ucsd math phd admissions

The Ph.D. in Mathematics, with a Specialization in Statistics is designed to provide a student with solid training in statistical theory and methodology that find 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, both in academia and industry, who will contribute to satisfy the tremendous need for new statistics theory and methodology following the rapid growth of computing power, high throughput technology, and the explosion of digital data acquisition technologies.

Prospective students must apply to the  Ph.D. program in Mathematics  and select "Statistics" in the "Current Area of Interest" section of their on line application (this means the person is applying the Specialization in Statistics degree). 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, S-PLUS or STATA are 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.

Program Requirements for the Specialization in Statistics

• The specialization requires completion of 72 units.
• 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.
• MATH 280A-B-C (Probability Theory)
• MATH 281A-B-C (Mathematical Statistics)
• MATH 282A-B (Applied Statistics)
• MATH 287A (Time Series Analysis)
• MATH 287B (Multivariate Analysis)
• MATH 287C (Advanced Time Series Analysis)
• MATH 287D (Statistical Learning)
• MATH 202A (Applied Algebra I)
• MATH 240A-B-C (Real Analysis)
• MATH 241A-B (Functional Analysis)
• MATH 261A-B-C (Probabilistic Combinatorics and Algorithms)
• MATH 270A-B (Numerical Analysis)
• MATH 271A-B-C (Numerical Optimization)
• MATH 283 (Statistical Methods in Bioinformatics)
• MATH 285 (Stochastic Processes)
• MATH 289A-B (Topics in Probability and Statistics)
• MATH 294 (The Mathematics of Finance)
• Candidates must acquire experience in statistical consulting and the practical analysis of data. To meet this requirement, students must participate in the MathStorm graduate student consulting seminar for one year. A project outside the consulting seminar can be substituted only if prior approval is obtained from the director of the consulting seminar and the student's advisor. Students should complete at least five quarters of coursework before taking the consulting seminar and are encouraged to fulfill the requirement in their third or fourth year.
• Students must pass two written qualifying exams. One of the required exams is in Mathematical Statistics (MATH 281A-B-C) the other is recommended to be in Real Analysis (MATH 240A-B-C). At least one of the exams should be passed at the Ph.D. level, and both exams should be passed at the provisional doctoral level or better.
• At least one of the exams should be passed at the provisional doctoral level before the start of the second year and both passed before the start of the third year, for the student to remain in the Ph.D. program.
• Before the start of the third year, the student is required to take Applied Statistics (MATH 282A-B) and pass the comprehensive exam in this subject.
• No foreign language requirement.

Advancement to Candidacy

It is expected that by the end of the third year (9 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 C. Phil. degree.

Dissertation and Final Defense

Students participating in the Ph.D. in Mathematics with a Specialization in Statistics must complete a dissertation and final defense that meets all requirements for the regular Ph.D. in mathematics.

Students who wish to switch between the regular Ph.D. program in Mathematics and the Specialization in Statistics must submit a written request to the graduate vice chair for consideration. Approval is not automatic, however.

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UC San Diego Graduate Application Management

At the University of California San Diego, diversity is a core component of excellence that further enhances our quality and achievement. We seek a diverse graduate student body to ensure that all of our students gain the educational benefits that result from being exposed to a broad spectrum of ideas and perspectives. These include the variety of personal experiences, values, and worldviews that arise from differences of culture and circumstance. Such differences include race, ethnicity, gender, age, religion, language, abilities/disabilities, sexual orientation, socioeconomic status, geographic region and more. We wish to broaden and deepen both the educational experience and the scholarly environment, as students and faculty learn to interact effectively with each other, preparing them to participate in an increasingly complex and pluralistic society. We also want all of our students to contribute to the campus community in a manner that enhances campus diversity and inclusiveness, consistent with the  University of California Principles of Community .

Applications for Fall 2025 will begin opening on September 4, 2024 no earlier than 12 pm PST.

Application opening dates and deadlines vary by department. Please visit the website for your department of interest to verify their application's opening and closing dates.

If your program of interest is not listed on the application, please contact the  department  to confirm availability.

If you experience technical issues with the application, please contact  [email protected]  with a description of the problem.  

