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Master of Science
MSCotermOverview
The Bulletin outlines the university’s basic requirements for the master’s degree. The Master of Science (AA-MS) degree program in Aeronautics and Astronautics is intended for students whose ultimate goal is to pursue a professional career in Aeronautics and Astronautics, or a related field.
Students with an aeronautical engineering background should be able to complete the master’s degree in five quarters; note that many courses are not taught during the summer. Students with a bachelor’s degree in Physical Science, Mathematics, or other areas of Engineering may find it necessary to take specific prerequisite courses, which may lengthen the time required to obtain the master’s degree.
The M.S. program is a terminal degree program. It is based on completing lectures focused on a theme within Aeronautics and Astronautics engineering. Research is optional (required to take the qualifying examination).
Students who ultimately intend to complete a Ph.D. degree are encouraged to apply directly to the Ph.D. program. Applicants will be able to apply directly to the Ph.D. program whether they hold an M.S. degree or a bachelor’s degree.
Requirements
Program Requirements
Course Requirements
The master’s degree program requires 45 quarter units of coursework, which must be taken at Stanford. All units must be in courses at or above the 100 level.
Students must also meet the university’s quarterly academic requirements for graduate students as described in this Bulletin and in the Degree Completion section of the Guide to Graduate Studies in Aeronautics and Astronautics. All courses (excluding seminars) used to satisfy the requirements for basic courses, mathematics, and technical electives must be taken for a letter grade. Insufficient grade points on which to base the GPA may delay expected degree conferral or result in the refusal of permission to take the qualifying examinations.
The coursework is divided into five categories:
Core Breadth courses
Advanced A/A courses
Mathematics courses
Technical electives
Other electives
Core Breadth Courses
A/A Core Breadth Courses
Master’s degree candidates must select five courses from the categories as follows:
Fluids
Structures
Controls
Dynamics
Propulsion
Course Waivers
M.S. waiver requests are due by the end of the first week of classes (Autumn Quarter, year 1). Waivers of the basic courses required for the M.S. degree in Aeronautics and Astronautics can only be granted by the instructor of that course. Waivers are applicable only to core courses, which include: AA 210A, AA 200, AA 256, AA 240, Engr 205, AA 203, AA 242A, AA 279A, AA 204, AA 283. Students who believe that they have had a substantially equivalent graduate-level course at another institution should consult with the course instructor to determine if they are eligible for a waiver, and with their advisor to judge the effect on their overall program plans. Students will complete a google form to submit their requests, which will be due by the end of the first week of classes. Examination rooms will be reserved for the second week of the Autumn Quarter.
Students must take the final exam* for the course and achieve a grade of A- or higher. Instructors will forward their waiver approvals to the Student Services Office. One additional technical elective must be added for each M.S. course that is waived. The advisor must sign the front of the program proposal acknowledging the waiver and approving the additional technical elective. *Midterm exam may be used as a substitute if there is no final exam.
Note: This process is distinct from the petition process. Students can still submit petitions for substitutions on the AA-MS program sheet, which will be reviewed by the academic advisor and DGS.
A/A Core Breadth Courses
(II) Advanced A/A Courses - Three courses of A/A 200+ with 3 or more units each
These units cannot be counted twice towards the Core Breadth Courses.
AA 200
Applied Aerodynamics
AA 201A
Fundamentals of Acoustics
AA 201B
Topics in Aeroacoustics
AA 203
Optimal and Learning-based Control
AA 204
Spacecraft Electric Propulsion
AA 205
Rarefied and Ionized Gases
AA 210A
Fundamentals of Compressible Flow
AA 212
Advanced Feedback Control Design
AA 214
Numerical Methods for Compressible Flows
AA 216
Projection-Based Model Order Reduction
AA 219
Physics-informed AI/ML for Engineering
AA 222
Engineering Design Optimization
AA 228
Decision Making under Uncertainty
AA 228V
Validation of Safety Critical Systems
AA 229
Advanced Topics in Sequential Decision Making
AA 232
Planetary and Geological Optical Remote Sensing
AA 234
Planetary Geophysics: Theory, Observational Techniques and Data Analysis
AA 235
Experimental Earth and Planetary System Analysis
AA 240
Analysis of Structures
AA 240B
Analysis of Structures
AA 241A
Aircraft Design: Synthesis and Analysis
AA 241B
Aircraft Design: Synthesis and Analysis
AA 242A
Classical Dynamics
AA 242B
Mechanical Vibrations
AA 244A
Fundamentals of Plasmas I
AA 244B
Fundamentals of Plasmas II
AA 245
Stability of Structures
AA 251
Introduction to the Space Environment
AA 252
Techniques of Failure Analysis
AA 254
Deployable Space Structures
AA 255
Origami Engineering
AA 256
Mechanics of Composites
AA 257
Structural Health Monitoring
AA 260
Sustainable Aviation
AA 261
Building an Aerospace Startup from the Ground Up
AA 272
Global Positioning Systems
AA 273
State Estimation and Filtering for Robotic Perception
AA 274A
Principles of Robot Autonomy I
AA 274B
Principles of Robot Autonomy II
AA 275
Navigation for Autonomous Systems
AA 276
Principles of Safety-Critical Autonomy
AA 277
Multi-Robot Control and Distributed Optimization
AA 278
Lunar Positioning, Navigation, and Timing (PNT)
AA 279A
Space Mechanics
AA 279B
Advanced Space Mechanics
AA 279C
Spacecraft Attitude Determination and Control
AA 279D
Control of Distributed Space Systems
AA 280
Smart Structures
Mathematics Courses
M.S. candidates are expected to exhibit competence in applied mathematics by taking two courses, for a minimum of six units, of either advanced mathematics offered by the Mathematics Department or technical electives that strongly emphasize applied mathematics. Students are encouraged to consult their advisors to select the most suitable classes for their specific field, as other advanced courses may also be acceptable. Please refer to the list of pre-approved mathematics courses below. Additionally, 200+ level or higher lecture courses in MATH taken for 3 or more units will fulfill this requirement.
