Overview. This is a course in proof-based Linear Algebra. The objective of the course will be to understand the rigorous foundations of the material covered in a standard upper-division course in Linear Algebra such as MA 351. The course will be divided into two roughly equal parts. The first part will consist of studying properties of abstract vector spaces and linear maps between them, including such concepts as dimension and the rank and nullity of a linear transform. The second part of the course will focus on inner product spaces, detailing the Gram-Schmidt process and culminating in the proof of the Spectral Theorem and Singular Value Decomposition. In this way the course will acquaint students with the basic theoretical background in linear algebra which serves as a vital compliment to numerically or computationally based applications such as to statistics, actuarial science, and machine learning.
Meeting Time and Location. TR; 3:00-4:15 (section 001), 4:30-5:45 (section 002), REC 317
Textbook. The textbook for the course is "Linear Algebra" by Friedberg, Insel, and Spence. Either of the fourth or fifth editions is acceptable.
Contact. The best way to contact me is by email. My email address is tsincla(at)purdue.edu. I will usually respond to emails fairly promptly during normal business hours. If you have not received a reply within 48 hours, feel free to follow up.
Office. My office is 744 in the Mathematical Sciences building.
Office Hours. See the course Brightspace page for details. Outside of regular office hours, I am also happy to meet by appointment. Please email me to schedule.
Brightspace. The course page on Brightspace will serve as the main point of contact for announcements, assignments, course policy, and virtual content. Students will be expected to check the course page regularly, at least before every class meeting.
Gradescope. Assignments and quizzes must be uploaded to Gradescope via the course page in Brightspace. No hard copies of assignments or quizzes will be accepted.
Course Notes. Handwritten course notes will be available in a OneNote Notebook accessible from the course Brightspace page.
Kaltura. Audio and screen captures of each lecture will be available via Kaltura on the course Brightspace page. Please allow up to 24 hours for processing.
Academic Calendar For ease of reference, here is a link to the academic calendar detailing all breaks, add/drop deadlines, etc.
Lecture. Lectures are held in-person, but written notes and audio will be recorded and posted to Brightspace. Students are strongly encouraged to attend lecture. In case that I need to quarantine or isolate, every effort will be given to maintaining the regular lecture schedule and time by meeting on Webex or by recorded lecture if that is not feasible. Class cancellations and other changes due to a health-related absence on my part will be communicated via the course page in Brightspace.
Accommodations. Purdue University strives to make learning experiences accessible to all participants. If you anticipate or experience physical or academic barriers based on disability, you are encouraged to contact the Disability Resource Center at: drc@purdue.edu or by phone: 765-494-1247. If you have been certified by the Disability Resource Center (DRC) as eligible for academic adjustments on exams or quizzes see www.math.purdue.edu/ada for exam and quiz procedures for your mathematics course. If you have questions please send email to Stephanie Foster (foster80@purdue.edu). In the event that you are waiting to be certified by the Disability Resource Center we encourage you to review our procedures prior to being certified. For all in-class accommodations please contact your instructor as soon as possible. Here are instructions for sending your Course Accessibility Letter to your instructor: https://www.purdue.edu/drc/students/course-accessibility-letter.php.
Exams. There will be no exams for the course.
Quizzes. There will be 10 quizzes in total for the course. The quizzes will be administered online through Gradescope. Each quiz will consist of 2 or 3 open response questions. There will be a three day window to take each quiz, but quizzes will have a time limit from when they are open to complete and upload solutions. The lowest two quiz scores will be dropped.
Homework. There will be 12 homework sets assigned on a near-weekly basis. Homeworks will be assigned on Thursdays and due the following Thursday. (See below for details and due dates.) Students are encouraged to collaborate on homeworks as long as each student turns in their own, individual work. Rote copying of solutions from peers, internet forums, or plagiarism of any kind will not be tolerated. The lowest two homework scores will be dropped.
Homework Formatting. Homeworks must be typed or neatly written and scanned. There is a preference for assignments to be prepared using LaTeX (see the section on LaTeX below) or other word processing application. There should be no significant cross-outs, rewrites, scratchwork, scribbling, etc. Problems should be clearly indicated and be placed in the correct sequence. Homework should be uploaded to Gradescope by 11:59 pm on the due date.
Late Homework. No penalty will be assessed for assignments which are not excessively late (less than one week past due).
