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 002), 4:30-5:45 (section 003), UNIV 101
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. (Select "Content" from the top pane in the Brightspace course home page then look for the "Gradescope" tab on the left.) 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 under "Content/Course Notes."
Kaltura. Audio and screen captures of each lecture will be available via Kaltura on the course Brightspace page under "Course Tools/Kaltura Media Gallery." 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. 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 welcome to let me know so that we can discuss options. You are also encouraged to contact the Disability Resource Center at: drc@purdue.edu or by phone at 765-494-1247.
If you have been certified by the Disability Resource Center (DRC) as eligible for accommodations, you should contact your instructor to discuss your accommodations 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. 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-. 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+ >85, B >78, B- >74, C+>70, C> 65, C- >60.
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 (archived) 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.
General Policies. General policies applying to all courses university wide can be found in the course Brightspace page under "Content/University Policies and Statements."
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, 8/21 Course Overview. Background. Sets, Functions, Proof Techniques, Induction, Complex Numbers (Appendices A-D).
Week 2, 8/28 Matrices and Systems of Linear Equations (1.1, 1.4), Abstract Vector Spaces (1.2)
Week 3, 9/4 Abstract Vector Spaces (cont'd), Subspaces (1.3)
Week 4, 9/11 Linear Combinations and Spans (1.4), Linear Dependence and Independence (1.5)
Week 5, 9/18 Bases and Dimension (1.6), LEEWAY/TOPICS
Week 6, 9/25 Linear Transformations, Composition, and the Rank-Nullity Theorem (2.1,2.3)
Week 7, 10/2 Matrix of a Linear Transform, Matrix Multiplication, Invertibility (2.2, 2.3, 2.4)
Week 8, 10/9 FALL BREAK, Elementary Matrix Operations (3.1)
Week 9, 10/16 Determinants (4.1-4.5)
Week 10, 10/23 Eigenvalues (5.1), Diagonalizablity (5.2),
Week 11, 10/30 Inner Product Spaces and Norms (6.1)
Week 12, 11/6 , Gram-Schmidt (6.2), Adjoint of a Linear Transform (6.3)
Week 13, 11/13 Self-Adjoint and Normal Linear Operators (6.4), Unitary and Orthogonal Operators (6.5)
Week 14, 11/20 LEEWAY/TOPICS, THANKSGIVING BREAK
Week 15, 11/27 The Spectral Theorem (6.6), Singular Value Decomposition (6.7)
Week 16, 12/4 LEEWAY or Selected Topics.
Week 1, 8/21 HW 1 Assigned.
Week 2, 8/28 HW 1 Due, HW 2 Assigned.
Week 3, 9/4 HW 2 Due, HW 3 Assigned. Quiz 1
Week 4, 9/11 HW 3 Due, HW 4 Assigned, Quiz 2.
Week 5, 9/18 HW 4 Due. HW5 Assigned, Quiz 3.
Week 6, 9/25 HW 5 due. HW 6 Assigned. Quiz 4.
Week 7, 10/2 HW 6 Due. Quiz 5.
Week 8, 10/9 HW 7 Assigned.
Week 9, 10/16 HW 7 Due, HW 8 Assigned.
Week 10, 10/23 HW 8 Due. HW 9 Assigned, Quiz 6.
Week 11, 10/30 HW 9 Due. HW 10 Assigned, Quiz 7.
Week 12, 11/6 HW 10 Due. HW 11 Assigned, Quiz 8.
Week 13, 11/13 HW 11 Due. Quiz 9.
Week 14, 11/20
Week 15, 11/27 HW12 Assigned. Quiz 10.
Week 16, 12/4 HW 12 Due.