PhD in Mathematical Sciences
The Doctor of Philosophy (PhD) program in Mathematical Sciences represents achievement of a broad knowledge of the various branches of mathematics, of the ability to communicate mathematics in both written and oral form, and of a demonstrated creative ability in a particular branch of mathematics.
The program prepares students for careers in academia and as professional mathematicians. Students have the opportunity to work with some of the world's leading experts in a variety of research areas. The Department has particular strength in the interrelated fields of analysis, partial differential equations, and probability. Students interested in more applied directions can work with experts in mathematical bioscience, computational finance, and cryptography..
Students applying for the program should have or be expecting to obtain a bachelor’s degree either in mathematics or a related field.
The following background is required:
- Multivariable calculus at the level of MATH 2063
- Ordinary differential equations at the level of MATH 2073 or MATH 2074
- Linear algebra at the level of MATH 2076
- Experience with reading and constructing mathematical proofs at the level of MATH 3001
The following background is recommended:
- Analysis at the level of MATH 3002 or MATH 5101/6001
- Abstract linear algebra at the level of MATH 5103/6003
- Additional advanced courses in pure or applied mathematics
An official general GRE score is required for admission. This requirement is waived for applicants with at least 6 graduate credits in a relevant field with a cumulative GPA of 3.2 or higher. The requirement is also waived for UC undergraduates with a degree in a relevant field and a cumulative GPA of 3.5 or higher. A quantitative score of 160 or higher is recommended.
|IELTS (overall band)||6.5||7|
The English proficiency requirement is met for applicants with degrees earned in English from accredited universities and colleges in the US or other English-speaking countries.
Most of our PhD students receive full financial support via a teaching or research assistantship, and most are supported through their entire UC career. Travel support is available for students to attend or present their work at conferences.
All applicants for the PhD program are automatically reviewed for graduate assistantship eligibility at the time of application.
Applicants will need to meet the minimum requirements to be considered for the program. Completed applications will be reviewed beginning February 1. We will continue to receive applications until all positions are filled.
All application materials from international students requiring a US visa must be received prior to April 1 (but sooner is better) in order to allow time for the necessary paperwork to be processed. The visa application process can often take 90 days or more to complete.
How to apply:
1. Create an online application
2. Include these documents in your application:
- Three letters of recommendation. The application system will automatically send an email to each of the recommenders with a link to submit their letters.
- Unofficial copy of transcript (official transcript will be required if you are admitted to the program).
- GRE general test score
- Statement of purpose/cover letter
- English Proficiency for international students
3. Pay the application fee
UC’s CEEB college code is 1833, as established by The College Board. CEEB codes are used to ensure that test scores are sent to the correct institution.
The credit-hour requirement includes a minimum of 90 graduate credits beyond the bachelor's degree or a minimum of 60 credits beyond a master's degree, including 7 hours in dissertation research, with a GPA of 3.3 or higher.
All incoming PhD students are required to take the qualifying exam before the beginning of their first semester. Students who do not pass this exam at the PhD level are placed in the appropriate 6000 - level courses. The Mathematics Qualifying Exam is based on the two-semester sequence Advanced Calculus MATH6001-6002 and the one semester course Abstract Linear Algebra MATH6003.
All PhD students must pass four preliminary examinations. Each Preliminary Exam is offered twice a year. Examinations based on a course given during Fall Semester are offered after the end of Spring Semester and at the beginning of the following Fall Semester. Examinations based on a course given during the Spring Semester are offered at the beginning of the Fall Semester and at the beginning of the following Spring Semester.
After the preliminary examinations, an advanced examination in the area of examination of the student is required. An advanced exam may either be a written exam, a presentation or a series of presentations. The exam will be administered by a committee. Generally, this committee will form the students’ dissertation committee.
Visit the curriculum guide to learn about the required courses. More details concerning the requirements of the program are explained in the Mathematical Sciences Department’s Graduate Handbook. See the course descriptions for information on the content.
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