7409 Applied Physics and Mathematics
Building, Muir College
All courses, faculty listings, and curricular and degree requirements described herein are subject to change or deletion without notice.
The Department of Mathematics offers graduate programs leading to the MA (pure or applied mathematics), MS (statistics), and PhD degrees.
The application deadline for fall admission is the second Monday in January for PhD candidates, and the first Monday in February for MA/MS candidates. Candidates should have a bachelor’s or master’s degree in mathematics or a related field from an accredited institution of higher education or the equivalent. A minimum scholastic average of B or better is required for course work completed in upper-division or prior graduate study. In addition, the department requires all applicants to submit scores from both the GRE General Test and Advanced Subject Test in Mathematics. Completed files are judged on the candidate’s mathematical background, qualifications, and goals.
Departmental support is typically in the form of teaching assistantships, research assistantships, and fellowships. These are currently only awarded to students in the PhD program.
All student course programs must be approved by a faculty adviser prior to registering for classes each quarter, as well as any changes throughout the quarter.
Full-time students are required to register for a minimum of twelve (12) units every quarter, eight (8) of which must be graduate-level mathematics courses taken for a letter grade only. The remaining four (4) units can be approved upper-division or graduate-level courses in mathematics-related subjects (Math 500 may not be used to satisfy any part of this requirement).
After advancing to candidacy, PhD candidates may take all course work on a Satisfactory/Unsatisfactory basis. Typically, students should not enroll in Math 299 until they have satisfactorily passed two qualifying examinations at the PhD or Provisional PhD level (see “PhD in Mathematics”) or obtained approval of their faculty adviser.
For all programs, a minimum of twenty-four units of Department of Mathematics course work must be completed with a letter grade.
There is no foreign language requirement for any of the graduate programs in the Department of Mathematics.
[Offered only under the Comprehensive Examination Plan.] The degree may be terminal or obtained on the way to the PhD. A total of forty-eight units of credit are required. No units of Math 299 (Reading and Research) may count toward this total. No more than four units of any combination of Math 295 (Special Topics) and/or Math 500 (Apprentice Teaching) may be used.
Twenty-four of the forty-eight units must be graduate-level mathematics courses approved in consultation with a faculty adviser. The remaining twenty-four units may contain no more than eight units of upper-division mathematics courses and no more than twelve units of graduate courses in a related field outside the department (approved by the Department of Mathematics).
Seven written departmental examinations are offered in three areas (refer to “PhD in Mathematics,” Areas 1, 2, and 3, for list of exams). A student must complete two examinations, one from Area 1 and one from Area 2, both with an MA pass or better.
Full-time students are permitted seven quarters in which to complete all degree requirements. While there are no written time limits for part-time students, the department has the right to intervene and set individual deadlines if it becomes necessary.
[Offered only under the Comprehensive Examination Plan] The degree may be terminal or obtained on the way to the PhD. Out of the total forty-eight units of required credit, two applied mathematics sequences comprising twenty-four units must be chosen from the following list (not every course is offered each year):
Math 202A-B-C. (Applied Algebra)
Math 210A-B-C. (Mathematical Methods in Physics and Engineering)
Math 261A-B-C. (Probabilistic Combinatorics and Algorithms)
Math 264A-B-C. (Combinatorics)
Math 270A-B-C. (Numerical Mathematics)
Math 271A-B-C. (Numerical Optimization)
Math 272A-B-C. (Numerical Partial Differential Equations)
Math 273A-B-C. (Advanced Techniques in Computational Math)
In certain cases, a petition may be approved to substitute one of these requirements from the following list of sequences:
Math 220A-B-C. (Complex Analysis)
Math 231A-B-C. (Partial Differential Equations)
Math 240A-B-C. (Real Analysis)
Math 280A-B-C. (Probability Theory)
Math 281A-B-C. (Mathematical Statistics)
Math 282A-B. (Applied Statistics)
In choosing course work to fulfill the remaining twenty-four units, the following restrictions must be followed:
Students are strongly encouraged to consult with a faculty adviser in their first quarter to prepare their course of study.
Two written comprehensive examinations must be passed at the master’s level in any of the required applied mathematics sequences listed above. The instructors of each course should be contacted for exam details.
