# 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).

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