The University of Colorado

Boulder, Colorado

Mathematics 5150, Spring 2002

Note change in date of third hour exam.

This page pertains only to Professor Taylor's section of Mathematics 5150, for the spring semester of 2002. As far as I know, this is the only section occurring this semester. For other sections or other semesters, other details and regulations will no doubt apply.

An attempt will be made to keep this page up-to-date, but this is not guaranteed. Students are responsible for every assignment made in class, whether or not it ultimately appears on this page.

General Statement.

This will be a lively jaunt through linear algebra, as epitomized by the theory of matrices. (Usually with real coefficients. Sometimes complex coefficients help.) Linear algebra at this level is a wonderful expression of the interplay between the theoretical and the practical. I plan to present reasoning at an abstract level, coupled with very concrete facts about matrices.

Likely topics:

This is a graduate-level class in linear algebra. The textbook, and my presentation, both feature matrices as our primary tool. Nevertheless, the material is really impossible to understand without the broader (structuralist) view of vector spaces and linear maps. We will do proofs, and they will be on the exams.!


The main thing is to have had a previous course in linear algebra, however elementary. The following concepts should seem familiar and workable: vector spaces, linear independence, basis, dimension, linear maps (otherwise known as linear transformations, homomorphisms, etc), row reduction (or possibly column reduction) of a matrix. It is probably OK if your knowledge of these things is rusty, for they will be reviewed, but you should have some experience working with these concepts.


Matrix Analysis, by Roger A Horn and Charles R. Johnson, Paperback Edition. The CU Bookstore is currently asking a mere $34.95.

ISBN: 0-521-38632-2.

Our book has blue letters on the cover. There is another book by these authors, with a similar title, which has has red letters on the cover. Two years ago, one of the bookstores here got mixed up and was offering the one with red letters. Do not buy that one; it is not correct for this course.

You also need these Supplementary Notes (16 pages, 186,000 bytes), with which we will begin the semester. They are given here in pdf format. Almost all computers nowadays have the Acrobat Reader built in, so the notes should be easy to acquire. (Just click on the link; as the file downloads, Acrobat should come into play and display it for you. Then simply ask Acrobat to print the file.)


There will be three hour exams. The final counts as two hour exams. Homework counts as one exam. Class participation counts in this way: habitual failure to show up will count negatively.

Final Grades and comments on the final exam



Except in extreme extenuating circumstances, homework must be submitted at the start of class on the day it is due. Four points out of ten will be deducted for late submission.