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[ graduate degrees offered | division of graduate education and postdoctoral affairs | general requirements for higher degrees | financial ]

Admission Requirements

Applicants for graduate admission must present official evidence of receipt of a baccalaureate degree from an accredited institution of higher education or the equivalent, with training comparable to that provided by the University of California. A minimum scholastic average of B (3.0 on a 4.0 scale) or its equivalent for course work completed in upper-division or prior graduate study.

Admission Policies

Duplication of advanced degrees.

Normally, duplication of advanced academic degrees—MA, MS, PhD—is not permitted. A duplicate academic degree is one at the same level (e.g., a second master’s degree or second PhD), regardless of the discipline or the specialization awarding the degree. A professional degree at the master’s or doctoral level (e.g., AuD, DMA, EdD, MAS, MBA, MSBA, MCEPA, MPH, MDSO, DDPM, MEd, MEng, MF, MTech, MFA, MIA, MPAc, MPP, MD, PharmD) is not regarded as a duplicate of an academic degree.

Students who already hold an advanced academic degree may be admitted to UC San Diego to pursue a second advanced academic degree at the same level only under limited circumstances, and only with the consent of the graduate dean (on behalf of the Graduate Council). Recognizing that there are circumstances in which it is appropriate for a student to pursue a second degree, the graduate dean will consider the following criteria when reviewing requests for permission to do so at UC San Diego:

• The degree already held by the student must be in a fundamentally different disciplinary field from the department or program to which the student is applying. A request for permission to be admitted to a degree program at UC San Diego should document this clearly and should indicate the differences both in intellectual training and in qualification for future employment that the second degree would confer.
• The department or program considering the applicant must make a clear case that there is no other way at UC San Diego for the student to obtain the same outcome for future employment prospects (e.g., by pursuing a master’s program or postdoctoral study rather than a second PhD).

If the decision of the graduate dean is that the student should be admitted to a particular department or program for a master’s degree alone, the student is barred from requesting permission to continue for a PhD in that department or program.

Departments and programs that award an MA or MS in the course of progress toward the PhD may confer the master’s degree on any enrolled PhD student who has met the departmental and university requirements for the degree, unless the student already holds an MA or MS in the same or related field. In particular, departments and programs may confer the MA or MS on a PhD student who holds a master’s degree in a different discipline without the need for a petition to the Graduate Council or the dean of the Division of Graduate Education and Postdoctoral Affairs.

Departments and programs are encouraged to consider waiving precandidacy requirements for students who already hold a master’s degree in the same or related field in order to decrease the time to degree.

Part-Time Study, Including Half-Time

Students who enroll in fewer than twelve graduate or upper-division units each quarter are considered part-time students. International students on F1 or J1 visas must be enrolled full-time each quarter. Students who are approved by their major department and by the dean of the Division of Graduate Education and Postdoctoral Affairs for enrollment in a program of half-time study (maximum of six units or fewer) for reasons of occupation, family responsibilities, or health, may be eligible for a reduction in fees. All other part-time students (seven to twelve units) pay the same fees as full-time students.

Part-time study may be pursued in several masters’ programs and a few doctoral programs at UC San Diego. In all instances, part-time students must satisfy the same admission requirements as full-time students and are eligible, at the discretion of a department, for appointment to 25 percent time teaching or research assistantships. Admitted students must file the petition for half-time study with the Division of Graduate Education and Postdoctoral Affairs no later than the last day of the second week of the quarter to be eligible for a fee reduction.

Application Procedures

When to apply.

Each graduate program sets a unique application deadline. Most deadlines occur between December and February for admission to fall quarter. A few programs accept applications for winter, spring, and summer admissions. For specific program deadlines, refer to the  Division of Graduate Education and Postdoctoral Affairs website or contact the specific graduate program office. Applicants need not have completed their undergraduate programs prior to applying.

How to Apply

UC San Diego utilizes an online application. Payment of the nonrefundable application fee is made by credit card. The online application can be accessed via the Division of Graduate Education and Postdoctoral Affairs website, where detailed instructions for completion of the application are provided.