Full-time MA students are permitted seven quarters in which to complete all requirements. While there are no written time limits for part-time students, the department has the right to intervene and set individual deadlines if it becomes necessary.
[Offered only under the Comprehensive Examination Plan.] The MS in statistics is designed to provide recipients with a strong mathematical background and experience in statistical computing with various applications. Out of the forty-eight units of credit needed, required core courses comprise twenty-eight units, including
and at least two topics comprising eight units chosen freely from Math 284, 287A-B-C-D, and 289A-B (see course descriptions for topics).
The students are also required to take four units of Math 297 (Mathematics Graduate Research Internship); although the course can be taken repeatedly for credits, only four units can be counted toward fulfilling the MS degree requirements. This Math 297 consulting requirement may be waived if a student has other qualified internship arrangements.
The following guidelines should be followed when selecting courses to complete the remaining twenty units:
Upon the approval of the faculty adviser, the rule above, limiting graduate units from other departments to eight, may be relaxed in making up these noncore units.
Two written comprehensive examinations must be passed at the master’s level in related course work (approved by a faculty adviser). Instructors of the relevant courses should be consulted for exam dates as they vary on a yearly basis.
Full-time MS students are permitted seven quarters in which to complete all requirements. While there are no written time limits for part-time students, the department has the right to intervene and set individual deadlines if it becomes necessary.
The department offers written qualifying examinations in seven subjects. These are grouped into three areas as follows:
Complex Analysis (Math 220A-B-C) Real Analysis (Math 240A-B-C)
Algebra (Math 200A-B-C) Applied Algebra (Math 202A-B-C) Topology (Math 290A-B-C)
Numerical Analysis (Math 270A-B-C) Statistics (Math 281A-B-C)
Department policy stipulates that at least one of the exams must be completed with a provisional PhD pass or better by September following the end of the first year. Anyone unable to comply with this schedule will lose their funding as a PhD student. They will be terminated from the doctoral program and transferred to one of our master’s programs.
Any master’s student can submit for consideration a written request to transfer into the PhD program when the qualifying exam requirements for the PhD program have been met and a dissertation adviser is found. Approval by the Qualifying Exam and Appeals Committee (QEAC) is not automatic, however.
Exams are typically offered twice a year, one scheduled in the spring quarter and again in early September (prior to the start of fall quarter). Copies of past exams are made available online or in the Graduate Office.
In choosing a program with an eye to future employment, students should seek the assistance of a faculty adviser and take a broad selection of courses including applied mathematics, such as those in Area #3.
It is expected that by the end of the third year (nine quarters), students should have a field of research chosen and a faculty member willing to direct and guide them. A student will advance to candidacy after successfully passing the oral qualifying examination, which deals primarily with the area of research proposed but may include the project itself. This examination is conducted by the student’s appointed doctoral committee. Based on their recommendation, a student advances to candidacy and is awarded the CPhil degree.
Submission of a written dissertation and a final examination in which the thesis is publicly defended are the last steps before the PhD degree is awarded. When the dissertation is substantially completed, copies must be provided to all committee members at least four weeks in advance of the proposed defense date. Two weeks before the scheduled final defense, a copy of the dissertation must be made available in the department for public inspection.
The normative time for the PhD in mathematics is five years. Students must have a dissertation adviser by the end of nine quarters. Students must be advanced to candidacy by the end of eleven quarters. Total university support cannot exceed six years. Total registered time at UC San Diego cannot exceed seven years.
A student making normal progress must meet the time limits described below. PhD students who fail to meet these time limits may lose their TA funding.
The PhD in mathematics, with a specialization in computational science is designed to allow a student to obtain standard basic training in his or her chosen field of science, mathematics, or engineering with training in computational science integrated into those graduate studies. The specialization in computational science recognizes the nation’s growing and continuing need for broadly trained advanced computational scientists in academic, industry, and government laboratories. Its graduates will be well-positioned to compete effectively for the best jobs in these areas.
Computational science refers to the use of computer simulation and visualization for basic scientific research, product development, and forecasting. It is an interdisciplinary field that combines mathematics (mathematical modeling, numerical analysis) and computer science (architecture, programming, networks, graphics) with one of the scientific or engineering disciplines.
