Math 20810: Honors Linear Algebra

Fall `08

Weekly schedule

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

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

Textbook: Linear Algebra Done Wrong by Sergei Treil. The good news is that the book is free. The bad news is that it's available only online. There are lots of linear algebra textbooks to choose from, and none of them seems perfect to me. This one covers approximately the material I'd like to cover at approximately the level I'd like to work at, and the price is right. If you find what you think is a typo or have some particular idea for how the book might be improved, please bring it to my attention. One of the ways we can show our appreciation to Treil is to help him make his book better.

Nevertheless, I recommend looking at the following other books that I've put on the reserve shelf in the math library:

Linear Algebra Done Right by Axler

Linear Algebra with Applications by Bretscher

Linear Algebra by Hoffman and Kunze

Linear Algebra and its Applications by Lax.

A Terse Introduction to Linear Algebra by Katznelson and Katznelson.

Axler's book is particularly well-written and has a very appealing point of view, though it more or less assumes some previous exposure to linear algebra. Bretscher's book is one of the best books out there written for a `standard' sophomore course in linear algebra. Refer to it, especially when you need more examples or when our textbook seems too difficult. The last three books, listed in roughly increasing order of difficulty, are more comprehensive. Hoffman and Kunze would be a plausible candidate for a textbook for this course. The other two are a little too hard for a first time around, but they'd be fantastic to own once you're a little more comfortable with linear algebra. Lax has all sorts of cool extra topics in it and approaches the subject with the attitude of an analyst and an applied mathematician. Katnelson x 2 is more of a pure algebra take on the subject.

What we'll cover: My plan for this semester (tentative, as always) is to cover Chapters 1-5 this semester, and then cover some ordinary differential equations for a change of pace. I won't necessarily take the material in the order it appears in the book. For instance, I'd like to talk about inner products at least a little bit early on in the course. The broad topics to cover are vector spaces, linear transformations, determinants, eigenvectors and diagonalization, inner product spaces, and linear differential equations.

In the second semester, I plan to take on more sophisticated topics and applications—possibilities include vector spaces over fields other than the real and complex numbers, abstract constructions involving vector spaces, operators on inner product spaces, canonical forms, convexity. Etc. Suffice it to say, we won't run out of things to talk about.

How you will be evaluated:

    Midterm Exam: Tuesday 10/28, 8-10 PM in Hayes-Healy 117, with take home problems due at noon on Thursday 10/30. Worth 20% of your final grade.