The PhD 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 PhD in Mathematics and select “Statistics” in the ‘Current Area of Interest’ section of their online application (this means the person is applying for the Specialization in Statistics degree). The admission requirements for the mathematics doctoral program are those outlined above. General computer literacy, knowledge of a statistical computing package (in particular, R, but also SAS, STATA, Python, Matlab, Julia, etc), and some foundations in programming, are highly 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.
Specialization in Statistics Policies
- 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. 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 (Reading and Research) until they have passed at least two Qualifying Examinations at PhD General Pass level, or obtained approval of their faculty advisor.
- The core curriculum consists of forty (40) units as follows:
- The basic curriculum consists of the following five courses (20 units) which all students must take:
- MATH 281A-B-C (Mathematical Statistics)
- MATH 282A-B (Applied Statistics)
- Students must also take at least five courses (20 units) to be chosen from the following:
- MATH 280A-B-C (Probability Theory)
- MATH 284 (Lifetime Data Analysis)
- MATH 287A (Time Series Analysis)
- MATH 287B (Multivariate Analysis)
- MATH 287C (Advanced Time Series Analysis)
- MATH 287D (Statistical Learning)
- MATH 287E (Bootstrap & Resampling Methods)
- MATH 287F (Causal Inference)
- Students are encouraged to take further courses among the following:
- MATH 202A-B-C (Applied Algebra)
- MATH 212A-B (Introduction to Mathematical Biology)
- MATH 214 (Introduction to Computational Stochastics)
- MATH 216A-B-C (Mathematical Methods in Data Science)
- MATH 240A-B-C (Real Analysis)
- MATH 241A-B (Functional Analysis)
- MATH 245A-B-C (Convex Analysis and Optimization)
- MATH 261A-B-C (Probabilistic Combinatorics and Algorithms)
- MATH 270A-B-C (Numerical Analysis)
- MATH 271A-B-C (Numerical Optimization)
- MATH 273A-B-C (Advanced Techniques in Computational Math)
- MATH 277A (Topics in Computational and Applied Math)
- MATH 285 (Stochastic Processes)
- MATH 286 (Stochastic Differential Equations)
- MATH 289A-B (Topics in Probability and Statistics)
- MATH 294 (The Mathematics of Finance)
- The basic curriculum consists of the following five courses (20 units) which all students must take:
- Instead of the qualifying requirements of the general PhD, students in the Specialization must pass two written qualifying exams and one comprehensive exam. One of the qualifying exams must be Mathematical Statistics (MATH 281A-B-C) and the other qualifying exam can be freely chosen among those offered by the department, typically either in Real Analysis (MATH 240A-B-C) or in Numerical Analysis (MATH 270A-B-C). At least one of the exams should be passed at PhD General level before the start of the second year, and both exams must be passed, with at least one of them at the PhD Area level, before the start of the third year.
- Students are required to pass the comprehensive exam in Applied Statistics (MATH 282A-B) before the start of their third year.
- To acquire experience in statistical data analysis, students are required to either take one quarter of MATH 297 (Mathematics Graduate Research Internship) or do a quarter-length internship, typically during a summer quarter, in either an academic institution (typically an applied lab) or in industry. The internship needs to be pre-approved by the student’s advisor. Students are encouraged to do this after passing their qualifying exams.
- Exceptions to the required courses may be considered with the endorsement of the student’s faculty advisor and with the approval of the Graduate Vice-Chair.
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 CPhil 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.
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.
