Math 407 Sections A-B |
Winter 2018 |
LINEAR OPTIMIZATION
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Instructor: |
James Burke |
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E-Mail: |
jvburke(at)uw(dot)edu |
Phone: |
543-6183 |
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Office Hours: |
MW 1:00-1:50pm |
Office: |
C-443 Padelford |
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& by appointment |
Pre-Requisites: |
Math 308 |
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Classroom: |
SIG 225 |
TA: |
Abraham Engle |
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Office hr: |
Th. 3-5pm MSC |
E-Mail: |
aengle2(dot)uw(dot)edu |
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Hours: |
TBA |
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URL for the course website:
- http://www.math.washington.edu/~burke/crs/407/
Text:
Online course notes:
http://www.math.washington.edu/~burke/crs/407/notes/
Course Content:
Math 407 is an introductory course in linear optimization with a focus on linear
programming (or LP), quadratic optimization, and least-squares.
The four
basic components of the course are modeling, solution methodology, duality
theory, and sensitivity analysis. Modeling concerns the question of how
problems posed in the real world can be formulated in terms of the
mathematical framework called linear programming. Solution methodologies
concern practical techniques for computing the solution of an LP. We focus
on the simplex algorithm due to George Dantzig since it offers a complete
framework for discussing both the geometry and duality theory for linear
programs. Duality theory illustrates the rich underlying mathematical
structure of linear programming and its extensions. We will interpret the
duality theory in a number of ways. In particular, we show how it can be
used to explain pricing systems in market economies. Sensitivity
analysis concerns the behavior of the optimal solution subject to changes in
the initial data describing the problem.
The final topic in the course concerns the optimization of quadratic functions
with a focus on linear least-squares problems. Here we consider the great variety
of problems that can be modeled withing this framework. Our numerical investigations
focus on properties of symmetric
matrices and orthogonal projections.
Add codes:
For those students looking for an add code, there will be no overloads for Math 407
and the Math Dept does not keep a wait list for this class.
Come to class the first week and keep checking on-line enrollments.
The only way to get in to this class is to find an opening online.
Grading:
Quizzes:
There are 8 twenty minute quizzes each worth 80 points. The
quizzes are given each Friday except Friday
February and March 9.
The quizzes cover the homework of the previous week.
The potential content of
the quiz will be announced the Wednesday before the quiz. Each quiz will
contain two questions. The first question will either be to recite the
definition of a vocabulary word or to formulate a problem as an
LP. The second question will be computational in nature.
Your top 5 quiz scores
count toward your grade.
Midterms:
There is one midterm: Wednesday, February 7. The
content of the midterm will be discussed in advance and a sample midterm
will be distributed before the exam. The midterm is worth 250 points.
Final Exam:
The final exam for 407A&B is to be given on
Wednesday, March 14, 2:30-4:20pm.
Both final exams will be given in SIG 225.
The final exam is comprehensive. A sample final exam
will be distributed. The final exam is worth 350 points.
Final Grade:
The total number of possible points is 1000:
400 quiz points 250 midterm points 350 final
exam points 1000 points. |
Your final grade will be based on these points.
Note that the quiz grades count for 40% of your grade.
One class curve for all sections is computed
after the final exam has been scored.
Time Conflicts with an Exam:
There will be no make-up quizzes or exams except
in the case of a documented emergency (medical, family, University, ...),
or a documented unavoidable
conflict whose validity is pre-authorized by the instructor.
For unavoidable pre-approved conflicts, the instructor requires at least one week notice
prior to the exam or quiz
so that it can arrange for you to take the exam or quiz BEFORE the
actual exam date.
Incomplete:
A grade of Incomplete will be given only
if a student is doing satisfactory
work up until the end of the quarter,
and then misses the final exam due to
a documented medical or family emergency.
Important Dates:
Holidays:
Martin Luther King Day, January 19:
President's Day, February 19.
Midterm Date: Wednesday, February 7.
Final Exam: 407A&B:
Wednesday, March 14, 2:30-4:20pm.