Grades. There will be 140 total points. Homework will be worth 10 points per assignment (100 points total). Quizzes will be worth 5 points each (40 points total). Grades will be determined by percentage of total points earned. For marginal cases, there will be some discretionary leeway in final grade assignment to account for course participation/engagement or extraordinary effort. The following is a sample cutoff distribution which is fairly typical for courses I have previously taught. The final grade cut-offs may differ slightly. A >92, A- >88, B+ >84, B >77, B- >73, C+>69, C> 64, C- >60. Students who get at least 97% of the total points in this course are guaranteed an A+,93% guarantees an A, 90% an A-, 87% a B+, 83% a B,80% a B-, 77% a C+, 73% a C, 70% a C-, 67% a D+, 63% a D, and 60% a D-.
LaTeX is the language for mathematical typesetting. If you are a CS, Math, or Stats major, I would strongly recommend becoming proficient in LaTeX. Here is the link to A.J. Hildebrand's excellent collection of beginner LaTeX resources. Another great place to start is Jon Peterson's advice and resources for new researchers. You will probably also frequently need to consult the LaTeX Wiki.
Academic Integrity. See the Academic Integrity webpage from the Office of the Dean of Students. Penalties for academic dishonesty will be, at minimum, a score of zero on the quiz or assignment. Egregious cases will be referred to the Dean of Students and may result in failure of the course or expulsion.
Attendance. Students should stay home and contact the Protect Purdue Health Center (496-INFO) if they feel ill, have any symptoms associated with COVID-19, or suspect they have been exposed to the virus. In the current context of COVID-19, in-person attendance will not be a factor in the final grades, but the student still needs to inform the instructor of any conflict that can be anticipated and will affect the submission of an assignment or the ability to take an exam. Only the instructor can excuse a student from a course requirement or responsibility. When conflicts can be anticipated, such as for many University-sponsored activities and religious observations, the student should inform the instructor of the situation as far in advance as possible. For unanticipated or emergency conflict, when advance notification to an instructor is not possible, the student should contact the instructor as soon as possible by email. When the student is unable to make direct contact with the instructor and is unable to leave word with the instructor’s department because of circumstances beyond the student’s control, and in cases of bereavement, quarantine, or isolation, the student or the student’s representative should contact the Office of the Dean of Students via email or phone at 765-494-1747. Our course Brightspace includes a link on Attendance and Grief Absence policies under the University Policies menu.
Guidance for Quarantine. If you become quarantined or isolated at any point in time during the semester, in addition to support from the Protect Purdue Health Center, you will also have access to an Academic Case Manager who can provide you academic support during this time. Your Academic Case Manager can be reached at acmq@purdue.edu and will provide you with general guidelines/resources around communicating with your instructors, be available for academic support, and offer suggestions for how to be successful when learning remotely. Importantly, if you find yourself too sick to progress in the course, notify your academic case manager and notify me via email or Brightspace. We will make arrangements based on your particular situation. The Office of the Dean of Students (odos@purdue.edu) is also available to support you should this situation occur.
Mental Health.
A link to CAPS (listed as Purdue Counseling and Psychological Services) is on the Brightspace template, under the Student Services and Resources section. If you find yourself beginning to feel some stress, anxiety and/or feeling slightly overwhelmed, try WellTrack. Sign in and find information and tools at your fingertips, available to you at any time.
If you need support and information about options and resources, please contact or see the Office of the Dean of Students. Call 765-494-1747. Hours of operation are M-F, 8 am- 5 pm.
If you find yourself struggling to find a healthy balance between academics, social life, stress, etc. sign up for free one-on-one virtual or in-person sessions with a Purdue Wellness Coach at RecWell. Student coaches can help you navigate through barriers and challenges toward your goals throughout the semester. Sign up is completely free and can be done on BoilerConnect. If you have any questions, please contact Purdue Wellness at evans240@purdue.edu.
If you’re struggling and need mental health services: Purdue University is committed to advancing the mental health and well-being of its students. If you or someone you know is feeling overwhelmed, depressed, and/or in need of mental health support, services are available. For help, such individuals should contact Counseling and Psychological Services (CAPS) at 765-494-6995 during and after hours, on weekends and holidays, or by going to the CAPS office of the second floor of the Purdue University Student Health Center (PUSH) during business hours.
Emergency Preparedness. In the event of a major campus emergency, course requirements, deadlines and grading percentages are subject to changes that may be necessitated by a revised semester calendar or other circumstances beyond the instructor’s control. Relevant changes to this course will be posted to the course page in Brightspace or can be obtained by contacting me via email. You are expected to read your Purdue email on a frequent basis.
