This is a Forum for exchange of ideas on the teaching of Linear Algebra on the Princeton Campus. You can participate by sending email to Harvey Lam, who will cut and paste your writings onto this web page. If you want to, you can write something and store you file in a `world readable' directory on your own computer, and send him the URL so that he can direct a link to it.
- Lam (4/1/99) The Engineering School requires Mat 201-202 or Mat 203-204 for engineering majors---in other words, Mat 202/204 will most likely to continue to be the required linear algebra course. The whole eigen stuff is, in my opinion, the heart of the matter, and I definitely include Jordon Form as required material (at least they should know what happens if the matrix is not diagonalizable). Since many students are likely to take MAT202 as their terminal linear algebra course, it is important for them to be aware of existence of `important' conceptual things. They should be made aware, at least, of major computational issues, the importance of the condition number, the existence (not the details) of the singular value decomposition and what it does for many practical problems.
- XiuXiong Chen (4/12/99) I was surprised how many of you are interested in "reforming" or "redesigning" of Linear algebar class and I am very happy about that. It will be nice if we can design a new class which are more closely related to the thing you wanted. For that reason, we need get a "wish list" from you---we might not be able to afford all of them, but we will try very hard to devlope a course as closed to your "wish list" as possible. The thing we mentioned last time during the lunch meeting, such as large sparse matrix, randomization, Jordon form, etc,, are all very nice topic. If each person can suggests a topic of interest in writing, and explain it roughly why it is important, and a list of reference books or papers which is readable to a mathematician, then that will be a great plus to me (to design a class which satisfies your needs).
- Bernard Chazelle (4/14/99) I am very happy with the way things are going in the matter of linear algebra teaching.
- Lam (4/1/99) I would like to see Mat 3XX to be numerical linear algebra oriented. The Penrose pseudo-inverse should always be a part of the material. It should be accessible to graduate students (unless enrollment can justify a separate graduate course).
- Sergio Verdu (4/14/99) Some of the kind of courses that would be nice to have here are
- MIT Numerical Methods of Applied Mathematics,
- Stanford Matrix Theory and Applications I,
- Stanford Matrix Theory and Applications II.
- Chris Floudas (4/21/99) Eigenvalues and their connection to stability, convexity, concavity nonconvexity, first and higher order saddle (transition) points; Singular Value Decomposition; Condition number; Error Analysis; Factorization methods (e.g., LU, QR, Cholesky, symmetric indefinite matrices); Least Square problems; Eigenvalue decomposition; Eigenvalue algorithms; Sparse systems of equations; Iterative methods (e.g., Lanczos, Arnoldi).
A course that will focus on NUMERICAL linear algebra will be very beneficial to the students. Also, the use of MATLAB will be very desirable.
- Lam (4/1/99) I would like CIT to offer, each semester, a one or two-week session on Matlab and/or Mathematica/Maple. It would be great if all faculty can safely assume that all science/engineering major are Matlab/Mathematica/Maple savvy. No, the instructors in the math/science/engineering courses should not teach how to use these packages. The instructors should take advantage of the assurance that all students in his/her class know how to work these packages.