Additional program and application information can be obtained from each graduate program office. Access the UC San Diego website and the appropriate program’s graduate study information. Telephone numbers and campus addresses are listed with the department information in this catalog. The primary documents required in support of an application are listed below. Each program may require additional documents.

Required Supporting Documents

All supporting documents, including letters of recommendation, should be completed using the online application. Any supplemental materials may be uploaded to the online application or emailed directly to the applicant’s prospective major department or program according to department or program specifications.

All required supporting documents must be submitted before the start of the quarter to which an applicant is admitted. Failure to submit required documents by Friday of the fourth week of the quarter will result in a hold on future registration until the documents are provided.

Academic Records

Transcripts for all previous academic work completed after high school graduation, including certification of degrees received or documentation of status upon leaving each institution, is required for each application submitted. Official records bearing the signature of the registrar and the seal of the issuing institution are required upon admission to the applicant’s program of interest. Applicants with academic work in progress who expect to complete a degree program before the intended date of enrollment at UC San Diego must submit evidence of degree conferral and a final academic record as soon as they are available. The undergraduate degree must be completed prior to the start of graduate study.

International Applicant Academic Records

All admitted applicants who have earned a degree(s) from an institution(s) outside of the United States and intend to enroll at UC San Diego are required to complete and submit a WES Course-by-Course evaluation . They may create their account via wes.org . Applicants will be prompted to input their academic history, and will then be provided with a list of documents required for the completion of their evaluation. Once the evaluation has been completed it must be sent directly to the Division of Graduate Education and Postdoctoral Affairs Admissions Office for review. Applicants with academic work in progress who expect to complete a degree program before the intended date of enrollment at UC San Diego must provide evidence of degree conferral and a final academic transcript as soon as they are available.

Foreign academic records should show titles of all courses attended each year, years of study (or duration of study), examinations passed, seminars completed, and grades or marks received in all institutions where formal records are maintained. Official evidence of degree conferral must also be supplied, together with evidence of rank in class if possible.

Graduate Record Examinations (GRE) Scores

Graduate applicants may be required to submit GRE scores for consideration for certain degree programs. Some programs may require additional tests or other alternatives.

Review program-specific admissions requirements by locating departments on this page to determine which tests may be required.

Applicants may be permitted to self-report scores at the time of application submission. Only official scores sent to UC San Diego by ETS will be accepted as official.

Letters of Recommendation

Applicants should arrange to have letters of recommendation submitted online to UC San Diego. The number of recommendations required by departments may vary. Review program-specific admissions requirements by locating departments on this page to determine which tests may be required. If paper letters are necessary, they must be mailed to the prospective major department, group, or school. It is most important that letters of recommendation be completed by individuals in a position to analyze an applicant’s abilities and academic or professional promise.

International Applicant Requirements

English language test.

Demonstrated proficiency in the English language is required for all international applicants whose native language is not English. Non-native English language speakers may be exempt from this requirement if they have earned or will be earning a bachelor’s, master’s, or doctoral degree with grades of B (3.0) or better from either:

• A regionally accredited US college or university where English is the sole language of instruction, or
• A foreign college or university which provides instruction solely in English. Applicants may verify whether they meet this requirement by using the IAU World Higher Education Database (WHED). If English is not the sole language of instruction listed, if no language is listed at all, or if the institution does not appear on the WHED website, applicants are required to submit English proficiency exam scores. No other documentation (e.g., letters, language certificates, school websites) may be used in place of WHED as a means to obtain an exemption from the English proficiency requirement.

The Test of English as a Foreign Language (TOEFL) : The minimum TOEFL score for admission is 85 for the Internet Based Test and 64 for the Paper Based Test. Please note the Paper Based Test does not have a speaking component. TOEFL information and forms are available at the TOEFL website.

The International English Language Testing System (IELTS) Academic Training exam: The minimum IELTS score is Band 7.0. IELTS registration information is available on the IELTS website.

The Pearson Test of English Academic (PTE Academic) . The minimum PTE academic score required for graduate admission is overall score 65. Registration and test information is available on the Pearson website.

International students whose native language is not English will be required to demonstrate English language proficiency before they may serve as teaching assistants.

