phd computer science caltech

Computer Science

Computing is a ubiquitous tool in all areas of study and research at Caltech. Computer science focuses on the theory and technology of computation itself: it is the study of information, and of the structures that communicate, store, and procegs information. Whether these structures are expressed in hardware and called machines, in software and called programs, or in nature or society, the fundamental concepts are similar.

Students of the computer science option within the Computing & Mathematical Sciences department at Caltech do not specialize along traditional lines that divide hardware and software, systems and applications, or theory and experiment. Rather, a unified approach to the design and analysis of computing structures is taken both in courses and in research. Managing the great complexity of useful systems requires a representation of computations amenable to both mathematical treatment and implementation. Whether the system is artificially designed (such as a multi-core processor), or naturally occurring (such as a molecule), the computer scientist formalizes the computation performed by the system and provides a systematic analysis of its requirements and formal guarantees on its outcomes.

Areas of Research

Research and advanced courses leading to the Ph.D. degree in computer science are concentrated in the following areas: quantum and molecular computation; parallel and distributed computation; theory of computation; information theory; machine learning and applications; computational economics; computer vision; computer graphics; discrete differential geometry; networking and power systems. Research projects frequently involve work in several of these areas, with both theoretical and experimental aspects, as well as connections with such fields as mathematics, physics, biology, economics, and electrical engineering. Crosscutting themes include:

• Physical Implementation of Computations. Computations must ultimately be implemented in some physical medium (e.g., semiconductor electronics, DNA self-assembly, quantum states of elementary particles, molecular electronics). Caltech has been a leader in the early development, engineering, and design of very large scale integrated (VLSI) circuits. Beyond VLSI, efforts are under way to understand quantum, biomolecular, and molecular electronic substrates as possible media for future computing machines. As was the case with semiconductor electronics, Caltech computing can draw on the world-class expertise of its biology, physics, and chemistry departments as it tackles the many challenging opportunities that these new substrates present.
• Robust Modeling of Physical Systems. Caltech computer science has a unique focus in developing rigorous and robust models of the physical world. These models are mathematically and physically sound, often derived from differential geometric principles, and serve as a basis for computer graphics and vision research, as well as the simulation of mechanical, optical, and biological systems.
• Systematic Design. A key theme in the Caltech computer science option is the systematic design of systems at all levels. This theme shows up in the design of numerical algorithms for physical simulation and computer graphics, design of concurrent and distributed systems, abstractions for physical computing substrates, design of learning systems, design of programming languages, automated optimization of computations for both software and hardware implementation, as well as control and optimization of networks. The success of computer systems has allowed the building of systems of unprecedented scale and complexity. These systems can only be understood and managed if we carefully contain the complexity involved by systematically defining and exploring their design space.
• Theory. A strong theoretical understanding is the necessary foundation for systematic design, analysis, and verification. The theory of computation focuses on deep mathematical problems, many of which have substantial technological impact. Theory in computer science at Caltech includes traditional areas such as complexity algorithms, theories of numerical computation, optimization, probability, and game theory. But theory is not relegated to a single group, and has strong connections to all disciplines represented at Caltech.
• Networks & Distributed Systems. Modern networks and distributed systems are undoubtedly the most complex and critical pieces of infrastructure that the world has created. This includes communication networks as well as power networks, social networks, cloud computing, and more. The massive scale and exponential growth of such networks presents unique algorithmic, computational, and economic challenges. Research at Caltech approaches these challenges through a combination of rigorous design, systematic analysis, and interdisciplinary collaboration.
• Machine Learning. In our increasingly data-rich world, it is more important than ever to develop principled approaches that can intelligently convert raw data into actionable knowledge. At Caltech, we take a broad and integrated view of research in data-driven intelligent systems. The Decision, Optimization and Learning group brings together researchers from machine learning, optimization, applied math, statistics, control, robotics, distributed systems and human-computer interaction to form an intellectual core pertaining fundamental and applied research from statistical machine learning to statistical decision theory through optimization.
• Interdisciplinary Research. Computer simulations, modeling, and analysis are key enablers, allowing all fields of science to advance rapidly. Furthermore, insights into computational management of information helps us understand information processing issues in natural systems (from cells and neurons to financial markets and social networks) and build hypothetical models that advance our understanding of natural cognition. These relations provide many opportunities for scholars in computer science to work closely with colleagues throughout Caltech. The Information Science and Technology (IST) initiative facilitates and promotes such interdisciplinary research (see ist.caltech.edu).

