This document begins by describing SEAS-wide course requirements for the Ph.D. degree. Following that is a description of area-specific course requirements, guidelines, and model programs that are intended to help students develop programs with sound intellectual frameworks.

These programs form a starting point for a discussion with the faculty about areas of interest. Students should work in close consultation with their advisers to develop an appropriate program of study. Courses provide the background knowledge that is often needed to successfully complete research and allow students to learn more broadly about a field or related fields in a structured fashion.

Courses are not meant as, and should not be seen as, an impediment to research, but as a means of enhancing one’s research ability and as part of the process of becoming a mature, well-rounded member of one’s field. We emphasize that the 10-course requirement is considered a minimum, and not a goal; students are encouraged to take additional courses whenever appropriate. Depending on each student's background, it may be necessary to take additional coursework in order to complete the 10 courses on the program of study.

The SEAS Committee on Higher Degrees (CHD) approves each graduate student’s plan of study (and any revisions to it), and monitors progress towards attainment of the degree. It is the student’s obligation to keep the CHD apprised of any departures from an approved course selection plan in timely fashion, as described below.

The course requirements discussed hereafter are phrased in terms of graduate-level half-courses taken at SEAS (200-level courses in SEAS nomenclature), in other departments of the Faculty of Arts and Sciences (FAS), or by cross-registration at other Harvard Faculties or at the Massachusetts Institute of Technology (MIT). Certain restrictions apply to courses taken by cross-registration.

As a general rule, students are expected to take SEAS courses, unless their program requires courses not offered by SEAS. Ordinarily, at least half of the courses taken to satisfy SEAS degree requirements must be drawn from those offered at SEAS. A course offered by a SEAS faculty member in another department of FAS is considered as being offered by SEAS for the purposes of this requirement. Provision is made for a limited number of upper-level undergraduate courses in FAS (100-level courses) to be counted towards a graduate degree.

SEAS Course Requirements

Ten half-courses. Of the 10 courses:

• At least eight courses will normally be disciplinary courses—i.e., courses that provide the scientific, mathematical, and technical depth that students need for our graduate programs in engineering and applied science.
• Up to two courses can normally be “298r” or “299r” courses, “Innovation”-style courses that broaden a student's perspective, suitable 100-level courses, or relevant courses at a suitable level in non-science departments (e.g. economics) or schools (Kennedy School, Business School).

Area Course Requirements, Guidelines, and Model Programs

• Applied Mathematics
• Applied Physics
• Photonics
  
• Nanoscale Electronic Devices
  
• Nanoscale Structures
• Biological and Soft Matter Physics
  
• Materials Science
• Computer Science
• Engineering Sciences
• Environmental Sciences and Engineering (AOSCE)
  
• Bioengineering
• Electrical Engineering
• Applied Mechanics

Applied Mathematics

All students pursuing a Ph.D. in Applied Mathematics should consult with Professor Michael Brenner concerning their degree programs.

Applied Physics

The Applied Physics Ph.D. program comprises four areas of research: Photonics, Nanoscale Electronic Devices, Nanoscale Structures, and Biological and Soft Matter Physics. The model programs for each of these areas consists of a number of core courses (defining the area), fundamental courses (basic physics knowledge required), and elective courses.

A total of 10 courses are required to fulfill the course requirements for a Ph.D. in Applied Physics. Only two courses below the 200 level may be included. Students who need additional 100-level courses may take more than 10 courses. For students whose thesis research does not involve any experimental work, at least one course must involve performing experiments (e.g., an experimental 299r).

Please note that these programs serve as models only. The final program final curriculum should be determined in consultation with your advisor.

Photonics

Photonics is a broad and diverse field at the crossroads of Electrical Engineering, Applied Physics and Physics. The central focus of the proposed PhD model program in Photonics is on core courses, which capture the main thrusts of this field, emphasizing the state-of-the-art of new discoveries in optical physics and photonics technology. These core courses require knowledge of fundamentals such as Quantum Mechanics, Solid-state Physics and Electromagnetism. A list of electives to provide additional breadth complements the program.

Associated Faculty

• Federico Capasso
• Ken Cozier
  
• Jene Golovchenko
• Lene Hau
• Eric Mazur
• Marko Loncar
• Peter Pershan

Core Courses

Three courses out of the following required.

• ES273 Optics and Photonics
• ES274 Quantum Technology
• ES275 Nanophotonics
• AP216 Modern Optics and Quantum Electronics
• AP217 Applications of Modern Optics

Fundamental Courses

One course in each category.

