Computing and Mathematical Science (CMS)

Algorithmic thinking is emerging as a fundamental tool for all researchers, not just computer scientists. Algorithmic thinking now drives 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 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. The master’s degree may be awarded in exceptional cases. The awarding of this 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 for preparation of 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:

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 the first year to prepare for the preliminary examination, while the remaining classes will be completed by the end of the student’s second year. The core CMS classes are CMS/ACM/IDS 107, CMS/ACM/EE 122, CMS 117, CMS/CS/IDS 139, CMS/CS/EE/IDS 144, CMS/CS/CNS/IDS 155. These classes must be taken for a grade.

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

All students must pass a preliminary examination on material from two CMS core classes in applied mathematics and two CMS core classes in computer science. The examination is administered by a committee consisting of at least three faculty selected 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 that consists of at least four faculty, that is approved by the CMS option representative, and that satisfies Institute regulations. In particular, the chair of the candidacy committee must a faculty member distinct from the student’s research adviser. The examination will occur during the student’s first three years.

CMS 290 is required for all CMS first-year graduate students during each term (fall/winter/spring).

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) that consists of at least four faculty, 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 as needed, but no less than once a year, in order to advise the student.

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 his or her specialized fields. Normally, the defense will consist of a one-hour public lecture followed by an examination of the thesis by the thesis committee.