Caltech    |    Engineering & Applied Science    |    Center for Advanced Computing Research C omputational S cience and E ngineering Minor in Computational Science and Engineering Aims and Scope of the Minor Computational Science and Engineering ( CSE ) may be pursued as a subject minor by graduate students who are pursuing Ph.D. degrees in any option. The CSE minor is intended to supplement one of Caltech's graduate degrees and is designed for students who wish to broaden their knowledge of CSE beyond their major field of study . The CSE minor is also intended to recognize graduate students' interest in and dedication to CSE as demonstrated by the successful completion of a program of study in the field. Completion of the CSE minor program of study will be recognized on the Ph.D. diploma by the statement: " [...] and by additional studies constituting a minor in Computational Science and Engineering". To receive the CSE minor, graduate students must take 18 units (two terms) from the classes listed below with a grey background , 18 units (two terms) from the classes listed below with a orange background , and 9 units (one term) from the classes listed below with a blue background : Option(s) Class Title ACM/EE 106 ab Introductory Methods of Computational Mathematics ACM/CMS 113 Mathematical Optimization ACM/CS 114 ab Parallel Algorithms for Scientific Applications ACM/ESE 116 Probability Models ACM/CMS 117 Probability and Random Processes ACM/CS 157 Statistical Inference ACM/CS 158 Mathematical Statistics ACM 210ab Numerical Methods for PDEs ACM 216 Markov Chains, Discrete Stochastic Processes and Applications CS 115 Functional Programming CS 138 abc Computer Algorithms CMS/CS 139 Analysis and Design of Algorithms CS/EE 143 Communication Networks CS 150 Probability and Algorithms CS/CNS/EE 155 Machine Learning Data Mining CS/CNS/EE 156 a Learning Systems CS 179 GPU Programming Ae/AM/CE/ME 214 abc Computational Solid Mechanics Ae/ACM/ME 232 ab Computational Fluid Dynamics Ay 199 Special Topics in Astronomy and Astrophysics (eScience) Ch 121 ab Atomic Level Simulations of Materials and Molecules Ge 263 Computational Geophysics Ph/CS 214 abc Quantum Computation All courses to be applied toward the CSE minor requirements must be taken on a graded basis and students must obtain a grade of B or higher on all courses. Courses that are used to satisfy the CSE minor cannot be used to satisfy course requirements in the major options unless absolutely required by the option. Courses taken as part of the CSE minor are counted toward the total number of units required for the completion of the Ph.D. degree. Note that a number of other (graduate or undergraduate) classes in the Caltech catalog can be of value to graduate students interested in broadening their knowledge. The table below gives a few examples: Option(s) Class Title ACM 256 & 257 Advanced Topics in ACM CDS 270 Advanced Topics in Systems and Control CS 24 Introduction to Computing Systems CS 38 Algorithms CS 121 Relational Databases CS 151 Complexity Theory CSE Minor Administration The CSE minor is administered by an oversight committee consisting of:      Peter Schröder (Chair) Shaler Arthur Hanisch Professor of Computer Science and Applied and Computational Mathematics, EAS; ps@cms.      Dan Meiron Fletcher Jones Professor of Applied and Computational Mathematics, EAS; dim@acm.      Michael Ortiz Dotty and Dick Hayman Professor of Aeronautics and Mechanical Engineering, EAS; ortiz@aero.      Mark Simons John W. and Herberta M. Miles Professor of Geophysics, GPS; simons@gps. These four faculty members report to the chair of the Engineering and Applied Science division . In consultation with the students' advisers and, if needed, with the CSE Oversight Committee, students formulate a program of approved courses individually tailored to each student's background and needs, with the objective that the student achieve a level of competence in specific subjects relevant to CSE. Students must petition the CSE Oversight Committee for approval of their program of study. Upon completion of the program of study, the CSE Oversight Committee will verify that the CSE minor requirements have been fulfilled. Caltech    |    Engineering & Applied Science    |    Center for Advanced Computing Research

Graduate Students

Applying to Caltech as a graduate student interested in QSE

• Prospective graduate students should apply to a graduate program (including Physics, Applied Physics, Material Science, Chemistry, Electrical Engineering, or Computer Science) depending on their research interest and background.
• In your application (e.g., at the end of your personal statement), list the faculty members across all divisions that you are most interested in. You can find the QSE faculty here .
• Importantly, at Caltech, you have the flexibility to work with a PhD supervisor outside of your assigned program/division. In fact, this is quite common and part of the interdisciplinary spirit here. Hence, your choice of a graduate program does not limit you to work with certain faculty.
• Graduate students may apply to only one academic option per admission cycle. In reviewing your application, the admission committee of the option to which you have applied may recommend that your application be reviewed by another option, if they foresee a better fit with that option. This internal review is automatic and does not require any additional fees, or duplicate application.
• In addition, Caltech offers a Quantum Science and Engineering Minor open to graduate students in all options. You can find more information for the QSE Minor here .
• Caltech offers a wide range of courses in Quantum Science and Engineering. A sample of courses can be found on the QSE Minor page.

More information about applying to options in each Academic Division is available at:

• Physics (PMA)
• Applied Physics (EAS)
• Material Science (EAS)
• Chemistry (CCE)
• Electrical Engineering (EAS)
• Computer Science (EAS)

Additional information about applying to Caltech as a graduate student is available through the Graduate Studies Office

Find a list of QSE Faculty along with information about their research area, their Academic Division and links to their websites on the QSE Faculty page.