Solid-state Physics

• AP195 Introduction to Solid State Physics
• AP295a Introduction to Quantum Theory of Solids

Quantum Mechanics

• P143B Quantum Mechanics II
• Chem243 Applied Quantum Mechanics
• P251A Advanced Quantum Mechanics I

Electromagnetism

• P232 Advanced Classical Electromagnetism
• ES151 Electromagnetic Engineering

Electives Courses

Four courses required. A minimum of two from this list.

• ES173 Electronic and Photonic Devices
• ES174 Photonic and Electronic Device Laboratory
• AP218 Electrical, Optical and Magnetic Properties of Materials
• AP225 Introduction to Soft Matter
• AP235 Chemistry in Materials Scienceand Engineering
• AP284 Statistical Thermodynamics
• AP291 Electron Microscopy Lab
• AP298r Interdisciplinary Chemistry, Engineering and Physics: Seminar
• Chem240 Statistical Mechanics
• P123 Laboratory Electronics

• P129 Energy Science
• P262 Statistical Physics
• MIT 6-634 Nonlinear Optics

Examples of Photonics Programs

Example 1

Core Courses

• ES275 Nanophotonics

• AP216 Modern Optics and Quantum Electronics
• AP217 Applications of Modern Optics

Fundamental Courses

• AP295a Introduction to Quantum Theory of Solids
• P251A Advanced Quantum Mechanics I
• P232 Advanced Classical Electromagnetism

Electives

• AP225 Introduction to Soft Matter
• P262 Statistical Physics
• ES174 Photonic and Electronic Device Laboratory
• ES274 Quantum Technology

Example 2

Core Courses

• ES275 Nanophotonics
• AP216 Modern Optics and Quantum Electronics
• AP217 Applications of Modern Optics

Fundamental Courses

• AP195 Introduction to Solid State Physics
• Chem243 Applied Quantum Mechanics
• ES151 Electromagnetic Engineering

Electives

• AP218 Electrical, Optical and Magnetic Properties of Materials
• AP284 Statistical Thermodynamics
• AP291 Electron Microscopy Lab
• AP298r InterdisciplinaryChemistry, Engineering and Physics: Seminar

Nanoscale Electronic Devices

The Nanoscale Electronic Devices program prepares graduate students to create new devices and systems that solve important problems, and emphasizes electronics instead of photonics. The core courses provide an introduction to condensed matter physics and the physics of electronic and photonic devices, while the fundamental courses provide a background in electromagnetism, quantum mechanics, and statistical mechanics. Selections of elective courses can be aimed either at a particular specialty, or provide breadth to the program.

Associated Faculty

• Federico Capasso
• Jene Golovchenko
• Donhee Ham
• Evelyn Hu
• Efthimios (Tim ) Kaxiras
• Venky Narayanamurti
• Shriram Ramanathan
• Robert Westervelt

Core Courses

Three graduate courses from the list below.

Condensed Matter Physics

• AP195 Introduction to Solid State Physics (if needed)
• AP295a, AP295b Introduction to the Quantum Theory of Solids I & II or
• P295a, P295b Introduction to the Quantum Theory of Solids I & II

Electronic and Photonic Devices

• ES173 Introduction to Electronic and Photonic Devices (if needed)
• ES274 Quantum Technology I

Fundamental Courses

Three or four courses, as indicated.

Electromagnetism

• P232 Advanced Classical Electromagnetism

Quantum Mechanics

• Chem243 Applied Quantum Mechanics or
• P251a, P251b Advanced Quantum Mechanics I & II

Statistical Mechanics

• AP284 Statistical Thermodynamics

Elective Courses

Elective courses to bring the total number to 10.

• AP216 Modern Optics and Quantum Electronics
• AP217 Application of Modern Optics
• AP218 Electrical, Optical and Magnetic Properties of Materials
• AP225 Introduction to Soft Matter
• AP235 Chemistry in Material Sciences and Engineering
• AP282 Solids: Structure and Defects
• AP291 Electron Microscopy Laboratory
• AP292 Kinetics of Condensed Phase Processes
• AP293 Dielectric, Magnetic, Electrical, Thermal and Mechanical Composites
• AP299r Special Topics in Applied Physics
• CS148 Design of VLSI Circuits and Systems
• ES154 Electronic Devices and Circuits
• ES159 Introduction to Robotics
• ES173 Introduction to Electronic and Photonic Devices
• ES227 Medical Device Design
• ES252 Micro/Nano Robotics
• ES272 RF and High-speed Integrated Circuits
• ES273 Optics and Photonics
• P247 Advanced Laboratory
• P270 Mesoscopic Physics and Quantum Information Processing
• P271 Topics in the Physics of Quantum Information
• P284 Strongly Correlated Systems in Atomic and Condensed Matter Physics

