Association of

Aeronautics &




IM Sports




Doctoral Qualifying Exam


Topical List for Basic Material on the Professional Area Questions from the Doctoral Qualifying Examination.

Please note that the list is only to be used as an orientation and is by no means exhaustive.


Based on 16.410 Principles of Autonomy and Decision Making

Learning Objectives:

  1. Model decision making problems using major modeling formalisms of
  2. artificial intelligence and operations research, including propositional logic, constraints, linear programs and Markov processes
  3. Evaluate the computational performance of search, satisfaction, optimization and learning algorithms.
  4. Apply search, satisfaction, optimization and learning algorithms to real world problems.

Upon successful completion of 16.410, students will be able to:

  1. Describe at an intuitive level the process of artificial intelligence and operations research: a real-time cycle of problem understanding, formulation, solution and implementation.
  2. Formulate simple reasoning, learning and optimization problems, in terms of the representations and methods presented
  3. Manipulate the basic mathematical structures underlying these methods, such as system state, search trees, plan spaces, model theory, propositional logic, constraint systems, Markov decision processes, decision trees, function approximators, linear programs and integer programs
  4. Demonstrate the hand execution of basic reasoning and optimization algorithms on simple problems
  5. Formulate more complex, but still relatively simple problems, and apply implementations of selected algorithms to solve these problems
  6. Evaluate analytically the limitations of these algorithms, and assess tradeoffs between these algorithms


Search and Reasoning: uninformed and informed search, game tree search, local

stochastic search and genetic algorithms, constraint satisfaction, propositional inference,

rule-based systems, planning, and model-based diagnosis.

Optimization: Linear programming, integer programming, Markov Decision Processes

Communication and Networks.

This is one of the newest sections of the exam, appearing for the first time in 2002. The material for the exam is drawn mostly from the class Communications Systems Engineering (16.36) whose prerequisites include Unified Engineering I (16.010), Signals and Systems (6.003), and Probabilistic Systems Analysis (6.041). 16.36 tends to overlap to some extent with Data Communication Networks (6.263/16.37J) and Principles of Digital Communication I (6.450), and so it has been suggested that students wanting a stronger background in this subject consider those courses as well.

The text for 16.36 in the Spring of 2003 was Communications Systems Engineering, Proakis and Salehi, and the homeworks were almost entirely drawn from there. The qualifying exam question is generally considered reasonable by those who have taken 16.36, but is not a question that can easily be done without this background or a similar knowledge of the language and notation of information theory.

Topics that might be covered by the exam include, but are not limited to:

  • Basics of information theory: Entropy of a random variable, Mutual information
  • Sampling and quantization: Sampling theorem, Fourier Transforms, signal detection, quantizer design and optimal quantizers,
  • Coding: Average codeword length, Kraft Inequality, Huffman codes, Lempel-Ziv, Channel Coding Theorem and decoding
  • Modulation: Bandwidth efficiency, power and energy, PAM and QAM
  • System performance in the presence of noise: white noise, filters, AWGN, error detection
  • Data networking: multiple access, reliable packet transmission, routing and protocols of the Internet


Based on 16.060

  • Introduction to design of feedback control systems
  • Properties and advantages of feedback systems
  • Time-domain and frequency-domain performance measures
  • Stability and degree of stability
  • Root locus method
  • Nyquist criterion
  • Frequency-domain design
  • State space methods

More detailed information is available at the class website:

Fluid Mechanics

Based on excerpts from MIT subjects: 2.25

  1. Continuum Viewpoint and the Equation of Motion
  2. Static Fluids
  3. Mass Conservation
  4. Inviscid Flow - Differential Approach: Euler's Equation, Bernoulli's Integral and the Effects of Streamline Curvature, the General Form of Bernoulli's Integral
  5. Vector fields and differential operators.
  6. Control Volume Theorems (Integral Approach): Linear Momentum Theorem, Angular Momentum Theorem, and First and Second Laws of Thermodynamics
  7. Navier-Stokes Equation and Viscous Flow
  8. Similarity and Dimensional Analysis
  9. Boundary Layers, Separation and the Effect on Drag and Lift
  10. Vorticity and Circulation
  11. Compressible flow
  12. Potential Flows: Lift, Drag, and Thrust Production
  13. Surface Tension and its effect on Flows
  14. Introduction to Turbulence

Familiarity with and the ability to use:

  • Inviscid Flow
    • Euler's Equation
    • Bernoulii's Equation
    • Compressible flow
    • Momentum Equation
    • Control Volumes
  • Viscous Flow
    • Navier-Stokes equations
    • Boundary Layer Theory
    • Momentum Equation
    • Control Volumes
    • Dimensional Analysis
    • Potential flows
    • Compressible flow
    • Turbulent flows

Human Factors Engineering

This written and oral question is traditionally based off the materials presented in the Human Factors course offered in the Aero/Astro department -- 6.400/16.453. After taking this course, you should feel fairly comfortable with most of the material. Listed below are the subject matters that are covered currently. This is not a complete list, but a taste of what is included in the course syllabus. It appears (from past exams) that the aero side and the Astro side take turns writing the human factors engineering question. But, of course, this is not guaranteed. Hence, always be prepared, or review, to see a question about airplane cockpits. Become

familiar with the words used and current displays and issues. It also might be

worthwhile becoming aware of current human factor related topics going on --

professors like to draw upon these. For example, a few years ago, when the cell phone boom was happening, the oral question was "Design an experiment that would test/explore the effect of cell phone use when driving." A current topic (in 2003) is UAVs -- unmanned aircraft vehicles. It would not be surprising if a question related to this came up!

