Math 20820: Honors Linear Algebra

Spring `08

Weekly schedule

Webpage for last semester

Instructor: Jeffrey Diller (click for contact info, general policies, etc.)

Official Time and place: MWF 8:30-9:20 AM, Hayes-Healy 229.

Textbook: We'll continue using Linear Algebra Done Wrong by Sergei Treil somewhat, but I'll be depending more heavily on other sources this term. When I talk about ODEs, I'll use Apostol's Calc books I and II (which I'll put on reserve), but also an online “minitext” by Bob Terrell at Cornell. When I discuss operators on inner product spaces, I'll probably follow Axler's book (on reserve) more than Treil's, though Treil certainly covers this topic. For other topics (e.g. canonical forms), I'm not quite sure yet.

As I did last term, I recommend looking at the following other linear algebra books that I've put on the reserve shelf in the math library:

Linear Algebra Done Right by Axler

Linear Algebra by Hoffman and Kunze

Linear Algebra and its Applications by Lax.

A Terse Introduction to Linear Algebra by Katznelson and Katznelson.

What we'll cover: My plan for this semester is to begin discussing operators and linear transformations on inner product spaces, including the spectral theorems for normal and self-adjoint operators and the singular value decomposition for more general linear transformations. Then I'll move on and talk about ordinary differential equations (henceforth 'ODEs') for several weeks. ODEs have some interesting connections with linear algebra, so they're not entirely out of place in this course. This should leave me with a little less than half the semester to spend. My current plan is to delve more deeply into the connection between polynomials and linear operators, getting to (among other things) the notion of Jordan canonical form. I can probably be talked into doing something else if you folks unify around some other linear algebra topic you're interested in (e.g. convexity, linear programming, graph theory, game theory, etc).

How you will be evaluated (nothing new here except the dates and times):

    Midterm Exam: Wednesday 3/18 at 7 PM in 129 HH, possibly with take home problems passed out in advance and due at exam time.