International Applicant Financial Statement

International applicants accepting admission to UC San Diego are required to certify that they possess sufficient funds to cover all fees, transportation, and living expenses during the first academic year of graduate enrollment at UC San Diego. Please refer to this link for required funding for your program and acceptable financial documents to submit: https://ispo.ucsd.edu/submit-request/i20-ds2019-funding.html

Opportunities for employment, on or off campus, are extremely limited, and international applicants should not base their educational plans on the hope of finding employment after arriving in the United States.

Admission and Registration

Official admission to graduate study at the university is contingent upon review of an applicant’s record; receipt of official final undergraduate transcript showing degree(s) awarded; receipt of official final graduate transcripts showing degree(s) awarded if applicable; receipt of post-graduate academic records; an affirmative recommendation by the prospective department, group, or school; and action by the Division of Graduate Education and Postdoctoral Affairs. The graduate dean or the prospective major department, group, or school may deny admission if an applicant’s scholastic record is undistinguished, if the preparation is judged inadequate as a foundation for advanced work, or in the event that no further students can be accommodated for a given quarter. Only the official Letter of Admission from the dean of the Division of Graduate Education and Postdoctoral Affairs constitutes formal approval of admission to a graduate program at UC San Diego.

Official notification of admission by the dean of the Division of Graduate Education and Postdoctoral Affairs will be sent via email well in advance of the beginning of the quarter for which application has been made. Applicants should contact their prospective major department if formal notification is not received four weeks prior to the beginning of the quarter for which they applied.

Admission to graduate standing does not constitute registration for classes. A student is not officially registered for classes until the entire registration procedure is completed each quarter. Information and all necessary registration materials will be available at department offices approximately two weeks before the opening of the quarter. (See Academic and Administrative Calendar .)

Deferral and Reapplication

Applicants who are admitted but decide not to register in the quarter for which they first apply may request deferral of their application for a later quarter within the same academic year or the academic year immediately subsequent. This request must be made no later than the first day of instruction of the quarter the applicant was originally admitted to. Application for admission of an approved deferred applicant for the subsequent academic year may be made by submitting a statement of activities and official transcripts of any academic work undertaken since the first application to the department or group. Admission is not guaranteed to previously admitted applicants who have an approved deferral. In no case are application files retained for more than four consecutive academic quarters from the date of first application. Application after this period may be made only by completing a new application and providing all necessary documents, including payment of the graduate application fee.

Students who are denied admission must submit a new application and fee together with required documentation in order to be considered for admission in another academic year.

Readmission

A graduate student whose status has lapsed because of an interruption in registration must petition his or her department for readmission at least eight weeks prior to the first day of the quarter in which reenrollment is intended. Do not submit an application for admission. Students must submit supplementary transcripts of all academic course work undertaken since last enrolled at UC San Diego to their home program, pay a readmission fee of $135, and complete a General Petition and a supplementary Statement of Activities. In addition, a Statement of Legal Residence is required for all students returning after an absence of two quarters or more.

Readmission is not automatic.  

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• Mathematics

CSME Ph.D. Program Structure

The structure of the CSME Ph.D. Program is described completely on this webpage. It is based on the CSME Ph.D. Proposal Document, which can be found on the CSME Resources webpage. However, as the program periodically evolves to address new developments, the information on this webpage should be viewed as the most accurate and current information about the CSME Ph.D. Program.

Ph.D. Program Overview

The CSME Ph.D. Program at UCSD is a campus-wide interdisciplinary training program designed to train the next generation of scientists, mathematicians, and engineers in the use of modern tools of computational science. The CSME Doctoral Program is integrated into the existing doctoral programs of a number of core participating departments (see the CSME Overview webpage for the list of participating departments). The CSME Doctoral Program leads to a normal Ph.D. in the field of the specific participating department, with an additional credential of ``Specialization in Computational Science''. A "Specialization" is a formal University of California mechanism that allows a graduate student pursuing a Ph.D. in the UC System to obtain the Doctoral equivalent of a minor in a particular area of specialization. The CSME Ph.D. program involves modification of the standard graduate degree requirements in the core participating departments to allow students to complete additional requirements to earn a computational science specialization to their doctoral degree. The overall CSME Graduate Program is administered by the Center for Computational Mathematics within the UCSD Mathematics Department, but in all other respects the core participating departments are completely equal partners in the design, development, management, and evolution of the CSME Graduate Program.