Examples

Example 1 — Experimental emphasis

• P232 Advanced Classical Electromagnetism
• Chem243 Applied Quantum Mechanics
• AP295a, AP295b Introduction to the Quantum Theory of Solids I & II
• AP284 Statistical Thermodynamics
• CS148 Design of VLSI Circuits and Systems
• AP291 Electron Microscopy Laboratory
• ES173 Introduction to Electronic and Photonic Devices
• ES274 Quantum Technology I
• P270 Mesoscopic Physics and Quantum Information Processing

Example 2 — Theoretical emphasis

• P232 Advanced Classical Electromagnetism
• Chem243 Applied Quantum Mechanics
• AP295a, 295b Introduction to the Quantum Theory of Solids I & II
• AP284 Statistical Thermodynamics
• P247 Advanced Laboratory
• ES173 Introduction to Electronic and Photonic Devices
• ES274 Quantum Technology I
• P270 Mesoscopic Physics and Quantum Information Processing
• P271 Topics in the Physics of Quantum Information

Nanoscale Structures

In addition to manipulating electrons and photons, many devices rely on the manipulation of the structure and properties of ‘atoms’ (either individual atoms or larger units).

The Nanoscale Stuctures program consists of a set of courses that describe how to make, test and understand systems with interesting shapes that contain relatively few atoms, as compared to regular solids.

These systems include nanoparticles, nanowires, heterostructures, etc., and their properties and behavior go beyond the traditional materials science for bulk structures. Experimentally, they involve advanced fabrication and imaging techniques. Theoretically, they involve simulations at the atomic scale using quantum methods that help us understand electron states and transport, as well as the interaction with photons. These systems exhibit fascinating physical behavior and have a very wide range of applications, from sensors to integrated circuits.

Associated Faculty

• Michael Aziz
• Ken Crozier
• Jene Golovchenko
• Lene Hau
• Evelyn Hu
• Efthimios (Tim) Kaxiras
• Marko Loncar
• Eric Mazur
• Peter Pershan
• Shriram Ramanathan
• Frans Spaepen
• Robert Westervelt
• Tai T. Wu
• David Clarke

Core Courses

Two courses out of the following required

• AP295a Introduction to Quantum Theory of Solids or
• AP195 Introduction to Solid State Physics (if no prior knowledge of the subject)
• AP282 Solids: Structure and Defects
• AP218 Electrical, Optical and Magnetic Properties of Materials

Fundamental Courses

One course in each category

Electromagnetism

• P232 Advanced Classical Electromagnetism

Quantum Mechanics

• P251a Advanced Quantum Mechanics I
• P251b Advanced Quantum Mechanics II

Statistical Mechanics and Thermodynamics

• AP284 Statistical Thermodynamics
• P262 Statistical Physics

Elective Courses

Five courses required.

A minimum of three from this list.

• AP291 Electron Microscopy Laboratory
• AP292 Kinetics of Condensed Phase Processes
• AP295b Quantum Theory of Solids
• AP298r Interdisciplinary Chemistry, Engineering and Physics: Seminar
• AP235 Chemistry in Materials Science and Engineering
• AP293 Dielectric, Magnetic, Electrical, Thermal and Mechanical Composites
• AM201 Physical Mathematics I
• AM202 Physical Mathematics II
• AM205 Advanced Scientific Computing: Numerical Methods
• AM207 Advanced Scientific Computing: Stochastic Optimization Methods

Examples

Example 1 - Experimental emphasis

Core Courses

• AP195 Introduction to Solid State Physics
• AP218 Electrical, Optical and Magnetic Properties of Materials

Fundamental courses

• P232 Advanced Classical Electromagnetism
• P251a Advanced Quantum Mechanics I
• AP284 Statistical Thermodynamics

Electives

• AP291 Electron Microscopy Laboratory
• AP292 Kinetics of Condensed Phase Processes
• AP298r Interdisciplinary Chemistry, Engineering and Physics: Seminar
• AP299r Special Topics in Applied Physics
• AP299r Special Topics in Applied Physics

Example 2 - Theoretical emphasis

Core Courses

• AP295a Introduction to Quantum Theory of Solids
• AP282 Solids: Structure and Defects

Fundamental Courses

• P232 Advanced Classical Electromagnetism
• P251a Advanced Quantum Mechanics I
• P262 Statistical Physics

Electives

• AP295b Quantum Theory of Solids
• AP298r Interdisciplinary Chemistry, Engineering and Physics: Seminar
• AM201 Physical Mathematics I
• AM205 Advanced Scientific Computing: Numerical Methods
• AP299r Special Topics in Applied Physics

Biological and Soft Matter Physics

The program in biological and soft matter physics focuses on physical principles underlying the behavior of complex fluids and biological systems. The length scales in these systems are much larger than atomic scales, leading to interesting dynamics, rheological properties, self-organizing behavior, and engineering applications. Courses therefore aim to provide a strong foundation in continuum mechanics, statistical mechanics, and experimental and mathematical methods.

