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|
| Recommended
Program: Optimization |
|
Jim Burke, Terry Rockafellar,
and Paul Tseng
| First Year |
| 554 |
555 |
556 |
(Linear Analysis) |
| 524 |
525 |
526 |
(Real Analysis) |
| 514 |
|
|
(Networks and Combinatorial Optimization) |
| |
515 |
|
(Fundamentals of Optimization) |
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and one of the following:
|
| |
|
516 |
(Numerical Optimization) |
| |
|
509* |
(Theory of Optimal Control) |
| |
|
517* |
(Optimization Under Uncertainty) |
| Second Year: |
|
One of the following two sequences:
|
| 534 |
535 |
536 |
(Complex Analysis) |
| 544 |
545 |
546 |
(Topology and Geometry of Manifolds) |
|
and a selection from the following
sequences:
|
| |
AMath 507 |
|
(Calculus of Variations I) |
| |
|
516 |
(Numerical Optimization) |
| |
|
509* |
(Theory of Optimal Control) |
| |
|
517* |
(Optimization Under Uncertainty) |
| AMath 584 |
|
|
(Applied Linear Algebra) |
| |
AMath 585 |
AMath 586 |
(Approximate and Numerical Analysis) |
| Stat 512 |
Stat 513 |
|
(Statistical Inference) |
| 527 |
528 |
529 |
(Functional Analysis) |
| 557 |
558 |
559 |
(Introduction to Partial Differential
Equations) |
*Math 509 and
517 are offered in alternate years, so be sure to check the schedule before
planning your program.
COMPUTER PROGRAMMING:
Students studying optimization should
have reasonable programming skills. In particular, PhD students are strongly
recommended to pass the computer programming
exam.
NOTES:
- This two year program is only a suggestion.
Of the three first-year sequences that must be completed by the beginning
of the third year in preparation for the preliminary examinations, only
the Linear Analysis sequence 554/5/6 is required of all optimization students.
The optimization courses (514-517, 509, and AMath 507) should be completed
by the end of the third year. Thus, in particular, it is not critical that
the 514/5/6 sequence be taken in the first year.
- If students consider their undergraduate
preparation in optimization to be deficient, they might consider taking
some of the undergraduate sequence in optimization (407/8/9) in their first
year.
- If a student wishes to pursue studies in
discrete optimization, then the 524/5/6 analysis sequence might be replaced
by the 504/5/6 algebra sequence in the first year. Further advice on course
selection for studies in discrete optimization should be obtained from a
prospective advisor.
- General deficiencies in undergraduate preparation
can to some extent be ameliorated by working through one or more of the
Schaum's outlines in real variables, complex variables, linear algebra,
and abstract algebra.
- Students planning to obtain a PhD in optimization
are strongly advised to take some of their courses outside the Math Department
and to develop an application area, such as scientific computing, statistics,
applied control (in electrical engineering), etc., to obtain a better sense
of how optimization is viewed from the perspective of applications.
RESEARCH INTERESTS:
For information about the research
interests of the optimization faculty, check out their home pages:
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