Ph.D. Program Admission

Prospective students must apply to the Ph.D. program of a participating home department, be admitted to that department and then be admitted to the specialization through the CSME Program. The participating academic departments which allow their doctoral students to specialize in computational science through the CSME doctoral program are listed on the CSME Overview webpage. For more information about admission see the CSME Application and Admission webpage.

Ph.D. Program Structure and Requirements

Requirements consist of those of the doctoral program in the admitting home department (one of the participating departments) as well as the CSME proficiency, qualifying and elective course requirements as outlined below. Requirements and policies relating to the home department can be found in the General Catalog under that department's name, or by contacting the home department directly.

• The specialization requires that students complete all home department requirements for the Ph.D. along with satisfying the CSME proficiency, qualifying and elective requirements (see below). Note that some participating departments have modified their internal Ph.D. requirements specifically for CSME Ph.D. students (for example, the Dept. of Mathematics ); contact the individual participating department for information.
• CSME Proficiency (see below) must be satisfied by the end of the first year.
• The CSME Qualifying Exams (see below) must be passed by the end of the second year or, on petition, by end of the third year.
• The CSME qualifying exams can be attempted repeatedly but no more than once per quarter per subject.
• The regular qualifying exams in the home department and the CSME qualifying exams must all be passed before the student is permitted to take the candidacy (senate) exam.
• Two CSME electives (see List B below) outside the home department must be taken.
• The two CSME electives can be taken at any time before defending the thesis.
• One of the CSME electives may be taken Pass/Fail; the other must be taken for a letter grade.
• Full-time students are required to register for a minimum of twelve (12) units every quarter. Eight (8) of these twelve (12) units must be graduate-level CSME Program courses taken for a letter grade.

Proficiency Requirements

All Ph.D. 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 UCSD's courses in both subjects while enrolled in the graduate program (4 units per course):

• Numerical Methods (MATH 174/274 or MAE 290A)
• Data Structures and Algorithms (CSE 100/101)

Alternatively, proficiency in the material contained in these courses may be satisfied by having previously taking these or equivalent courses at other institutions, or through other evidence of sufficient knowledge of this material. Demonstrating proficiency without taking these courses at UCSD is subject to approval by the CSME Executive Committee on an individual basis.

Qualifying Requirements

In addition to the home department doctoral program qualifying exam requirements, Ph.D. 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 (4 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. The following CSME qualifying courses must be taken for a letter grade:

• MATH 275 or MAE 290B (Numerical PDE)
• PHYS 244 or CSE 260 (Parallel Computing)
• Course to be selected from LIST A

LIST A: CSME Qualifying Exam Courses

The LIST A set of courses is a fairly small collection of computational science and applied mathematics courses that represents core knowledge in modern computational science. Courses taken from LIST A to satisfy the qualifying requirements cannot be used to satisfy the LIST B elective requirement.

• MATH 270A, B or C (Numerical Analysis; Not permitted for Math Students, who typically take MATH 270ABC as a normal mathematics qual course)
• MATH 271A, B or C (Numerical Optimization)
• MATH 272A, B or C (Numerical Partial Differential Equations)
• MATH 273A, B or C (Advanced Techniques in Computational Mathematics)
• MAE 223 (Computational Fluid Dynamics)
• MAE 232 / SE 276A, B or C (Computational Solid Mechanics)
• MAE 280A or B (Linear Systems Theory)
• MAE 294 / SIO 203A, B or C (Introduction to Applied Mathematics)
• PHYS 221 AB (Nonlinear dynamics)
• PHYS 243 (Stochastic Methods)
• SE 233 (Computational and Technical Aspects of Finite Element Methods)
• CHEM 285 (Introduction to Computational Chemistry)
• (Additional Courses To Be Determined by Executive Committee or Allowed by Petition)

Elective Requirements

To encourage CSME Ph.D. students 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, 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 courses must be selected from the following approved List B (4 units per course). 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 can not count toward the qualifying requirements (and vice-versa) if the particular course appears on both List A and List B.

