# Ph.D. in Mathematics with a Specialization in Statistics

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.

## Admission

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 before advancement to Ph.D. candidacy.
- 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 core curriculum consists of the following (48 units), and a student is expected to take substantially all of them (subject to approval by the faculty advisor):
- 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)

- Additional coursework to complete the 72 units should be selected from the following:
- 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.