Just to keep you in shape over the summer, here are a few extra sheets for your mathematical pleasure. Miklos wrote these sheets for his 2005-06 course, and I have edited them slightly. Sheet 22 introduces the complex numbers, arithmetic on the complex numbers, and some of their basic properties. Sheets 23 defines abstract topological and metric spaces. Sheet 24 focuses on the important example of R^n as a metric space. (This is the only one of the sheets that is not self-contained, since it relies on Sheet 23.) For those of you who are interested in getting a flavor for algebra and number theory, Sheet 25 recalls the definition of the integers mod n and introduces some of the main theorems of modular arithmetic.
Material:
Further Reading:
If you're interested in doing some reading, rather than working on sheets, consider the following list of recommendations from Ed and myself. This reading list will extend your understanding of linear algebra and geometric linear algebra, since there are many more topics than we had time to cover this spring. All four texts cover much of the same material, so pick your favorite.
Link to Fall 2006 course materials.
Link to Winter 2007 course materials.
Link to Spring 2007 course materials.