It is very important to know how to design an experiment. There are many variations

to this question but knowing and applying key concepts of experiment design seems to always come up in the examination. For example, what would be the control group?

The independent and dependent variables? The methods of analysis? How would you balance the groups?

Topics (based from 16.400 Syllabus (Fall 2003) and textbooks):

  • situational awareness
  • workload and attention
  • primary and secondary tasks
  • task analysis
  • performance
  • memory and mental resources
  • spatial disorientation
  • controls (i.e. controllers)
  • some basic controls (e.g. feedback, disturbances)
  • visual displays (this includes different types of displays, advantages, disadvantages, head-up vs. head-mounted displays, layout, etc).
  • statistics
  • experimental design
  • decision making warnings -- alert systems
  • manual control
  • training schedules
  • some anthropometry
  • space human factors
  • circadian rhythms
  • cockpit management
  • basic understanding of visual sensory, auditory, tactile and vestibular systems (as to how they affect human factor engineering)

Among other topics of interest would be:

  • What are the issues with humans using automation? What about automation reliability? Trust vs. complacency? How does it affect workload, for example?
  • Human in the loop for control systems -- how does it affect the system? How does one go about modeling that?
  • Safety engineering -- how does human factors play a role in this? (though this could be considered a bit more about Software Engineering -- it would not hurt to know something about it).

Books used in the past for teaching Human Factors:

Wickens, C. D. and J. G. Hollands Engineering Psychology and Human Performance

Wickens, C. D., S. E. Gordon, and Y. Liu An Introduction to Human Factors


Propulsion and Thermodynamics

Based in 16.050 and in the Thermodynamics classes from Unified Engineering.

A rough idea of what the topics can be obtained from the following list:

Energy exchange in propulsion and power processes; the second law of thermodynamics; reversible and irreversible processes; quantification of irreversibility and connection to lost work; application of the first and second laws to engineering systems (propulsion cycles, gas and vapor power cycles, reacting flows); rates of energy transfer and heat exchange in aerospace devices. Rocket propulsion.

More detailed information about what may be expected from someone taking this part of the exam may be found on the class website:


  1. Thermal Energy (16.050) Class Notes - Fall 2002.
  2. Understanding Thermodynamics, by Van Ness, H. C., Dover Press Publishers

Other Reference Material

  1. Thermodynamics Notes for Unified Engineering, compiled by Professor Waitz
  2. Fundamentals of Thermodynamics, Sonntag, R. E., Borgnakke, C, and Van Wylen, G. J., John Wiley Publishers, 1998

Software Engineering

Based on 16.35 (Real-Time Systems and Software).

Covers: Concepts, principles, and methods for specifying and designing real-time computer systems. Topics include operating system architecture, process management, concurrency, networking, scheduling,execution time analysis, real-time features of operating systems and software engineering concepts. Current issues in software engineering; process and life-cycle models; requirements and specification; design; testing, analysis, quality assurance and reviews; metrics and reliability assessment; COTS and reuse; formal verification; team organization and people management; software engineering aspects of programming languages; software safety.

Structures and Materials

Based in topics from Unified and 16.20.

  • free body diagrams
  • tensor notation
  • the concepts of stress and strain
  • basic equations of elasticity: equilibrium, stress-strain, strain-displacement orthotropic constitutive relations
  • transformation of stress and strain
  • beam theory
  • basic concepts of structural instability
  • (basics of) structural failure analysis
  • design considerations for aerospace structures
  • anisotropic constitutive relations and engineering constants
  • environmental stresses and strains
  • alternate coordinate systems
  • stress potentials

Additional information may be found in the following website:

Vehicle Design and Performance

This question often offers a choice between an spacecraft system and an aeronautical one. The topics will be discussed separately.

Vehicle Design and Performance (spacecraft system)

Initial caveat: The VD&P subject area is a new addition to the quals replacing (or rather refining) the Systems area that existed before 2002. My estimates of the expected requirements for this area are therefore weighted heavily towards the previous two years' tests. The key difference seems to be the introduction of quantitative analysis to the problems.

  • Required knowledge
    • Basic familiarity with traditional space missions
      • Satellites (telecommunication, interplanetary, etc.)
      • Payloads (rovers, landers, orbiters, etc.)
    • System-level design
      • Requirements analysis
      • Functional decompositions and subsystem mappings
      • Block diagrams
      • Tradespace analysis and exploration
      • Optimization
    • Subsystem performance
      • Power, communications, attitude control, propulsion, thermal control, structures and mechanisms, trajectory analysis, etc.
    • Costing
      • Basic understanding of cost modeling
      • Cost-estimation relationships
  • Recommended courses
    • 16.83/16.89 Space Systems Engineering
    • 16.851 Satellite Engineering
    • 16.882 System Architecture
  • Recommended reading
    • Wertz&Larson, Spacecraft Mission Analysis and Design

Vehicle Design And performance (aero-part)

Familiarity with range equation

Ability to analyze aircraft performace (first order calculations)

Familiarity with aircraft systems and tradeoffs made during design

Websites of classes of interest:


Aircraft Design: A Conceptual Approach, Daniel Raymer



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