Notes: Students without prior experience in differential equations should take AM105b (Ordinary and Partial Differential Equations). Other prerequisites may be necessary for advanced classes, and, depending on a student's background, it may be appropriate to take additional preparatory courses. As biological physics is a very broad field, students should consult with their adviser to develop a course of study appropriate for their interests. A wide range of classes is available in SEAS and in other departments such as Physics, Chemistry & Chemical Biology, and Molecular and Cellular Biology. Students might also wish to explore course offerings in the Biological and Biomedical Sciences (BBS) program at Harvard Medical School.

Associated Faculty

• Joanna Aizenberg
• Philippe Cluzel
• Jene Golovchenko
• Lene Hau
• Vinothan Manoharan
• Eric Mazur
• Daniel Needleman
• Peter Pershan
• Sharad Ramanathan
• Frans Spaepen
• David Weitz
• Robert Westervelt

Core Courses

Three courses out of the following required:

• AM201 Physical Mathematics I
• AP225 Introduction to Soft Matter
• AP284/P262 Statistical Thermodynamics; or Chem240, Statistical Mechanics
• ES212 Quantitative Cell Biology: Self-Organization and Cellular Architecture
• MCB212 Topics in Biophysics
• MCB225 Interesting Questions in Physical Biology

Fundamental and Elective Courses

Five or more courses distributed among the following categories. Students may also take additional core courses.

Continuum Mechanics and Materials

• ES220 Fluid Dynamics
• ES240 Solid Mechanics
• AP235 Chemistry in Materials Science and Engineering
• AP282 Solids: Structure and Defects
• AP292 Kinetics of Condensed Phase Processes
• AP293 Deformation of Solids
• ES241 Advanced Elasticity

Biophysics and Quantitative Biology

• AM215 Fundamentals of Biological Signal Processing
• BioP204 Structural Biology from Molecules to Cells
• Cell Biology 201 Molecular Biology of the Cell (BBS program, Medical School)
• Chem163 Frontiers in Biophysics
• ES224 Laboratory in Engineering and Physical Biology
• P215/AP215 Biological Dynamics
• P269r Topics in Statistical Physics and Quantitative Biology
• Systems Biology 200 Dynamic and Stochastic Processes in Cells
• Systems Biology 202 Modeling and Measurement in Cell Biology

Experimental, Analytical, and Numerical Methods

• AM202 Physical Mathematics II
• AM204 Geometrical Methods in the Physical and Engineering Sciences
• AM205 Practical Scientific Computing
• AM205b Advanced Scientific Computing
• AM211 Introduction to Numerical Mathematics
• AM212 Numerical Solution of Differential Equations
• AP216 Modern Optics and Quantum Electronics
• AP217 Applications of Modern Optics
• AP291 Electron Microscopy Laboratory
• BioP205 Computational and Functional Genomics
• CS266 Biologically-Inspired Distributed and Multi-Agent Systems
• CS278 Rendering and Image Processing in Computer Graphics
• CS283 Computer Vision
• ES173 Electronic and Photonic Devices
• ES174 Photonic and Electronic Device Laboratory
• P123 Laboratory Electronics
• P232 Advanced Classical Electromagnetism
• Statistics 210 Probability Theory
• Statistics 211 Statistical Inference
• Statistics 220 Bayesian Data Analysis

Examples

Example 1 — Soft Matter focus

Core Courses

• AP225 Introduction to Soft Matter
• AM201 Physical Mathematics I
• AP284 Statistical Thermodynamics

Fundamental and Elective Courses

• AP291 Electron Microscopy Laboratory
• AM205 Practical Scientific Computing
• AP216 Modern Optics and Quantum Electronics
• ES220 Fluid Dynamics
• AP235 Chemistry in Materials Science and Engineering
• AP298r Interdisciplinary Chemistry, Engineering and Physics: Seminar
• AP299r Special Topics in Applied Physics

Example 2 — Biophysics Focus

Core Courses

• AP201 Physical Mathematics I
• ES212 Quantitative Cell Biology: Self-Organization and Cellular Architecture
• MCB212 Topics in Biophysics