The specialization draws upon the expertise of faculty from bioengineering, biological sciences, chemistry and biochemistry, computers and engineering, electrical and computer engineering, mathematics, mechanical and aerospace engineering, physics, Scripps Institution of Oceanography, structural engineering as well as research staff from the San Diego Supercomputer Center.
Prospective students must apply to the PhD program of a participating home department, be admitted to that department and then be admitted to the specialization. The five participating academic departments that have a specialization in computational science are chemistry and biochemistry, computer science and engineering, mathematics, mechanical and aerospace engineering, and physics. Requirements consist of those of the admitting home department (one of the five participating departments) as well as the proficiency, qualifying. and elective course requirements as outlined below. Requirements and policies relating to the home department can be found in the UC San Diego General Catalog under that department’s name. In the case of the mathematics department, the admission requirements for the mathematics doctoral program are those outlined above.
Proficiency Requirements: All PhD students participating in the CSME doctoral program must demonstrate advanced undergraduate level proficiency in numerical analysis and in computer algorithms and data structures. Proficiency may be demonstrated by taking UC San Diego’s courses in both subjects while enrolled in the graduate program (four units per course):
Alternatively, proficiency in the material contained in these courses may be satisfied by having previously taken these or equivalent courses at other institutions, or through other evidence of sufficient knowledge of this material. Demonstrating proficiency without taking these courses at UC San Diego is subject to approval by the CSME Executive Committee on an individual basis.
Qualifying Requirements: In addition to the home department qualifying exam requirements, PhD students participating in the CSME doctoral program must pass the final exams in all three qualifying exam courses listed below. The three qualifying exam courses have been selected to provide a general broad set of tools in computational science. It is expected that most students will register for and take these courses (four units per course), but the CSME Qualifying Exam Committee may allow an exceptionally well-prepared student to take the final exams without taking the courses. Students must pass the qualifying examinations by the end of the second year or, on petition, by the end of the third year.
Courses taken to satisfy the qualifying requirements cannot count toward the elective requirements.
Elective Requirements: To encourage PhD students specializing in computational science to both broaden themselves in an area of science or engineering as well as to obtain more specialized training in specific areas of computational science, students will be required to take and pass two elective courses from the following approved List B (four units per course), both of which must be outside of their home department, the first of which must be taken for a letter grade, and the second of which may be taken pass/fail. The CSME Executive Committee may approve the use of courses not appearing on the following list on a case-by-case basis. Courses taken to satisfy the elective requirements cannot count toward the qualifying requirements.
Thesis/Dissertation: Students participating in the PhD in mathematics with a Specialization in Computational Science must complete a dissertation that meets all requirements for the regular PhD in the home department. In addition, it is expected that the PhD dissertation will be interdisciplinary in nature and involve some aspect of computational science.
Final Examination: Students participating in the PhD in mathematics with a Specialization in Computational Science must meet the regular final examination requirements of the home department.
The PhD in mathematics with a specialization in statistics is designed to provide a student with solid training in statistical theory and methodology that finds broad application in various areas of scientific research including natural, biomedical and social sciences, as well as engineering, finance, business management, and government regulations. It aims to produce future researchers in contemporary statistics, as well as give students an advantage as they seek careers in industry where there is a tremendous need for statistics knowledge following the rapid growth of computing power, high throughput technology, and the explosion of digital data.
Prospective students must apply to the mathematics PhD program. The admission requirements for the mathematics doctoral program are those outlined above. Demonstration of computer literacy is highly desired; knowledge of a programming language such as PERL or C; and knowledge of a statistical computing package such as SAS, R, SPLUS, or STATA is also desirable. The program may admit students without this level of preparation with the understanding that the student will promptly make up any deficiencies by taking additional courses upon entering the program.
Advancement to Candidacy: A student may advance to candidacy only after the course requirements, the qualifying examinations requirements, and comprehensive exam requirement have been completed. The remaining requirements for advancement to candidacy are the same as for the regular PhD in mathematics.
Dissertation and Final Defense: Students participating in the PhD in mathematics with a specialization in statistics must complete a dissertation and final defense that meets all requirements for the regular PhD in mathematics.
Time Limits: The time limits for the PhD in mathematics with a specialization in statistics are the same as for the regular PhD in mathematics.
Students who wish to switch between the regular PhD program in mathematics and the specialization in statistics must submit a written request to the graduate vice chair. Approval is not automatic, however.