This is an intermediate linear algebra course aimed at a diverse group of students, including sophomores in applied and computational mathematics, computer science, and information and data sciences, as well as graduate students in science and engineering. The main goal of the course is to provide an introduction to the fundamental ideas, concepts, and methods of applied linear algebra and illustrate them with important applications. Topics covered include linear systems, vector spaces and bases, fundamental matrix subspaces, inner products, norms, k-means algorithm, positive-definite and Gram matrices, application to text classification, least squares solutions and applications to data fitting, orthogonality, the QR factorization, eigenvalues and eigenvectors, the Gerschgorin theorem, the Perron-Frobenius theorem, the PageRank algorithm, the spectral theorem, optimization principles for eigenvalues, principal component analysis, spectral method for graph partitioning, and singular value decomposition with its applications.

• Ma 1 abc.
• Some familiarity with MATLAB, e.g. ACM 11, is desired.

Each lecture will be accompanied by two Practice Problems: a somewhat easier, more practical Problem A, and a more difficult, more conceptual Problem B. The main goal of the practice problems is threefold: to help you better understand the material covered in the corresponding lecture, to help you prepare to solve problems in problem sets and exams, and to accommodate the diversity of students’ math backgrounds by providing both easier and more challenging problems. These problems are for self-practice: they will not be graded, and the solutions (posted on Piazza) also illustrate the expected level of rigor for problem sets and exams.

Your final grade will be based on your total score. Your total score is a weighted average of Problem Sets (60%), Midterm exam (20%), and Final exam (20%). You can increase your total score by up to 5% if you participate actively in Piazza discussions in the Q&A section. Every answer submitted before TAs or instructor answer, which is later endorsed as a “good answer” by TAs or instructor, gets 1% of the total score. There are no fixed thresholds for grades, but if your total score is 90% (80%, 70%, 60%), then you are guaranteed at least “A” (“B”, “C”, “D”). If you are interested in being a TA next year, try to be active on Piazza and help other students by answering their questions.

There will be six Problem Sets. Problems (and solutions) will be posted on Piazza. For assignment and due dates see “Important Dates” below. Late submissions will not be accepted for any reason, but the Problem Set with the lowest score will be dropped and not counted toward your total score. Submitting wrong files or files in a wrong format is considered as a late submission. Extensions may be granted for academic, personal, or medical reasons. For extensions, please email the Head TA.