LIST B: Elective Graduate Courses in Mathematics, Science, and Engineering

The LIST B set of courses is a slowly expanding collection of computational science, science, and applied mathematics courses that encourages CSME doctoral students to increase their breadth across disciplines, and also gives students the opportunity to achieve substantial depth in a particular secondary discipline. (LIST B is a superset of LIST A above.) A course taken from LIST A to satisfy the qualifying exam requirement cannot be used to satisfy the LIST B Elective requirement.

• Any course appearing on List A above
• PHYS 241 (Computational Physics I)
• PHYS 242 (Computational Physics II)
• MAE 222 (Flow Control)
• MAE 261 (Cardiovascular Fluid Mechanics)
• SE 277 (Error Control in Finite Element Methods)
• SE 278A (Computational Fluid Dynamics)
• SE 278B (Computational Fluid-Structure Interaction)
• CHEM 215 (Modeling Biological Macromolecules
• BGGN 260 (Neurodynamics)
• ECE 272 (Dynamical Systems under Uncertainty)
• CSE 250A or B (Principles of Artificial Intelligence)
• MATH 210A, B or C (Mathematical Methods in Physics and Engineering)
• MATH 282A or B (Applied Statistics)
• MATH 231A, B, or C (Partial Differential Equations)

CSME electives from list B do not have to be taken for a letter grade, subject to item 9 in the above PhD Program Structure and Requirements list.

Thesis/Dissertation

Ph.D. students participating in the CSME doctoral program must complete a dissertation which meets all requirements for the regular Ph.D. in the home department. In addition, it is expected that the Ph.D. dissertation will be interdisciplinary in nature and involve some aspect of computational science. Final Examination

Ph.D. students participating in the CSME doctoral program must meet the regular final examination requirements of the home department.

Time Limits and other Requirements for the Ph.D.

All requirements for the Ph.D. in the home department are enforced for CSME Ph.D. students, unless the specific department has modified the internal structure of their Ph.D. program to allow for CSME participation (for example, the Dept. of Mathematics ).

Relationship of the CSME Ph.D. Program with Existing Graduate Programs at UCSD

See the CSME MS Program webpage for a discussion on this topic.

General Catalog 2010-2011

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Mathematics

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OFFICE: 7018 Applied Physics and Mathematics Building, Muir College http://math.ucsd.edu

The Graduate Program

The Department of Mathematics offers graduate programs leading to the M.A. (pure or applied mathematics), M.S. (statistics), and Ph.D. degrees.

The application deadline for fall admission is January 7 for Ph.D. candidates, and February 7 for M.A./M.S. 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 no older than twelve months 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 Ph.D. program.

General Requirements

All student course programs must be approved by a faculty advisor 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, Ph.D. candidates may take all course work on a Satisfactory/Unsatisfactory basis. Typically, students should not enroll in Math. 299 until they have satisfactorily passed both qualifying examinations (see “ Ph.D. in Mathematics ”) or obtained approval of their faculty advisor.

Master of Arts in Pure Mathematics

[Offered only under the Comprehensive Examination Plan.] The degree may be terminal or obtained on the way to the Ph.D. A total of forty-eight units of credit is required. Twenty-four of these units must be graduate-level mathematics courses approved in consultation with a faculty advisor.

In the selection of course work to fulfill the remaining twenty-four units, the following restrictions must be followed:

• No more than eight units of upper-division mathematics courses.
• No more than twelve units of graduate courses in a related field outside the department (approved by the Department of Mathematics).
• No more than four units of Math. 295 (Special Topics) or Math. 500 (Apprentice Teaching).
• No units of Math. 299 (Reading and Research) may be used in satisfying the requirements for the master’s degree.

Comprehensive Examinations

Seven written departmental examinations are offered in three areas (refer to “ Ph.D. 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 M.A. pass or better.

Foreign Language Requirement

A reading knowledge of one foreign language (French, German, or Russian) is required. In exceptional cases other languages may be substituted. Testing is administered by faculty in the department who select published mathematical material in one of these languages for a student to translate.

Time Limits

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.