Fundamental and Elective Courses

• ES240 Solid Mechanics
• AP284 Statistical Thermodynamics
• AP225 Introduction to Soft Matter
• AM202 Physical Mathematics II
• ES224 Laboratory in Engineering and Physical Biology
• Biophysics 204 Structural Biology From Molecules to Cells
• AP298r Interdisciplinary Chemistry, Engineering and Physics: Seminar
• AP299r Special Topics in Applied Physics
  

Materials Science

Faculty in this area:

• J. Aizenberg
• M.J. Aziz
• D.R. Clarke
• S. Ramanathan
• F. Spaepen
• J.J. Vlassak
• J. Lewis
  

Materials Science is a highly interdisciplinary field drawing on foundations in physics, chemistry, and various branches of engineering. Research involving materials is widespread within Harvard, not only in SEAS but also in several departments within the Faculty of Arts and Sciences, e.g. Physics; Chemistry & Chemical Biology. But for Materials Scientists, these separate foundational areas come together to form a discipline of its own, comprising the scientific basis for an understanding of the synthesis and processing of materials, their properties, and their performance in devices and engineering applications. Graduate students specializing in Materials Science earn a Ph.D. in Applied Physics or Engineering Science but from their course work they acquire a broad, rigorous background in the foundational elements of structure and defects; chemistry; thermodynamics and kinetics; mechanical, electrical, magnetic, and optical properties of materials. This course work helps prepare them for careers in a world with a rapidly changing landscape of exciting materials research directions. Accordingly, their Ph.D. thesis research is typically interdisciplinary, with a specialization as described below in some field, supported by advanced course work to support leading edge research in the area of specialization. Their eight "disciplinary courses" required by HSEAS should come from the list below of 200-level or pre-approved 100-level courses. Exceptions may be obtained for unusual programs by presenting compelling reasons in a petition to the Committee on Higher Degrees.

Core courses in Materials Science

There are four core courses typically taught every year and taken by every graduate student in materials science:

• AP 282: Solids: structure and defects
• AP 218: Electrical, optical, and magnetic properties of materials
• AP 292: Kinetics of condensed phase processes
• AP 235: Chemistry in materials science and engineering

Track courses

Materials Science students typically specialize in one of three "tracks". For each track, the corresponding courses below are considered core courses normally taken by every graduate student in that track. Some of these courses are offered every year and some every other year - please consult the course catalogue.

Track A: mechanical materials

• AP 293: Dislocations and other deformation mechanisms
• ES 240: Solid mechanics
• One of ES 246: Plasticity; or ES 247: Fracture mechanics

Track B: solid-state materials

• AP 284 or Ph 262: Statistical thermodynamics
• One AP 195: Introduction to solid state physics; or AP 295a: Introduction to quantum theory of solids
• One of ES 173: Electronic and photonic semiconductor devices; or ES 274: Quantum technology

Track C: soft / bio materials

• One of AP 225: Introduction to soft matter; ES 216: Biological dynamics; or ES 222: advanced cellular engineering
• One of AP 217: Applications of modern optics; ES 240: Solid mechanics; ES 224: Laboratory in Engineering and Physical Biology; or Chemistry 163: Frontiers in biophysics
• One of ES 230: Advanced tissue engineering; ES 252: Micro/nano robotics; or AP 291: Electron microscopy laboratory

Three courses from any one of the tracks identified above are supplemented by an eighth course which provides breadth or additional depth and may be any of the courses listed above or: AM 201: Physical mathematics I; AM 202: Physical mathematics II; AM 205: Practical scientific computing; ES 241: Advanced Elasticity; ES 275: Nanophotonics; Physics 123: Electronics laboratory; and Physics 251a: advanced quantum mechanics I

Breadth courses

For further breadth, up to two of the ten courses required by SEAS can normally come from this non-exclusive list: AP 294hfr: materials science seminar; AP 298r: materials chemistry and physics seminar; AP 299r: research project for a grade; ES 239: Advanced innovation in science and engineering; ES 242r: Solid Mechanics: Advanced Seminar; Biophysics 242r:Special Topics in Biophysics and Physics 269r: Topics in Statistical Physics and Quantitative Biology.

SPECIFIC EXAMPLES

• Materials Science core
• Mechanical materials track
• Solid-state materials track
• Soft/bio-materials track

Computer Science

We expect students to obtain broad knowledge of computer science by taking graduate level courses in a variety of sub-areas in computer science, such as systems, networking, databases, algorithms, complexity, hardware, human-computer interaction, graphics, and/or programming languages.

Within SEAS, CS courses are roughly organized according to sub-area by their middle digit, so we expect students to take courses in a minimum of three distinct sub-areas, one of which should be theory (denoted by the middle digit of 2). Theory is specifically required as we expect all students to obtain some background in the mathematical foundations that underlie computer science. The intention is not only to give breadth to students, but to ensure cross-fertilization across different sub-disciplines in Computer Science.