Protect Purdue. The Protect Purdue Plan, which includes the Protect Purdue Pledge, is campus policy and as such all members of the Purdue community must comply with the required health and safety guidelines. Required behaviors in this class include: staying home and contacting the Protect Purdue Health Center (496-INFO) if you feel ill or know you have been exposed to the virus, properly wearing a mask in classrooms and campus building, at all times (e.g., mask covers nose and mouth, no eating/drinking in the classroom), disinfecting desk/workspace prior to and after use, maintaining appropriate social distancing with peers and instructors (including when entering/exiting classrooms), refraining from moving furniture, avoiding shared use of personal items, maintaining robust hygiene (e.g., handwashing, disposal of tissues) prior to, during and after class, and following all safety directions from the instructor.
Students who are not engaging in these behaviors (e.g., wearing a mask) will be offered the opportunity to comply. If non-compliance continues, possible results include instructors asking the student to leave class and instructors dismissing the whole class. Students who do not comply with the required health behaviors are violating the University Code of Conduct and will be reported to the Dean of Students Office with sanctions ranging from educational requirements to dismissal from the university.
Any student who has substantial reason to believe that another person in a campus room (e.g., classroom) is threatening the safety of others by not complying (e.g., not wearing a mask) may leave the room without consequence. The student is encouraged to report the behavior to and discuss next steps with their instructor. Students also have the option of reporting the behavior to the Office of the Student Rights and Responsibilities. See also Purdue University Bill of Student Rights.
Nondiscrimination Statement. Purdue University is committed to maintaining a community which recognizes and values the inherent worth and dignity of every person; fosters tolerance, sensitivity, understanding, and mutual respect among its members; and encourages each individual to strive to reach his or her own potential. In pursuit of its goal of academic excellence, the University seeks to develop and nurture diversity. The University believes that diversity among its many members strengthens the institution, stimulates creativity, promotes the exchange of ideas, and enriches campus life. More details are available on our course Brightspace table of contents, under University Policies.
The following is a tentative outline of topics covered and is subject to change. If you are absent from class it is your responsibility to find out what material was covered and to obtain notes from classmates.
Week 1, 8/23 Background. Sets, Functions, Proof Techniques, Induction, Complex Numbers (Appendices A-D).
Week 2, 8/30 Matrices and Systems of Linear Equations (1.1, 1.4), Abstract Vector Spaces (1.2)
Week 3, 9/6 Vector Spaces (cont'd), Subspaces (1.3)
Week 4, 9/13 Linear Combinations and Spans (1.4), Linear Dependence and Independence (1.5)
Week 5, 9/20 Bases and Dimension (1.6), Bases in Infinite Dimensions (1.7)
Week 6, 9/27 Linear Transformations, Composition, and the Rank-Nullity Theorem (2.1,2.3)
Week 7, 10/4 Matrix of a Linear Transform, Matrix Multiplication, Inveritibility (2.2, 2.3, 2.4)
Week 8, 10/11 FALL BREAK, Elementary Matrix Operations (3.1)
Week 9, 10/18 Facts About the Determinant (4.4), Eigenvalues (5.1)
Week 10, 10/25 Diagonalizablity (5.2), Inner Product Spaces and Norms (6.1)
Week 11, 11/1 Inner Product Spaces (cont'd), Gram-Schmidt (6.2)
Week 12, 11/8 Adjoint of a Linear Transform (6.3), Self-Adjoint and Normal Linear Operators (6.4)
Week 13, 11/15 Unitary and Orthogonal Operators (6.5), The Spectral Theorem (6.6)
Week 14, 11/22 The Spectral Theorem (cont'd), THANKSGIVING BREAK
Week 15, 11/29 Singular Value Decomposition (6.7)
Week 16, 12/6 LEEWAY or Selected Topics.
Week 1, 8/23 HW 1 Assigned.
Week 2, 8/30 HW 1 Due, HW 2 Assigned.
Week 3, 9/6 HW 2 Due, HW 3 Assigned, Quiz 1.
Week 4, 9/13 HW 3 Due, HW 4 Assigned, Quiz 2.
Week 5, 9/20 HW 4 Due. HW5 Assigned, Quiz 3.
Week 6, 9/27 HW 5 due. HW 6 Assigned. Quiz 4.
Week 7, 10/4 HW 6 Due. Quiz 5.
Week 8, 10/11 HW 7 Assigned.
Week 9, 10/18 HW 7 Due, HW 8 Assigned.
Week 10, 10/25 HW 8 Due. HW 9 Assigned, Quiz 6.
Week 11, 11/1 HW 9 Due. HW 10 Assigned, Quiz 7.
Week 12, 11/8 HW 10 Due. HW 11 Assigned, Quiz 8.
Week 13, 11/15 HW 11 Due. Quiz 9.
Week 14, 11/22
Week 15, 11/29 HW 11 Due. HW 12 Assigned, Quiz 10.
Week 16, 12/6 HW 12 Due.