Master of Arts in Applied Mathematics

[Offered only under the Comprehensive Examination Plan] The degree may be terminal or obtained on the way to the Ph.D. 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):

202A-B-C. (Applied Algebra)

210A-B-C. (Mathematical Methods in Physics and Engineering)

261A-B-C. (Probabilistic Combinatorics and Algorithms)

264A-B-C. (Combinatorics)

270A-B-C. (Numerical Mathematics)

271A-B-C. (Numerical Optimization)

272A-B-C. (Numerical Partial Differential Equations)

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:

220A-B-C. (Complex Analysis)

231A-B-C. (Partial Differential Equations)

240A-B-C. (Real Analysis)

280A-B-C. (Probability Theory)

281A-B-C. (Mathematical Statistics)

282A-B. (Applied Statistics)

In choosing course work to fulfill the remaining twenty-four units, the following restrictions must be followed:

• At least eight units must be approved graduate courses in mathematics or other departments [a one-year sequence in a related area outside the department such as computer science, engineering, physics, or economics is strongly recommended];
• A maximum of eight units can be approved upper-division courses in mathematics; and
• A maximum of eight units can be approved upper-division courses in other departments.
• A maximum of four units of Math. 500 (Apprentice Teaching).
• NO UNITS of Math. 295 (Special Topics) or Math. 299 (Reading and Research) may be used.

Students are strongly encouraged to consult with a faculty advisor 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.

There is no foreign language requirement for the M.A. in applied mathematics.

Full-time M.A. 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.

Master of Science in Statistics

[Offered only under the Comprehensive Examination Plan.] The M.S. 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

• Math. 281A-B-C. (Mathematical Statistics)
• Math. 282A-B. (Applied Statistics)

and any two topics comprising eight units chosen freely from Math. 287A-B-C and 289A-B (see course descriptions for topics).

The following guidelines should be followed when selecting courses to complete the remaining twenty units:

• For a theoretical emphasis, Math. 280A-B-C (Probability Theory) is required.
• For an applied orientation, Math. 270A-B-C (Numerical Mathematics) is recommended.
• A maximum of eight units of approved upper-division applied mathematics courses (see faculty advisor) and Math. 500 (Apprentice Teaching).

Upon the approval of the faculty advisor, the rule above, limiting graduate units from other departments to eight may be relaxed in making up these twenty non-core units.

Two written comprehensive examinations must be passed at the master’s level in related course work (approved by a faculty advisor). Instructors of the relevant courses should be consulted for exam dates as they vary on a yearly basis.

There is no foreign language requirement for the M.S. in statistics.

Full-time M.S. 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.

Ph.D. in Mathematics

Written qualifying examinations.

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)

• Three qualifying exams must be passed. At least one must be passed at the Ph.D. level, and a second must be passed at either the Ph.D. or Provisional Ph.D. Level The third exam must be passed at least at the master’s level.
• Of the three qualifying exams, there must be at least one from each of Areas #1 and #2. Algebra and Applied Algebra do not count as distinct exams in Area #2.
• Students must pass a least two exams from distinct areas with a minimum grade of Provisional Ph.D. (For example, a Ph.D. pass in Real Analysis, Provisional Ph.D. Pass in Complex Analysis, M.A. pass in Algebra would NOT satisfy this requirement, but a Ph.D. Pass in Real Analysis, M.A. pass in Complex Analysis, Provisional Ph.D. Pass in Algebra would, as would a Ph.D. Pass in Numerical Analysis, Provisional Ph.D. Pass in Applied Algebra, and M.A. pass in Real Analysis.)
• All exams must be passed by the September exam session prior to the beginning of the third year of graduate studies. (Thus, there would be no limit on the number of attempts, encouraging new students to take exams when they arrive, without penalty.)

Department policy stipulates that at least one of the exams must be completed with a Provisional Ph.D. 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 Ph.D. 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 Ph.D. Program when the qualifying exam requirements for the Ph.D. Program have been met and a dissertation advisor 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 for purchase in the Graduate Office.

In choosing a program with an eye to future employment, students should seek the assistance of a faculty advisor and take a broad selection of courses including applied mathematics, such as those in Area #3.

A reading knowledge of one foreign language (French, German, or Russian) is required prior to advancing to candidacy. In exceptional cases other languages may be substituted. Testing is administered within the department by faculty who select published mathematical material in one of these languages for a student to translate.