Just as we expect all students obtaining a Ph.D. to have some knowledge of the theoretical foundations of computer science, we expect all students to have some knowledge of how to build large software and/or hardware systems. Roughly speaking, the students’ contribution to the system should be on the order of thousands of lines of code, or the equivalent complexity in hardware. In most cases the requirement can be met by projects undertaken as part of an appropriate undergraduate or graduate level class.

The system may be part of a group project but the individual’s contributions should be clearly delineated to meet this requirement. The project must be approved by the Committee on Higher Degrees subsequent to completion. The student is expected to write a note explaining the project, include a copy of any relevant artifacts or outcomes, and where appropriate obtain a note from their advisor, their class instructor, or their supervisors confirming their contributions.

Computer science is an applied science, with connections to many fields. Learning about and connecting computer science to other fields is a key part of an advanced education in computer science. These connections may introduce relevant background, or they may provide an outlet for developing new applications.

For example, mathematics courses may be appropriate for someone working in theory, linguistics courses may be appropriate for someone working in computational linguistics, economics courses may be appropriate for those working in algorithmic mechanism design, electrical engineering courses may be appropriate for those working in circuit design, and design courses may be appropriate for someone working in user interfaces.

The course requirements for a computer science Ph.D. include the following:

1. Of these 10 courses, at least 7 must be technical courses drawn from the Harvard School of Engineering and Applied Sciences, Math, or MIT’s engineering program.
2. Of these 7 courses, at least 3 must Computer Science courses, with 3 different middle digits, and with one of these three courses having a middle digit of 2 (i.e., a “theory” course.)
3. Students must take 2 courses constituting an external minor in an area outside of computer science. These courses should be clearly related; generally, this will mean the two courses are in the same discipline, although this is not mandatory. These courses must be strictly disjoint from the 7 courses of requirement 2.
4. Students must demonstrate practical competence by building a large software or hardware system during the course of their graduate studies. This requirement will generally be met through a class project, but it can also be met through work done in the course of a summer internship, or in the course of research.
5. Undergraduate courses and CS 299 courses cannot be used to fulfill the requirements above, unless specifically approved by the Committee on Higher Degrees as an exceptions.
6. Exceptions to any of these requirements require a detailed written explanation of the reasoning for the exception from the student and the student’s research advisor. Exceptions can only be approved by the Committee on Higher Degrees, and generally exceptions will only be given for unusual circumstances specific to the student’s research program.

Engineering Sciences

Environmental Sciences and Engineering

Atmosphere/Oceans/Surface/Climate/Environmental Engineering (AOSCE) Model Program

Note: Many courses in AOSCE are taught by SEAS faculty jointly with the Earth and Planetary Sciences (EPS) department, and are listed as EPS courses.

AOSCE covers the broad areas of the science of the atmosphere, oceans, and the earth's surface and hydrosphere: dynamics (weather, ocean circulation, physical climate, atmosphere-ocean interactions, glaciology, geomorphologic and hydrogeologic processes), chemistry (atmospheric composition, global and local pollution, aerosols, free radicals, marine biogeochemistry), biology (atmosphere-biosphere interactions, microbial transformations in the environment), and engineering (urbanization, water resources, development, geologic hazards).

Graduate programs in AOSCE are diverse, but with strong common elements. Programs are built around introductory courses that apply principals of physics and chemistry to the atmosphere, oceans, and surface and near-surface earth processes. Students build on a strong foundation of mathematics, physics, chemistry, and computational science, and learn about the fundamentals and research frontiers of atmospheric, ocean, and earth surface chemistry and dynamics.

Climate phenomena are a strong part of the curriculum, entraining advanced applications of statistics and large scale data analysis, and including transient/accelerated glacial processes. Air and water pollution, the science of geologic hazards (earthquakes, volcanic eruptions, and landslides), energy-related geoscience, and engineering applications are a growing component in SEAS.

Requirements

Students take at least 8 disciplinary courses which do not include 298r or 298r, at least 6 are at the 200 level; at least one is from EPS 200, EPS 202, and EPS 208. Most students take two or more of EPS 200, 202 and 208 and 9 to 10 disciplinary courses. Seminar, research, and reading courses fill out the balance of the program requirements. Students normally take two introductory graduate courses and two more advanced courses in their areas, two applied mathematics courses, and two graduate level courses in engineering sciences, earth science, biology, physics, or other areas where breadth of preparation is needed.

