STANFORD UNIVERSITY

INSTITUTE FOR COMPUTATIONAL AND MATHEMATICAL ENGINEERING

Master of Science

The M.S. program in Computational and Mathematical Engineering is very unique. In today's world of virtual research, "mathematical modeling" will be the key word. iCME leverages a deep background in mathematical modeling with exceptional breadth in traditional science and engineering fields. It is also an excellent preparation for future entry into a Ph.D. program at Stanford or elsewhere. Individual programs can be customized to enhance any area of physical sciences or traditional engineering fields.

The M.S. degree in Computational and Mathematical Engineering may be a terminal degree or a stepping stone to the Ph. D. program. Master's students who have maintained a minimum grade point average (GPA) of 3.5 are eligible to take the Ph.D. qualifying exam; those who pass this examination may transfers to the Ph.D. program after the first academic year and will be considered a second year Ph.D. student.

The master's program consists of 45 units of course work taken at Stanford, which usually takes between 4 and 6 quarters to complete. The core course requirements are identical to those for the Ph.D. program. No thesis is required; however, students may become involved in research projects during the master's program, particularly to explore an interest in continuing to the doctoral program. Although there is no specific background requirement, significant exposure to mathematics and engineering course work is necessary for successful completion of the program.

Requirements

A candidate is required to complete a program of 45 units of courses numbered 200 or above. At least, 36 of these must be graded units, passed with a grade point average (GPA) of 3.0 (B) or better. Master's students interested in continuing to the doctoral program must maintain a 3.5 or better grade point average in the program.

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Requirement 1

The following courses may be needed as prerequisites for other courses in the program: MATH 41, 42, 51, 52, 53, 103, 113, 130, 220A; CS 106A, 106X, 108, 205, 229, 237B; ENGR 62; ME 346, 355A, 355B; MS&E 211, 310, 311, 312, 314, 315; STATS 116 or 202.

Computational and Mathematical Engineering
Number Title Instructor Quarter Units Notes
CME 100 Vector Calculus for Engineers Eric Darve Autumn 5 GER:DB-Math
CME 102 Ordinary Differential Equations for Engineers Eric Darve Winter 5 GER:DB-Math
CME 104 Linear Algebra and Partial Differential Equations for Engineers Vadim Khayms Spring 5 GER:DB-Math
CME 106 Introduction to Probability and Statistics for Engineers Vadim Khayms Winter 3 - 4 GER:DB-Math
CME 108 Introduction to Scientific Computing James Lambers Winter 3 - 4 GER:DB-EngrAppSci
CME 200 Linear Algebra with Application to Engineering Computations Parviz Moin Autumn 3  

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Requirement 2

Students must demonstrate breadth of knowledge in the field by completing the following six core courses:

Computational and Mathematical Engineering
Number Title Instructor Quarter Units Notes
CME 302 Numerical Linear Algebra Gene Golub Autumn 3  
CME 303 Partial Differential Equations of Applied Mathematics James Nolen Autumn 3  
CME 304 Numerical Optimization Walter Murray Winter 3  
CME 305 Discrete Mathematics and Algorithms Amin Saberi Winter 3  
CME 306 Numerical Solution of Partial Differential Equations Ron Fedkiw Spring 3  
CME 308 Stochastic Methods in Engineering Peter Glynn Spring 3  

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Deviations from the core curriculum must be justified in writing and approved by the student's iCME adviser and the chair of the iCME curriculum committee. Courses that are waived may not be counted towards the master's degree.

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Requirement 3

12 units of electives in the eight application areas listed below must be completed. The elective course list represents automatically accepted electives within the program and the list is expanded on a continuing basis; the elective part of the iCME program is meant to be broad and inclusive of relevant courses of comparable rigor to iCME courses. Courses outside this list can be accepted as electives subject to approval of the student's iCME adviser and the chair of the iCME curriculum committee.

Aeronautics and Astronautics
Number Title Instructor Quarter Units Notes
AA 214A Numerical Methods in Fluid Mechanics Tom Pulliam Autumn 3  
AA 214B Numerical Computation of Compressible Flow Robert MacCormack Winter 3  
AA 214C Numerical Computation of Viscous Flow Robert MacCormack Spring 3  
AA 215B Advanced Computational Fluid Dynamics Anthony Jameson Spring 3  
AA 218 Introduction to Symmetry Analysis Brian Cantwell Spring 3  

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Civil and Environmental Engineering
Number Title Instructor Quarter Units Notes
CEE 281 Finite Element Structural Analysis Staff Spring 3 - 4  

