the end of the next business day.

## Textbook

David Lay, Linear Algebra and its Applications, Fifth Edition, Pearson. (Fourth Edition is also acceptable.)

Do NOT buy the "MyMathLab Online Course for Linear Algebra and Its Applications". We will NOT use it.

## Electronic Devices

No electronic devices are allowed on quizzes and examinations.

## Homework

Homework will be assigned but will not be graded.

## Quizzes

A mandatory quiz will be assigned (almost) every class and is due six days later unless specified otherwise.

There will be no makeup quizzes.

All quizzes will have equal weight.

#### Instructions for quizzes:

2. Print the PDF on white letter-size printer paper.
3. Solve the problems on the printout using a black pen. Show all your work. Final answers without supporting work will not receive credit.
4. Write your name on each page. Your name must be written at the top of 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.
5. Scan your work, and submit as one single PDF file on canvas.psu.edu. Multiple submissions, late submissions, and/or unreadable work will result in a zero score. Quizzes dropped in the instructor's mailbox or slipped under his office door will not be graded and will be shredded. Quizzes emailed to the instructor are not acceptable, will not be acknowledged, and will be ignored. You must submit your work through canvas.psu.edu.
6. Check that your submission is complete, that you have submitted all pages, and that your name is legible on each page.

There are document scanners in the university libraries. If you don't have access to a real document scanner, I recommend you install Scanbot on your phone or tablet. Scanbot's document boundary detection feature works best if the document to be scanned is placed on a contrasting uniform background.

If you'd rather work on the quiz directly on your pen-enabled tablet, make sure to submit all layers of the PDF document.

## Examinations

One midterm examination will be given during the semester and a final examination will be given during the final examination period.

You must bring your University ID card to all exams.

No books, notes, or calculators may be used on the examinations.

All electronic devices must be turned off and stowed away during examinations. Unauthorized use of any electronic device will result in a zero score on the exam — no exceptions.

Personal business, such as travel, employment, weddings, graduations, or attendance at public events such as concerts, sporting events, and Greek Rush events, is not a valid excuse for missing an examination. Forgetting the date, time or room of an examination is not a valid excuse.

### Midterm Examination

A 75-minute evening examination will be given on Thursday October 17, 2019 from 6:15 to 7:30 PM.

The room for the evening examination will be announced by your instructor at a later date and may also be found on the Courses website when it is available.

#### Conflict and makeup exam policy:

In addition to the regularly scheduled midterm examination, the math department schedules two additional options:

• a conflict exam scheduled from 4:50 to 6:05 pm on the same night (Thursday October 17) as the regularly scheduled exam
• and a makeup exam scheduled on Monday October 21, 2019 from 6:30 to 7:45 PM.

#### Who may take the conflict exam?

If a student has a valid, documented conflict with the regular examination time, such as a class or another official university activity, (s)he may sign up for the conflict exam. If (s)he has not signed up for the conflict exam a week in advance, he or she will not be permitted to take the exam.

If you need to schedule the conflict exam, you must sign up at least one full week ahead of the scheduled exam date.

#### Instructions on conflict exam night:

The student is responsible for knowing the room and time of the conflict examination. Each student must bring his or her University ID to the conflict examination. The ID will be checked by the proctor. Although the conflict examination will end at 6:05 PM, no student will be permitted to turn on his/her cell phone nor leave the examination room before 6:10 PM. Any student who leaves before 6:10 PM will receive a grade of zero on the examination and will not be allowed to retake it.

#### Who may take the makeup exam?

Students who have a valid, documented reason, such as a class conflict or illness, during both the conflict and regular examination times are permitted to schedule a makeup examination with no penalty. The student must be prepared to verify the reason for taking the makeup. Students who have taken either the regularly scheduled examination or conflict examination are not permitted to take the makeup examination. Students who do not have a valid reason (such as illness or official university business) for missing the evening examination may be allowed to take the makeup exam, but 20% points will be deducted from their score.

Students must sign up for the Makeup Exam in class. The student is responsible for knowing the room and time of the makeup examination. This information is on the sign-up sheet. Instructors must turn in the sign-up sheet 3 class days prior to the examination date. A student who is ill on exam night must contact his or her instructor within 24 hours of the exam. If a student has not signed up with his or her instructor, the student will not be allowed to take the makeup exam.

#### Instructions on makeup exam night:

The student is responsible for knowing the room and time of the makeup examination. Each student must bring his or her PSU ID to the makeup examination. The ID will be checked by the proctor.

#### What if a student misses both the regularly scheduled exam and the makeup exam?

If a student misses both the regularly scheduled examination and the scheduled makeup due to a valid, verifiable reason, it may be possible to take a makeup examination by appointment. All such makeup examinations by appointment must be scheduled through the classroom instructor and must be completed no later than one week after the scheduled makeup examination.

