Computing and Mathematical Sciences (CMS)

Algorithmic thinking and machine learning are fundamental tools for all researchers, not just computer scientists. They drive disciplines ranging from statistics and electrical engineering to biology and physics to economics and the social sciences. Computing and Mathematical Sciences (CMS) is an interdisciplinary Ph.D. program that trains students to apply algorithmic thinking and machine learning to problems across science and engineering. Our research mission is to build the mathematical and algorithmic foundations required to move from data to information to action. Students will study structures and mechanisms that store, process, and communicate information and that make decisions based on this information. These systems may be expressed in silicon and called computers, in lines of code called programs, or in abstract notation called mathematics. They may appear in economics as markets or social networks, as sequences of amino acids in DNA, or in the organic structure of the human brain.

Only students who expect to pursue the Ph.D. degree will be admitted to the option. PhD students in good standing may petition to add the MS degree upon completion of all course requirements. The awarding of an MS degree requires fulfilling the Institute requirements for a master’s degree, satisfying the core course requirements, and receiving a recommendation for awarding of the degree from the preliminary exam committee.

Institute requirements for the Ph.D. degree are described in the section on degree requirements. Approximately two years of coursework are required, and two or more years are usually needed to prepare the dissertation.

To be recommended for candidacy for the Ph.D. degree in computing and mathematical sciences the student must, in addition to meeting the general Institute requirements, do the following:

The course requirements are broken into three categories. All courses used to fulfill requirements must be taken for grades.

Core requirement: Each student will take six core CMS classes, three in applied mathematics (ACM) and three in Computer Science (CS). In both fields, at least two of the three classes will be taken in the first year to prepare for the preliminary examination, while the remaining classes may be completed by the end of the student’s second year. The core CMS classes are CMS/ACM/IDS 107a; CMS/ACM 117; CMS/ACM/EE 122; CMS/CS/IDS 139 or CMS/CS/IDS 150a; CMS/CS/Ec/EE/IDS 144; EE/CMS/CNS/CS/IDS 181. Students may petition the option representative to replace one core course requirement with an alternative ACM, CDS, CS, CMS, or EE graduate-level course. Additionally, CMS 290 is required for all CMS first-year graduate students during each term (fall/winter/spring).

Depth requirement: At least 27 units of courses in one particular subject area. The plan for these 27 units must be approved by the CMS option representative.

Breadth requirement: At least 27 units of advanced courses in mathematics, engineering, science, or social science. The plan for these 27 units must be approved by the CMS option representative.

All students must pass a preliminary examination on material from the CMS core class requirements. The examination is administered by a committee consisting of at least three faculty members approved by the CMS option representative. The exam will occur during the student’s first year.

All students must pass an oral candidacy examination to ascertain the breadth and depth of preparation for research in the chosen field. The examination will be administered by a committee consisting of at least four faculty members, at least 2 of whom are CMS faculty members, that is approved by the CMS option representative, and that satisfies Institute regulations. In particular, the chair of the candidacy committee must be a faculty member distinct from the student’s research adviser. The examination will occur during the student’s first three years.

Upon admission, each student will be assigned a primary adviser in the option. This adviser will be replaced by a research adviser (possibly the same faculty member) once a direction of specialization is determined, and not later than the beginning of the second year. After completion of the candidacy exam, each student will form a thesis committee (possibly the same as the candidacy committee) consisting of at least four faculty members, at least two of whom are CMS faculty members, that is approved by the CMS option representative, and that satisfies Institute regulations. In particular, the chair of the thesis committee must be a faculty member distinct from the student's research adviser. The thesis committee will meet at least once a year to advise the student.

Academic progress will be reviewed regularly, including at least once annually by the option representative.

An ability to explain concepts and to verbally present one’s work is vital to a successful career in research and/or teaching. To this end, students may be required by their advisor and the option representative to occasionally serve as a teaching assistant.

A final oral examination will be scheduled and given after the Ph.D. thesis has been submitted for review to the student’s adviser and thesis committee. The thesis examination is a defense of the thesis research and a test of the candidate’s knowledge in their specialized fields. Normally, the defense will consist of a one-hour public lecture followed by an examination of the thesis by the thesis committee.