Core Courses

Mathematics
Preparation in mathematics is required for all AOSCE students, and many students also need training in statistics. Since students have diverse backgrounds and a broad range of educational goals, they undertake mathematics at different levels. Generally students will take 2 courses in the mathematical sciences which include math, applied math, and statistics.

Minimum levels

• AM 101 Statistical inference for scientists and engineers
• AM 105b Ordinary and partial differential equations
• AM 115 Mathematical modeling

Typical programs include at least one of the following courses

• AM 201 Physical Mathematics I
• AM 202 Physical Mathematics II (partial differential equations)
• AM 203 Non-linear Dynamics
• AM 205 Scientific Computing.
• AM 211, AM 212 Numerical methods

Sub-areas of AOSCE each have additional requirements for foundation courses covering various aspects of physics, chemistry, engineering sciences or biology, such as fluid mechanics, spectroscopy, laser physics, ecosystem dynamics, etc. In consultation with his/her advisor, each student will develop a program that includes the relevant graduate courses of this type.

Generally students must take at least one of the following courses. In most cases students take two of the following.

• EPS 200 Atmospheric Chemistry and Physics (includes computer laboratory)
• EPS 202 Mechanics in Earth and Environmental Science
• EPS 208 Physics of Climate

Track Courses

More advanced courses (many accessible to advanced students outside the track).

Students divide roughly by physics and chemistry foci, but many students do some of each.

Physics/Dynamics oriented courses

• EPS 231 Climate Dynamics
• EPS 232 Dynamic Meteorology
• ES 262 Advanced Hydrology and Environmental Geomechanics

Chemistry and oriented courses

• EPS 236 Modeling and Data Analysis (includes computer laboratory)
• ES 268 Environmental Chemical Kinetics
• ES 267 Aerosol physics and chemistry (new in 2008-2009)

Breadth Courses

Most programs will have courses outside of the students direct research area. These courses ensure that there is breadth in the student’s education. A typical program will contain two courses which provide breadth. The following is a list of course which will often satisfy the breadth requirement:

• EPS209 Paleoclimate
• EPS 237 Advanced Biogeochemistry
• EPS 238 Spectroscopy and Radiative Transfer in Atmospheres
• ES 123 or Es 220 Fluid Mechanics
• ES 240 Solid Mechanics
• ES 262 Advanced Hydrology and Environmental Geomechanics
• OEB 157 Global Change Biology
• OEB 160 Forest Ecology
• Physics 123 Electronics

This is list is by no means comprehensive. Courses at the graduate level in Physics and Chemistry (e.g. quantum mechanics, molecular structure, electronics) are commonly included.

Please note that many students studying Geophysical Fluid Dynamics take 1 or 2 MIT courses.

Bioengineering

This is a diverse and growing area for the School of Engineering and Applied Sciences. It encompasses many areas including biomaterials, biomechanics including robotics, biophysics and neuromotor control. The model programs for most of these areas are under development. Students should consult their field advisor and Professors Howe or Mooney for guidance in constructing a program in an area other then cells, tissue and biomaterials.

Cells, Tissues, and Biomaterials Area

Rationale Students must achieve graduate-level competence in the following areas:

• Cell biology
• Organ-level physiology
• Chemistry, at least through one year of organic chemistry
• Transport mechanics

Core Courses

• ES 222 Advanced Cellular Engineering
• ES 230 Advanced Tissue Engineering
• ES 221 Drug Delivery
• ES 228 Biomaterials
  

Depth
Two courses from the following; at least one must be an Applied Math course.

• AM 201 Physical Mathematics I
• AM 205 Practical Scientific Computing
• AM 121 Introduction to Optimization: Models and Methods
• AP 225 Introduction to Soft Matter
• CS 266 Biologically-inspired Distributed and Multi-agent Systems
• ES 220 Advanced Fluid Dynamics
• ES 216 Biological Dynamics
• Physics 269r Topics in Statistical Physics and Quantitative Biology
• MCB 212 Topics in Biophysics

Electives
Five courses selected for the student’s research and career plans.

• Additional courses from the “Depth” list above; other 200-level technical courses from SEAS, Physics, Applied Physics, Chemistry, Biology; or MIT H-level technical courses.
• Up to one “Innovation” style course that broadens a student's perspective (e.g. ES 239), or relevant courses at a suitable level in non-science departments (e.g. technology transfer).
• Up to two may be E S299r independent study courses, if undertaken with different faculty.
• At least eight of the ten courses must be graduate-level technical courses (200-level or equivalent). At most two courses in the entire plan of study may be undergraduate (100 level).

