Attending
Jont Allen, Yuliy Baryshnikov, Subhonmesh Bose, Zuofu Cheng, Minh Do, Mark Hasegawa-Johnson, Erhan Kudeki, Steve Lumetta, Andrew Miller, Umberto Ravaioli, Chris Schmitz, Lara Waldrop
New Business
- Re-organization of Math 415: a meeting with Professor Philipp Hieronymi.
"When developing our linear algebra courses, it is crucial for us to know what engineering faculty think should be taught in our linear algebra courses. I have spoken with engineering faculty from various Departments, and I am currently working with CS and MechSE faculty on a project to revamp Math 415. I am very happy to report on this, but I am also very eager to hear from you and your colleagues what kind of linear algebra knowledge you expect (or want to expect) from your students."
Current Courses in Linear Algebra taught by the Math Department: there are perhaps 8, including:
- Math 225: a 2-hour sophomore-level service course for students who have not previously studied linear algebra. Taken, e.g., by students in ABE
- Math 286: a 3-hour course taken almost exclusively by ECE students, including 2 hours of diff Eq + 1 hour linear algebra
- Math 415: a 3-hour sophomore-level service course for students who have not previously studied linear algebra. This course has a 400-level course number only because it is taken by many graduate students, entering quantitative graduate research in departments that do not require linear algebra of their undergraduates. Despite its number, the Math Department considers this essentially a sophomore-level course, essentially at the same level as multivariate calculus (Math 241). Math 225 and Math 415 cover almost identical material, but Math 415 also covers (1) linear transformations, and (2) positive definite matrices. Math 415 is a 3-hour course, taught in the format of: 3 lecture hours/week + 1 discussion hour. The discussion hours are considered by the Math Department to be extremely effective, and it is their intention to include discussion sections in any new linear algebra course to be developed. Recently, Math 415 has grown dramatically; it is now typically 800 students per semester.
- Math 416: the first course in linear algebra for Math majors; differs from 415 in being more proof-oriented. Math majors take the same calculus sequence as engineers, then they take Math 347 (Intro to Proofs), and then they take 400-level courses in all other subjects, e.g., Diff Eq (Math 441), Linear Algebra (Math 416), Complex Variables (Math 448), and Real Analysis (Math 447). 200-level courses in these subjects are primarily service courses (e.g., Math 285/286).
Prof. Hieronymi is in the process of developing a 3-hour sophomore level linear algebra course. It will be taught as a 299 temporary course in spring 2020 (with about 30 James Scholar students taking it), and the intention is to scale it up to a larger course (probably called Math 247) by fall 2020. The key objectives of this course are
- To maintain the coverage of Math 415.
- Expanded group-based active learning component, as part of the weekly discussion section.
- To introduce a computational/lab-based component, teaching students to handle large-scale computations. In order to introduce the computational component, it is possible that the course format will consist of 2 hours of lecture, 1 hour of lab, and 1 hour of discussion. Material currently covered in 415 but not 225 (e.g., positive definite matrices, linear transformations, Gram-Schmidt orthogonalization, singular value decomposition) will be covered in Math 247, and this will be possible because many of these subjects are quite naturally taught by way of visualization and computational exercises.
At the close of discussion, the Curriculum Committee discussed three possible future directions for Linear Algebra for EE and CE students. (1) Linear Algebra might remain optional for CE students, who will take Math 247 only if they are interested in Data Science (~50% of CE students). (2) Math 247 might be added to the EE "3 of 5" list, as a restricted elective, or (3) Math 286 might be removed from the curriculum, and Math 247 required instead.