Linear Algebra with Applications

Homework: There will be a weekly homework, due on Wednesdays.

Exams and grading: There will be two midterms in addition to the final. The final is
worth 50% of the grade, the midterms are worth 20% each and the remaining 10% can be
earned by handing in homeworks. The final is scheduled for Dec 17 at 2pm.

Syllabus: The course will cover the basic topics of linear algebra, as outlined below. There
will be a significant emphasis on practical applications. At this point, requests from students
to discuss particular topics (e.g. biology, electrical engineering, economics, web searching,
. . . ) are welcome. Furthermore, we will touch briefly upon computational issues relating
to very large systems of equations . (Some methods that make perfect sense from an exact
mathematical point of view turn out to be less suitable in an environment where noisy data
and round-off errors are present .)

Whichever applications we choose to include, the following topics form the core syllabus:

 • Systems of linear equations : sections 1.1, 1.2, 1.3, 1.4, 1.5, 1.7, 1.8, 1.9.
 • Matrix algebra : sections 2.1, 2.2, 2.3, 2.5.
 • Vector spaces: sections 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7.
 • Eigenvectors and eigenvalues: sections 5.1, 5.2, 5.3, 5.4.
 • The singular value decomposition , determinants: class notes.
 • Orthogonality and least squares : sections 6.1, 6.2, 6.3, 6.4, 6.5.
 • Symmetric matrices and quadratic forms : sections 7.1, 7.2.

Note that this is a tentative syllabus; some application areas will be added . A detailed
syllabus specifying what is covered in each of the three exams will be found on the course
web-page in due time.

A remark: You have probably heard this said many times before, but please keep in mind
that for most of us, learning mathematics is a matter of doing mathematics rather than
reading. So try to work as many of the examples as you can stomach (more than just the
homeworks if at all possible).