Overview. This course serves as a higher-level introduction to linear algebra. The focus of the course will be on building intuition as well as a sound knowledge of procedure. Critical thinking and analytic reasoning about the concepts taught will be emphasized alongside computation.
Meeting Time and Location. TR; 3:00-4:15, SCHM 122.
Textbook. The textbook for the course is "Linear Algebra: Ideas and Applications," fourth edition, by Richard C. Penney. The third and fifth additions are also acceptable. You can access a copy of the e-book from the Purdue Library here. (Requires Boiler Key.)
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.
MATLAB. MATLAB is a numerical computing platform designed for linear algebra. Some exercises on the homework may use MATLAB for exploration/intuition building. (Feel free to use your preferred programming language instead, no code will need to be submitted.) You may also find it useful to check your computations using MATLAB. The main science computing labs have access to MATLAB. An online version of MATLAB is accessible to all Purdue students here. (You will need to create an account. Click "Sign In," then use your Purdue email to register.) Here is a tutorial on basic MATLAB functions by Aaron Yip.
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 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 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, as soon as possible. If the Disability Resource Center (DRC) has determined reasonable accommodations that you would like to utilize in this class, you must send your Course Accommodation Letter to the instructor. Instructions on sharing your Course Accommodation Letter can be found by visiting: https://www.purdue.edu/drc/students/course-accommodation-letter.php. Additionally, you are strongly encouraged to contact the instructor as soon as possible to discuss implementation of your accommodations.
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 quiz score 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. All work must be shown to receive full credit; answers alone are insufficient. 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 above) 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. Students should strive to complete homework assignments on time. However, no penalty will be assessed for assignments which are not excessively late (less than one week past due).
Grades. There will be 181 total points. Homework will be worth 10 points per assignment (100 points total). Quizzes will be worth 9 points each (81 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 final grade cut-offs may differ slightly.
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.
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, 1/13 Systems of Linear Equations (1.2), Gaussian Elimination (1.3)
Week 2, 1/20 MLK DAY 1/20, Gaussian Elimination (cont'd) (1.3), Vector Spaces and Matrices (1.1)
Week 3, 1/27 Rank and Row/Column Space (1.4), Linear Independence (2.1)
Week 4, 2/3 Linear Independence (cont'd) (2.1), Dimension (2.2)
Week 5, 2/10 Rank and Nullity (2.3), LEEWAY
Week 6, 2/17 Linear Transformations (3.1), Matrix Multiplication and Composition (3.2)
Week 7, 2/24 Inverses (3.3), Matrix of a Linear Transform (3.5)
Week 8, 3/3 LU Decomposition (3.4), Determinants (4.1)
Week 9, 3/10 PI DAY 3/14, Determinants (4.2), Markov Chains (5.1)
Week 10, 3/17 SPRING BREAK
Week 11, 3/24 Eigenvectors and Eigenvalues (5.1, 5.3)
Week 12, 3/31 Diagonalization (5.2), Scalar Products (6.1)
Week 13, 4/7 Gram-Schmidt (6.2), Fourier Series (6.3)
Week 14, 4/14 Orthogonal Matrices (6.4), Singular Value Decomposition (6.7)
Week 15, 4/21 Least Squares (6.5), Quadratic Forms (6.6)
Week 16, 4/28 LEEWAY or Selected Topics.
Week 1, 1/13 HW 1 Assigned.
Week 2, 1/20 HW 1 Due, HW 2 Assigned.
Week 3, 1/27 HW 2 Due, HW 3 Assigned.
Week 4, 2/3 HW 3 Due, HW 4 Assigned, Quiz 1.
Week 5, 2/10 HW 4 Due. HW5 Assigned, Quiz 2.
Week 6, 2/17 HW 5 Due. HW 6 Assigned. Quiz 3.
Week 7, 2/24 HW 6 Due. HW 7 Assigned. Quiz 4
Week 8, 3/3 HW 7 Due. HW8 Assigned. Quiz 5.
Week 9, 3/10 HW 8 Due.
Week 10, 3/17 Enjoy Spring Break!
Week 11, 3/24 HW 9 Assigned, Quiz 6.
Week 12, 3/31 HW 9 Due. HW 10 Assigned, Quiz 7.
Week 13, 4/7 HW 10 Due. HW 11 Assigned. Quiz 8.
Week 14, 4/14 HW 11 Due. HW 12 Assigned. Quiz 9.
Week 15, 4/21 HW 12 Due. Quiz 10.
Week 16, 4/28