# AP PhD Model Program

**This description of the Applied Physics PhD course expectations augments the school-wide PhD course requirements. Students should make themselves familiar with both.**

Proposed Ph.D. plans that follow these guidelines, including one of the "tracks", will be automatically approved by the CHD, provided that they also comply with the overall SEAS Ph.D. requirements, in particular: 10 courses overall (8 disciplinary, 2 breadth), 5 of which must be 200-level SEAS or SEAS equivalent courses (courses taught in FAS by SEAS faculty), no more than 2 that are 100-level courses (of which only 1 counts as disciplinary).

Students following these model programs/guidelines must take the Core Courses below as well as choose one of the Tracks described below.

Plans that deviate from these guidelines will be reviewed by the CHD and approved on a case-by-case basis, although all plans must comply with the overall SEAS Ph.D. requirements.

## Core Courses

One graduate course in each of the three fields listed below (electromagnetism, quantum mechanics, statistical mechanics). In exceptional cases, the CHD may approve substituting one of the listed undergraduate courses.

**Electromagnetism**:

- Graduate level: Physics 232, AP 216, AP 217, ES 273
- Undergraduate level (CHD approval required): ES 151

**Quantum Mechanics**:

- Graduate level: Quantum Science and Engineering (QSE 200/ES 200), Physics 251a, Physics 251b, AP/Physics 295a, AP/Physics 295b, Chem 243
- Undergraduate level (CHD approval required): AP/Physics 195, Physics 143a, Physics143b, ES 170

**”Living Matter/Bio”-track students: see also the note regarding Quantum Mechanics in the track description given later on this page.*

**Statistical Mechanics**:

- Graduate level: AP 284, AP 286, Physics 262
- Undergraduate level (CHD approval required): Physics 181, or (for students doing bio-related research) MCB 199

**Track Courses**

In addition to three core courses, Applied Physics Ph.D. students may choose one of the tracks below:

Take one course from each field below, preferably at the graduate level:

- Solid State: AP/Physics 295a, AP/Physics 195 (undergraduate level)
- Quantum Devices: ES 274
- Photonics/Nanoelectronics: AP 218, ES 273, Physics 223, ES 173 (undergraduate level)

Take one course from each field below:

- Continuum Mechanics: ES 220, ES 240
- Math and Computational Techniques: AM 201, AM 202, AM 203, AM 205, AM 207
- Soft Matter and Materials: AP 225, AP 226, AP 227, AP 282, AP 235

Take three of the four courses listed below:

- Solids: Structures and Defects: AP 282
- Properties of Materials: AP 218
- Kinetics of Condensed Phase Processes: AP 292
- Chemistry in Materials Science and Engineering: AP 235

AP graduate students are required to take a graduate-level quantum mechanics course. However, for students on the bio track whose work does not require expertise in this topic, the CHD may waive this requirement if the student petitions to do so and (a) submits proof of a good grade on an undergraduate level course in this topic, taken previously or at Harvard or (b) enrolls in a suitable undergraduate course. Students interested in option (a) should submit with their petition a syllabus for the course taken or specify the textbook, course instructor(s), and institution of the course. Approval is at the discretion of the CHD. A waiver from the CHD does not reduce the required total number of courses. Suitable Harvard courses include Physics 143a/b, AP195, and forthcoming courses offered under the Quantum Science & Engineering program.

Take at least one biology course, for example:

- MCB 291 (Genetics, Genomics and Evolutionary Biology)
- MCB 292 (Cellular Biology, Neurobiology and Developmental Biology)
- MCB293 (Biochemistry, Chemical and Structural Biology)
- OEB 242 (Population Genetics)
- Math 243 (Evolutionary Dynamics)
- BCMP 200 (Biochemistry, Chemical and Structural Biology)
- BCMP 234 (Cellular Metabolism and Human Disease)
- BCMP 250 (Biophysical and Biochemical Mechanisms of Protein Function)
- CB 201 (Principles of Cell Biology)
- Genetics 201 (Principles of Genetics)
- CB 207 (Vertebrate Developmental, Stem Cell and Regenerative Biology)

At least one course in “Math and Computational Techniques” is strongly recommend, for example:

- AM 201 (Physical Mathematics)
- AM 203 (Stochastic Processes)
- AM 205 (Numerical Methods)
- AM 207 (Stochastic methods for data analysis, inference, optimization)
- Physics 201 (Data Analysis)
- CS 205 (Computing Foundations)
- CS 281 (Advanced Machine Learning)
- AM 216 (Inverse Problems)
- ES 250 (Information Theory)
- ES 255 (Statistical Inference)
- AP 286 (Inference, Info Theory, Learning)

Students are encouraged students to consider AP242 (Introduction to Single-Molecule Biophysics), ES 297 (Professional Writing for Scientists and Engineers), as well as ES 220 (Fluid Mechanics), ES 240 (Solid Mechanics), and AP 225 (Soft condensed matter).

In addition, calculus, linear algebra, classical mechanics, and thermodynamics and statistical mechanics are fundamental to much biophysical research. *If a student has specific gaps in their training in these areas that will impede their progress, the CHD, the advisor, or the qualifying exam committee may make specific binding recommendations to address such gaps by coursework.*

**Timeline**: We recommend that students have completed a minimum of four courses at the end of their first year, and of six at the end of their second year. Students should aim to meet their full course requirements by the end of their fourth year.