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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___