Graduate Degree in Applied Computational Mathematics

Reflecting the interdisciplinary nature of the program, several different groups (in addition to the applied and computational mathematics faculty) contribute to the teaching and supervision of research. Students in applied and computational mathematics are expected to combine their basic mathematical studies with deep involvement in some field of application. Students are expected to do research closely related to an application area and it must be publishable. In addition to the independent research PhD students are doing in a specific area, students are expected to master an extensive amount of subject matter in ACM. A number of PhD students have co-advisors in the application area to ensure that their work is worthy of recognition there as well. A regular ACM colloquium provides the opportunity for visitors, faculty, and students to discuss current research in a variety of subfields within applied mathematics. Mission of the Caltech Applied and Computational Math Graduate Program An advanced degree in applied and computational mathematics at Caltech is contingent upon an extensive research achievement. Students in the program are expected to join a research group, carry out independent research, write publications for peer-reviewed journals as well as a thesis. The thesis work is then presented and evaluated by a Caltech thesis committee in a close defense. Initially, students are required to consolidate their knowledge by taking advanced courses in different subjects of applied and computational mathematics. Students then must pass a candidacy exam in applied and computational physics in order to progress into the research phase of the degree. Graduates of our program are expected to have extensive experience with modern research methods, a broad knowledge of contemporary applied and computational mathematics, and the ability to perform as independent researchers at the highest intellectual and technical levels. Upon Admission Each new graduate student admitted to work for the PhD in applied and computational mathematics is given an informal interview on Thursday or Friday of the week preceding the beginning of instruction for the fall term. The purpose of this interview is to ascertain the preparation of the student and assist him or her in mapping out a course of study. The work of the student during the first year will usually include some independent reading and/or research. Course Requirements All ACM students are required to take a total of 18 nine-unit courses at the graduate level (or the equivalent of 162 units) during their graduate study at Caltech. Among these 18 courses, the following core courses, typically taken during the student’s first year of study, are required: ACM 101 ab, CMS/ACM 104, ACM 105 or Ma 108 abc, ACM 106 ab, CMS/ACM/EE 116, and an application elective course. The application elective course in the first year is selected, with the recommendation of the student’s adviser, from among a wide range of courses offered by an outside option within the Institute. In the second and third years, students are expected to take graduate-level courses appropriate to their chosen research area. The remaining courses towards the 162 unit requirement would normally include graduate-level ACM or CDS courses such as CMS/ACM 113, 201 ab, 210 ab, 216, 217, CDS 140, etc., as deemed appropriate to the student’s research program, and which must be selected in consultation with the student’s research adviser. Students who have already taken some of the required courses may use them to satisfy the course requirements, even though the units may not be used to satisfy the total unit requirement for CMS 290 for each quarter that he or she is in residence. Master's Degree Students are not admitted to work toward the master's degree. The master's degree may be awarded to an ACM student only in exceptional circumstances. Of the 135 units of graduate work required by Institute regulations, at least 81 units of advanced graduate work should be in applied mathematics. Degree of Doctor of Philosophy Candidacy. In order to be recommended for candidacy, the student must, in addition to satisfying the general Institute requirements, pass an oral or written candidacy examination administered by a faculty committee. This examination is offered during one week at the end of the first year of graduate residence at the Institute, typically near the beginning of the fall term. The material covered in this examination is based on the three core sequences described above. For students who have already taken the required courses before coming to Caltech, the examination can also be based on the substituted courses taken in the first year. Advising and Thesis Supervision. Upon passing the candidacy examination (usually by the end of the second year), the student is required to choose a thesis supervisor who assumes the major responsibility in supervising the PhD thesis. At the same time, an advising committee consisting of three faculty members is formed to help oversee the advising process. This committee should be formed no later than the third year of graduate study. The student’s supervisor is part of this committee, but does not chair the committee. The student is encouraged to meet with the committee members informally for advice or suggestions. Joint supervision between two faculty members is also possible, as is seeking a thesis adviser outside the core applied and computational mathematics option, although in this case it is mandatory that an applied mathematics faculty member be nominated as a co-adviser. Should a disagreement of any kind occur between the student and his or her supervisor as regards the timely completion of the thesis, the student is encouraged to direct his or her concerns to the committee chair. If this is not workable, the student should feel free to consult with the option representative, the executive officer, or an applied and computational mathematics faculty member of the student’s choice. If the student’s concerns cannot be resolved through consultation with these individuals, the student is encouraged to pursue resolution of his or her concerns through other channels as outlined in the Student Grievance Procedure section of the Caltech Catalog. Thesis Submission. On or before the first Monday in April of the year in which the degree is to be conferred, a candidate for the degree of PhD in applied and computational mathematics must deliver a typewritten or printed copy of the completed thesis to his or her research supervisor. Final Examination. The final oral examination is held within four weeks after the submission of the thesis. The examination covers the thesis and related areas.