### Final Examination

A 110-minute comprehensive final examination will be given during the week December 16 to 20, 2019 (the final examination period). The final examination is a 110-minute comprehensive examination, which may be scheduled on any day during the final examination period. Do not plan to leave University Park until after Friday, December 20, 2019.

Students may access their final exam schedules Monday, September 23, through their Lionpath account. The room for the final examination will be announced by your instructor at a later date and may also be found on the Courses website when it is available. Notification of conflicts is given on the student's final exam schedule. There are two types of conflict examinations: direct and overload. Direct conflicts are two examinations scheduled at the same time. Overload examinations are defined as three or more examinations scheduled in consecutive time periods or within one calendar day. Students may elect to take the three or more examinations on the same day if they wish or request a conflict final examination. A student must take action to request a conflict exam through Lionpath between September 23 and October 13, 2019. Conflict final examinations cannot be scheduled through the Mathematics Department.

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, time, or room of an examination is not a valid excuse. If the student does not have a valid reason, as explained above, a 25% point penalty will be imposed. 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 have taken the original final examination are not permitted to take a makeup examination.

Grades will be assigned on the basis of 300 points, distributed as follows:

 Weekly Quizzes 100 points Midterm Examination 80 points Final Examination 120 points

Final course grades will be assigned as follows:

300 ⩾ A ⩾ 279 > A- ⩾ 270 > B+ ⩾ 261 > B ⩾ 249 > B- ⩾ 240 > C+ ⩾ 231 > C ⩾ 210 > D ⩾ 180 > 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 quizzes, the midterm examination, and the final examination. There is no "extra-credit" work.

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 DF grade.

## 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 for Fall 2019 is November 15, 2019 at 23:59.

## Tutors and Penn State Learning

Free mathematics tutoring is available at Penn State Learning located in 220 Boucke Building. Tutoring will begin during the second week of the semester. For more information, go to PSU Learning. For more help, a private tutor list is available on the Courses website (scroll to "Additional Information" for the link).

## Additional Help at Penn State's Counseling & Psychological Services

Students with a need or interest in obtaining counseling services may wish to contact the Penn State Counseling & Psychological Services Office. More information about the Counseling & Psychological Services Office can be found here: studentaffairs.psu.edu/counseling.

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.

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

• Copying the work of another student on an exam, quiz, or assignment;
• Passing off the work of another individual as your own;
• Using non-approved devices or aids on exams, quizzes, or assignments;
• Having unauthorized possession of exams or quizzes;
• Engaging in deception in order to extend or reschedule an exam, quiz, or assignment;
• Facilitating acts of academic misconduct by others.

### When Academic Misconduct is Suspected

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

• Confidentially inform the student of the allegation;
• Enter the charge and recommended sanctions on an Eberly College of Science Academic Integrity form;
• Ask the student to meet in order to review the form and discuss the charges and sanctions. The student can choose to accept or contest the allegation at this point.

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:

• A warning and
• Reduction of the assignment grade to zero or
• Reduction of the quiz or exam grade to zero.

• Reduction in the final course grade;
• An F in the course.

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.

## 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.

## Tentative Lecture Schedule

Week Day Date Book Topic
1 Tue Aug 27 1.1 Systems of linear equations
Thu Aug 29 1.1 Systems of linear equations
2 Tue Sep 3 1.2 Row reduction algorithm
Thu Sep 5 1.2 Row reduction algorithm
3 Tue Sep 10 1.3 Linear combinations, span
Thu Sep 12 1.4 Linear systems as matrix equations
4 Tue Sep 17 1.5 Homogeneous linear systems
Thu Sep 19 1.7 Linear independence of vectors
5 Tue Sep 24 1.8 Linear transformations and their matrices
Thu Sep 26 1.9 Examples of linear transformations
6 Tue Oct 1 2.1 Operations on matrices
Thu Oct 3 2.2 Matrix inversion
7 Tue Oct 8 2.3 Invertible matrices
Thu Oct 10 6.1 Dot product
8 Tue Oct 15 Review
Thu Oct 17 Midterm Examination
9 Tue Oct 22 3.1 Determinant of a square matrix
Thu Oct 24 3.2 Properties of determinants
10 Tue Oct 29 2.8 Linear subspaces
Thu Oct 31 2.9 Dimension of a subspace and rank of a matrix
11 Tue Nov 5 6.2 Sets of orthogonal vectors
Thu Nov 7 6.3 Orthogonal projections
12 Tue Nov 12 6.4 Gram-Schmidt algorithm
Thu Nov 14 5.1 Eigenvalues and eigenvectors
13 Tue Nov 19 5.2 Characteristic polynomial of a square matrix
Thu Nov 21 5.3 Diagonalization of a square matrix
14 Tue Nov 26 THANKSGIVING
Thu Nov 28 THANKSGIVING
15 Tue Dec 3 7.1 Symmetric matrices
Thu Dec 5 Review
16 Tue Dec 10 Review
Thu Dec 12 Review
17 TBA Final Examination