AA 201A
Fundamentals of Acoustics
AA 203
Optimal and Learning-based Control
AA 212
Advanced Feedback Control Design
AA 214
Numerical Methods for Compressible Flows
AA 216
Projection-Based Model Order Reduction
AA 222
Engineering Design Optimization
AA 228
Decision Making under Uncertainty
AA 242B
Mechanical Vibrations
AA 273
State Estimation and Filtering for Robotic Perception
AA 276
Principles of Safety-Critical Autonomy
AA 277
Multi-Robot Control and Distributed Optimization
CEE 201E
Nonlinear Dynamics
CEE 281
Mechanics and Finite Elements
CEE 284
Finite Element Methods in Structural Dynamics
CME 108
Introduction to Scientific Computing with Machine Learning Applications
CME 215
Machine Learning and the Physical Sciences
CME 216
Machine Learning for Computational Engineering.
CME 241
Foundations of Reinforcement Learning with Applications in Finance
CME 262
Imaging with Incomplete Information
CME 270
Advances in Computing with Uncertainties
CME 298
Probability and Stochastic Differential Equations for Applications
CME 302
Numerical Linear Algebra
CME 303
Partial Differential Equations of Applied Mathematics
CME 306
Computational Methods of Applied Mathematics
CME 308
Stochastic Methods in Engineering
CME 330
Applied Mathematics in the Chemical and Biological Sciences
CS 221
Artificial Intelligence: Principles and Techniques
CS 229M
Machine Learning Theory
CS 233
Geometric and Topological Data Analysis
CS 250
Algebraic Error Correcting Codes
CS 254
Computational Complexity
CS 261
Combinatorial Optimization
CS 264
Beyond Worst-Case Analysis
CS 265
Randomized Algorithms and Probabilistic Analysis
EE 261
The Fourier Transform and Its Applications
EE 263
Matrix Methods: Singular Value Decomposition
EE 264
Digital Signal Processing
EE 276
Information Theory
EE 278
Probability and Statistical Inference
EE 364A
Convex Optimization I
EE 364B
Convex Optimization II
ENGR 209A
Analysis and Control of Nonlinear Systems
MS&E 211
Introduction to Optimization
MS&E 220
Probabilistic Analysis
MS&E 221
Stochastic Modeling
MS&E 229
Bayesian Linear Regression
MS&E 232
Introduction to Game Theory
MS&E 233
Game Theory, Data Science and AI
MS&E 311
Optimization
MS&E 312
Optimization Algorithms
MATH 113
Linear Algebra and Matrix Theory
MATH 115
Functions of a Real Variable
MATH 120
Groups and Rings
MATH 171
Fundamental Concepts of Analysis
ME 300A
Linear Algebra with Application to Engineering Computations
ME 300B
Partial Differential Equations in Engineering
ME 300C
Introduction to Numerical Methods for Engineering
ME 335A
Finite Element Analysis
ME 338
Continuum Mechanics
ME 408
Spectral Methods in Computational Physics
ME 469
Computational Methods in Fluid Mechanics
PHYSICS 210
Advanced Mechanics
PHYSICS 212
Statistical Mechanics
STATS 110
Introduction to Statistics for Engineering and the Sciences
STATS 117
Introduction to Probability Theory
STATS 118
Probability Theory for Statistical Inference
STATS 200
Introduction to Theoretical Statistics
STATS 202
Statistical Learning and Data Science
STATS 203
Regression Models and Analysis of Variance
STATS 204
Sampling
STATS 205
Introduction to Nonparametric Statistics
STATS 206
Applied Multivariate Analysis
STATS 207
Time Series Analysis
STATS 208
Resampling Methods: Bootstrap, Cross Validation and Beyond
STATS 209
Introduction to Causal Inference
STATS 214
Machine Learning Theory
STATS 217
Introduction to Stochastic Processes I
STATS 218
Introduction to Stochastic Processes II
STATS 219
Stochastic Processes
STATS 232
Machine Learning for Sequence Modeling
STATS 263
Design of Experiments
STATS 270
Bayesian Statistics
STATS 271
Applied Bayesian Statistics
STATS 290
Computing for Data Science
STATS 292
Statistical Models of Text and Language
STATS 300A
Theory of Statistics I
STATS 300B
Theory of Statistics II
STATS 300C
Theory of Statistics III
STATS 305A
Applied Statistics I
STATS 305B
Applied Statistics II
STATS 305C
Applied Statistics III
STATS 311
Information Theory and Statistics
STATS 315A
Modern Applied Statistics: Learning
STATS 315B
Modern Applied Statistics: Learning II
STATS 317
Stochastic Processes
STATS 325
Multivariate Analysis and Random Matrices in Statistics
STATS 361
Causal Inference
STATS 362
Topic: Monte Carlo
STATS 369
Methods from Statistical Physics
Technical Electives
*Up to three seminar units can be counted toward the M.S. program and will be considered one technical elective. Seminar courses may be taken for a credit grade.