Advancement to Candidacy

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 C.Phil. degree.

Dissertation and Final Defense

Submission of a written dissertation and a final examination in which the thesis is publicly defended are the last steps before the Ph.D. 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 Ph.D. In mathematics is five years. Students must have a dissertation advisor 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 UCSD cannot exceed seven years.

A student making normal progress must meet the time limits described below. Ph.D. students who fail to meet these time limits may lose their TA funding.

• Pass Qualifying Exams requirement by the fall quarter of the beginning of the third year.
• Find Thesis advisor by the end of nine quarters.
• Advance to Candidacy by the end of eleven quarters.
• Final Defense by the end of the fifth year.

Ph.D. in Mathematics with Specialization in Computational Science

The Ph.D. 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 Ph.D. 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.

Specialization in Computational Science Policies

• The specialization requires that students complete all home department requirements for the Ph.D. along with satisfying the CSME proficiency, qualifying, and elective requirements. In the case of the mathematics department, the requirements and timelines for the normal mathematics Ph.D. program are as described above.
• CSME Proficiency (see below) must be satisfied by the end of the first year.
• The CSME qualifying exams must be passed by the end of the second year or, on petition, by end of the third year.
• The CSME qualifying exams can be attempted repeatedly but no more than once per quarter per subject.
• The regular qualifying exams in the home department and the CSME qualifying exams must all be passed before the student is permitted to take the candidacy (Senate) exam.
• Two CSME electives outside the home department must be taken.
• The two CSME electives can be taken at any time before defending the thesis.
• One of the CSME electives may be taken Pass/Fail; the other must be taken for a letter grade.
• No CSME field examination requirements will be imposed beyond those of the admitting home department.
• No CSME foreign language requirements will be imposed beyond those of the admitting home department.

Proficiency Requirements: All Ph.D. 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 UCSD’s courses in both subjects while enrolled in the graduate program (four units per course):

• Numerical Methods (Math. 174/274 or MAE 290A)
• Data Structures and Algorithms (CSE 100/101)

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 UCSD is subject to approval by the CSME Executive Committee on an individual basis.

Qualifying Requirements: In addition to the home department qualifying exam requirements, Ph.D. 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.

• Math. 275 or MAE 290B (Numerical PDEs)
• Phys. 244 or CSE 260 (Parallel Computing)
• Course to be selected from List A

LIST A: CSME Qualifying Exam Courses

Courses taken to satisfy the qualifying requirements cannot count toward the elective requirements.

• Phys. 243 (Stochastic Methods)
• Math. 270A, B, or C (Numerical Analysis; not permitted for math. students, who typically take Math. 270A-B-C as a normal mathematics qualifying course.)
• Math. 272A, B, or C (Advanced Numerical PDEs)
• MAE 223 (Computational Fluid Dynamics)
• MAE 232A or B (Computational Solid Mechanics)
• MAE 280A or B (Linear Systems Theory)
• (To be determined by Executive Committee)

Elective Requirements : To encourage Ph.D. 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.

LIST B: Elective Graduate Courses in Mathematics, Science, and Engineering

• Math. 270A-B-C (Numerical Analysis; not permitted for math. students, who typically take Math. 270A-B-C as a normal mathematics qualifying course.)
• Math. 271A-B-C (Optimization)
• Math. 272A-B-C (Advanced Numerical PDEs)
• Math. 273A-B-C (Computational Mathematics Project)
• Phys. 141/241 (Computational Physics I)
• Phys. 142/242 (Computational Physics II)
• Phys. 221 AB (Nonlinear dynamics)
• Chem. 215 (Modeling Biological Macromolecules)
• BGGN 260 (Neurodynamics)

Thesis/Dissertation: Students participating in the Ph.D in mathematics with a Specialization in Computational Science must complete a dissertation that meets all requirements for the regular Ph.D. in the home department. In addition, it is expected that the Ph.D. dissertation will be interdisciplinary in nature and involve some aspect of computational science.

Final Examination: Students participating in the Ph.D. in mathematics with a Specialization in Computational Science must meet the regular final examination requirements of the home department.

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