NOTES:

1) Required Background

• Students without prior background in organ-level physiology are required to take at least one appropriate course from an FAS biology department, Harvard Medical School, Harvard School of Public Health, or the Harvard-MIT Division of Health Sciences and Technology.
• Similarly, students without preparation in probability and biostatistics are required to take at least one course in this area.
• These courses should be selected in consultation with the advisor to match the student's background and research area.
• Students whose preparation does not include prerequisites for graduate-level study in this area will take more than ten courses.

We have 5 distinct subfields of electrical engineering at SEAS. Each subfield has its own recommendation for a model program. For all programs, generally approved programs will contain two or less 100 level courses. In addition to AP 298r and ES 299r, programs will often contain courses from SEAS, mathematics, physics, and chemistry.

Computer Engineering Area

Core

Breadth
Students are asked to take at least one course in circuits and devices , EE systems and statistics, and Cs software systems. The goal of the CS and EE systems courses is to provide technical breadth across the discipline and to provide exposure to emerging application areas that are of interest to designers of next-generation computing systems (interfaces with communication/networking, signal/image processing, etc).

EE Systems and Statistics (One of the following)

CS Software Systems (One of the following)

• CS 244 Advanced Networking

• CS 261 Research Topics in Operating Systems

• CS 262 Introduction to Distributed Computing

• CS 265 Database Systems

• CS 252r Advanced Topics in Programming Languages

• CS 253r Advanced Topics in Programming Language Compilation

The remaining 5 courses should be selected in consultation with the field adviser. Appropriate courses come from those listed above and courses in Architecture and VLSI-CAD. These include MIT 6.823 Computer System Architecture, MIT 6.846 Parallel Computing, and MIT 6.375 Complex Digital Systems.

Control and Robotics Area

Core Courses

• ES 202 Estimation and Control of Dynamic Systems
• ES 203 Stochastic Control
• ES 209 Nonlinear Control
• ES 259 Robotics
• CS 283 Computer Vision

At least one course in decision theory or estimation

• ES 201 Decision Theory
• ES 255 detection and Estimation Theory and Applications

At least one course in Information and Communications

• ES 250 Information Theory
• ES 258 Advanced Digital Communications

The remaining three courses may be 100 or 200 level courses from other EE tracks in Solid State Physics/ Electromagnetism/Circuit Design or other 200 level courses in SEAS/Physics/Math/Chemistry/Biology/MIT as suits a person's individual preparation, taste and research program.

Electronics Area

19 The goal of the program is to provide graduate students with deep and broad understanding of modern solid-state electronics and closely related areas (e.g., lasers). The core courses in the program come from circuits and devices.

At least 2 Circuits courses from:

• ES 271 Topics in Mixed-signal Integrated Circuits
• ES 272 RF Integrated Circuits (In the 2009-2010 academic year, ES 272 is bracketed. MIT 6.776 “High-speed communication circuits” (spring 2010), which is commensurate with ES 272, may be taken in place of ES 272, in the 2009-2010 academic year only.)
• CS 248 Advanced Design of VLSI Circuits and Systems
• PH 123 Laboratory Electronics (This will be an extremely useful course in understanding electronics, but given that it is not focused on integrated circuits, students are advised to still take 2 courses from the above list of 4 courses).

At least one course in Devices from:

• APH 195 Introduction to Solid State Physics
• APH 218 Electrical, Optical, and Magnetic Properties of Matter
• APH 295 Quantum Theory of Solids

Breadth

Students can choose the remaining 5 courses from the 200-level technical courses SEAS, Physics, Applied Physics, Chemistry, Biology programs or from MIT. These could include up to two courses labels AP 29r or ES 299. Please note that several additional courses are in development and could be used for different areas. An advanced analog integrated circuits course is planned to be added to the circuit’s area. A solid-state devices course is planned for the device area and finally an advanced electromagnetism which covers microwave is planned for the electromagnetism area.

Photonics Area

Photonics is a broad and diverse field which straddles Electrical Engineering and Applied Physics. The central focus of the proposed PhD model program in Photonics is on core courses, which capture the main thrusts of this field and provide some flexibility in choosing either a more EE oriented or a more Applied Physics oriented program. These core courses require knowledge of fundamentals such as Electromagnetism, Quantum Mechanics and Solid-state Physics (depth). In the depth category advanced (200 level) or less advanced (100 level) course options are given, to account for the different students’ backgrounds. A list of electives to provide additional breadth complements the program.

Core Courses

Three of five:

• ES273 Optics and Photonics
• ES274 Quantum Technology
• ES275 Nanophotonics
• AP216 Modern Optics and Quantum Electronics
• AP217 Applications of Modern Optics

Applied Mechanics

Core Courses

Electives