AA290 Option
AA 290
Problems in Aero/Astro
A maximum of six units of AA290 (or research/independent study in another department) may be counted toward the M.S. program*. These units can be used to satisfy the technical elective, free elective, and/or experimentation/design requirements. If these units are used to meet the experimentation/design requirement, a signature certifying the experimentation/design content is required.
*Students pursuing the M.S. with Distinction in Research (AA-MS DiR) may apply a maximum of 12 units to be counted toward the 45 units required for the AA-MS degree.
Other Electives
Experimentation and Design Requirements
M.S. candidates must complete a minimum of 3 units to fulfill the experimentation/design requirement, please refer to the list of pre-approved courses below. Students should consult their advisors to select the most appropriate classes for their field. Other advanced courses may also be acceptable. If a course is not on the pre-approved list, students may petition for approval.
AA 254
Deployable Space Structures
AA 256
Mechanics of Composites
AA 274A
Principles of Robot Autonomy I
AA 274B
Principles of Robot Autonomy II
AA 290
Problems in Aero/Astro
CS 225A
Experimental Robotics
EE 233
Analog Communications Design Laboratory
EE 251
High-Frequency Circuit Design Laboratory
EE 312
Integrated Circuit Fabrication Laboratory
ME 203
Design and Manufacturing
ME 210
Introduction to Mechatronics
ME 218A
Smart Product Design Fundamentals
ME 218B
Smart Product Design Applications
ME 218C
Smart Product Design Practice
ME 218D
Smart Product Design: Projects
ME 220
Introduction to Sensors
ME 324
Precision Engineering
ME 354
Experimental Methods in Fluid Mechanics
ME 367
Optical Diagnostics and Spectroscopy Laboratory
Master’s Degree with Distinction in Research (AA-MS DiR)
A student who wishes to pursue the M.S. in Aeronautics and Astronautics with distinction in research (AA-MS DiR) must first identify a faculty member who agrees to serve as the advisor, supervise the research work, and read the research report. The research advisor must be a member of the Academic Council, supervision by faculty outside of Aero/Astro is permitted. When the research advisor is from outside the Aero/Astro Department, the student must also identify a faculty co-advisor from within the department to provide guidance on departmental requirements and opportunities. The co-advisor must also approve the research report. The faculty commitment may be submitted after the completion of at least on quarter of AA 290 (3 units) and must be submitted prior to the quarter in which the student graduates. In addition, the student must complete the following requirements:
Research Experience
The program should include significant research designated by at least 9 units, and up to 12 units, of independent study (AA 290) over the course of at least 3 academic quarters. A maximum of 12 units may be counted toward the 45 units required for the AA-MS degree. These units may be used to satisfy the technical elective, free elective and/or the experimentation/design requirements of the AA-MS program. All AA 290 units must be completed for letter grades, with a minimum grade of B+ required in each AA 290 course to continue in the program.
Research Report
Students must complete a significant research report detailing their work and its conclusions. The research report represents work that could be publishable in a journal or at a high- quality conference with peer-reviewed proceedings. The student should engage in a discussion with the advisor(s) early in this AA-MS DiR program about the level of contribution and time commitment required to produce the research report. A copy of the research report, with a cover page signed by the advisor (and co-advisor if required) to confirm approval, must be submitted to the AA Student Services Office no later than three weeks before the last day of classes of the quarter in which the student graduates before the distinction-in-research designation can be conferred.
Certificate of Completion
Students who successfully complete the AA-MS DiR program will receive a department certificate of completion and will be listed in the Commencement Program. Please be aware that this will not be reflected on your official transcript or diploma.