Download procedures for proposing entries for the mit course bulletin

Department of Aeronautics and Astronautics
Section 3.
Graduate Subject Proposal Form
(The information provided below will be used to seek departmental and Institute
approval and advertise the subject.)
1. Effective Academic Year: (2003-2004)
2. Subject Number:
16.399
3. Subject Title: Random matrix theory and its applications in Engineering and Science
4. If subject is joint, SWE, meets with another course, list other #s:
6.976, 18.996
5. Equivalent Subjects: No precisely equivalent subjects are offered at MIT
6. Credit: _______ G-Level
__X__ G/H-Level*
7. Prerequisites:
18.06 – Linear Algebra
6.431 – Applied Probability
or permission of instructor
8. Unit distribution: _3_ Lecture
___Lab
Can units be arranged? ___ Yes
__9_ Preparation
_X_No
9. Grading: ___ P/F _X_ Letter (A-F) ___ Can Use J Grade _X_Can Repeat for Credit
10. Term(s) offered: __Fall
___IAP
_X__Spring
___Summer
11. If subject is not to be offered every year, what years?
___ 2003-04
___ 2004-2005
___2005-06
Provide a subject description as it will appear in the Catalogue.
This course provides a rigorous introduction to fundamentals of random matrix
theory motivated by engineering and scientific applications while emphasizing the
informed use of modern numerical analysis software. Topics include Matrix Jacobians,
Wishart Matrices, Wigner's Semi-Circular laws, Matrix beta ensembles, free probability
and applications to engineering, science, and numerical computing. Lectures will be
supplemented by reading materials and expert guest speakers, emphasizing the breadth of
applications that rely on random matrix theory and the current state of the art.
13. Participating Faculty (list the lead instructor first): Alan Edelman and Moe Z. Win
Rationale for offering this subject
Random matrices arise frequently in many aspects of scientific and engineering
applications. Examples include wireless communications such as multiple input
multiple output (MIMO) systmes, code division multiple access (CDMA) systems,
multiuser detection, array processing , unmmanned aerial vehicle (UAV)
communication using multiple antenna arrays, communication networks, graph
theory and statistics.
Although applications and analysis using random matrix methods have emerged over
the past decade or so, there is a gap between the mathematical theories and
understanding of it by engineers. This is primarily because the theory on random
matrices, developed almost concurrently by mathematicians, statisticians, and physicists
tends to be scattered and often inaccessible because of inconsistent notation.
By the end of the course, the students will be able to:
1)Derive the eigenvalue density for Wishart Matrices
2)Derive Wigner's semicircle law using combinatorial, free probability and resolvent
based approaches.
3)Use MATLAB to develop tests that assess whether a pair of random matrices is
asymptotically free
4)Use the Marcenko-Pastur theorem to determine the empirical distribution function
for some classes of random sample covariance matrices.
Besides the measurable learning objectives described above, the students will also
1)Understand the state of the art in the mathematics of finite random matrices
2)Understand the fundamental mathematics and intuition for the mathematics of
infinite random matrices including the tools of free probability
3)Recognize the manner in which these results have been applied so far and be
aware of the limitations of these techniques
4)Use numerical tools such as MATLAB to understand more difficult open questions
in random matrix theory.
15. Will the subject have a Final Exam?
__Yes
_____No __X___