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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 roundoff 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
webpage 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).
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