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Computational and Mathematical Engineering
Number Title Instructor Quarter Units Notes
CME 204 Partial Differential Equations in Engineering Eric Shaqfeh Winter 3  
CME 208 Mathematical Programming and Combinatorial Optimization Amin Saberi Winter 3  
CME 210 Multiscale Methods in Engineering Eric Darve   3  
CME 212 Introduction to Large-Scale Computing in Engineering James Lambers Winter 3  
CME 215A Advanced Computational Fluid Dynamics Anthony Jameson Winter 3  
CME 300 Departmental Seminar Series Walter Murray Winter 1 Will meet in Durand 450 on 1/11/2008 and in Terman 453 for the rest of the quarter from 4:00-5:00pm.
CME 324 Advanced Methods in Matrix Computation: Iterative Methods Gene Golub   3 Not given this year
CME 325 Numerical Approximations of Partial Differential Equations in Theory and Practice Staff Winter 1 - 2 Abbreviated meeting pattern: from January 31 to March 8 only. Please be aware that even though the course is starting late, the normal add/drop deadlines will apply.
CME 326 Numerical Methods for Initial Boundary Value Problems Staff Winter 3 Not given this year
CME 330 Applied Mathematics in the Chemical and Biological Sciences Eric Shaqfeh Autumn 3  
CME 332 Computational Methods for Scientific Reasoning and Discovery Pat Langley   3 Not given this year
CME 334 Advanced Methods in Numerical Optimization Walter Murray Autumn 3  
CME 336 Linear and Conic Optimization with Applications Yinyu Ye Autumn 3 Not given this year
CME 337 Information Networks Amin Saberi Autumn 3 Not given this year
CME 338 Large-Scale Numerical Optimization Michael Saunders Spring 3  
CME 340 Computational Methods in Data Mining Sep Kamvar Winter 1 - 3  
CME 342 Parallel Methods in Numerical Analysis Staff Spring 3  
CME 346A Introduction to Molecular Simulations Eric Darve Spring 3  
CME 352 Molecular Algorithms Ashish Goel Winter 3  
CME 380 Constructing Scientific Simulation Codes Patrick Miller Spring 3 This class is web based; it will use podcasts and Skype videocasts to deliver the material. See http://wilkinson.stanford.edu/cme380
CME 444 Computational Consulting Margot Gerritsen Spring 7  
CME 500 Numerical Analysis and Computational and Mathematical Engineering Seminar Amin Saberi Spring 1  
CME 510 Linear Algebra and Optimization Seminar Michael Saunders Spring 1  

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Computer Science
Number Title Instructor Quarter Units Notes
CS 205 Mathematical Methods for Robotics, Vision, and Graphics Ron Fedkiw Autumn 3  
CS 221 Artificial Intelligence: Principles and Techniques Andrew Ng Autumn 3 - 4  
CS 228 Probabilistic Models in Artificial Intelligence Daphne Koller Winter 3  
CS 229 Machine Learning Andrew Ng Autumn 3  
CS 255 Introduction to Cryptography Dan Boneh Winter 3  
CS 261 Optimization and Algorithmic Paradigms Serge Plotkin Winter 3  
CS 315A Parallel Computer Architecture and Programming Kunle Olukotun Winter 3  
CS 348A Computer Graphics: Geometric Modeling Leo Guibas Autumn 3  
CS 365 Randomized Algorithms Rajeev Motwani Autumn 3  

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Electrical Engineering
Number Title Instructor Quarter Units Notes
EE 222 Applied Quantum Mechanics I Staff Autumn 3  
EE 223 Applied Quantum Mechanics II David Miller Winter 3  
EE 262 Two-Dimensional Imaging Staff   3 Not given this year
EE 278 Introduction to Statistical Signal Processing Abbas El Gamal Spring 3  
EE 292E Analysis and Control of Markov Chains Staff   3 Not given this year
EE 363 Linear Dynamic Systems Staff   3 Not given this year
EE 364 Convex Optimization Stephen Boyd   3 Not given this year
EE 376A Information Theory Tsachy Weissman Winter 3  

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Engineer
Number Title Instructor Quarter Units Notes
ENGR 209A Analysis and Control of Nonlinear Systems Stephen Rock Winter 3  

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Management Science and Engineering
Number Title Instructor Quarter Units Notes
MS&E 220 Probabilistic Analysis Sam Chiu Autumn 3 - 4  
MS&E 221 Stochastic Modeling Ramesh Johari Winter 3  
MS&E 223 Simulation Peter Haas Spring 3  
MS&E 251 Stochastic Decision Models Staff Winter 3  
MS&E 310 Linear Programming Yinyu Ye Autumn 3  
MS&E 313 Vector Space Optimization David Luenberger Autumn 3  
MS&E 316 Stochastic Systems Peter Glynn Spring 3  
MS&E 323 Stochastic Simulation Peter Glynn   3 Not given this year

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Mathematics
Number Title Instructor Quarter Units Notes
MATH 220B Partial Differential Equations of Applied Mathematics Tai-Ping Liu Winter 3  

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Mechanical Engineering
Number Title Instructor Quarter Units Notes
ME 335A Finite Element Analysis Peter Pinsky Winter 3  
ME 335B Finite Element Analysis Peter Pinsky Spring 3  
ME 335C Finite Element Analysis Peter Pinsky   3 Not given this year
ME 469A Computational Methods in Fluid Mechanics Staff Winter 3  
ME 469B Computational Methods in Fluid Mechanics Staff Spring 3  
ME 484 Computational Methods in Cardiovascular Bioengineering Charles Taylor Spring 3  

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Statistics
Number Title Instructor Quarter Units Notes
STATS 227 Statistical Computing Staff   3 Not given this year
STATS 237 Time Series Modeling and Forecasting Staff Summer 3  
STATS 250 Mathematical Finance George Papanicolaou Winter 3  
STATS 345 Computational Molecular Biology Wing Wong Autumn 2 - 3  

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Requirement 4

9 units of focused graduate application electives, approved by iCME graduate adviser, in the areas of Engineering, Mathematics, and Physical, Biological, and other quantitative sciences.

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Requirement 5

3 units of iCME Colloquium (CME 500) or other approved seminar sequence.

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