Doctor of Philosophy in Mathematics - Algebra and Number Theory

The faculty of the Department of Mathematics at the University of California, Irvine are prominent scholars engaged in teaching, fundamental research in both pure and applied mathematics, and service to the local community with outreach efforts to foster success in STEM disciplines (science, technology, engineering, and mathematics). The Department includes 34 permanent faculty members together with 4 permanent adjunct instructors and is augmented by an equal number of postdoctoral researchers, lecturers, and visiting assistant professors, who play a vital role in teaching and research. Founded in 1965, the University of California, Irvine combines the strengths of a major research university with the perfect Southern California location, wonderful weather, and a diversified campus community and culture. We offer undergraduate and graduate students a program of study leading to professional competence in teaching, mathematical research, or in an area of application. Additionally, we serve the entire student population at UCI by providing required courses in Mathematics. The Department population includes approximately 110 graduate students, over 615 undergraduate majors, and numerous students completing minors, specializations, and concentrations.

When accepted into the doctoral program, the student embarks on a program of formal courses, seminars, and individual study courses to prepare for the Ph.D. written examinations, advancement to candidacy oral examination, and dissertation. By the start of the second year, students must achieve at least two passes at the M.S. level among three exams in Real Analysis, Complex Analysis and Algebra. By the start of the third year, students must achieve at least two passes at the Ph.D. level among three exams in Real Analysis, Complex Analysis and Algebra. To satisfy the exam requirements, students may take the Core Assessment Exams (offered in the Spring of every year) or the Qualifying Exams (offered before the start of the fall quarter) in these areas. Students may not attempt to take an exam in a particular subject area more than 3 times. A student who passes a Qualifying examination prior to taking the corresponding course will be exempted from taking the course.

Members of the Algebra and Number Theory group at UCI work in several areas of number theory and algebraic geometry, including coding theory, cryptography, elliptic curves and abelian varieties, Iwasawa theory, noncommutative geometry, special values of L-functions, and varieties over finite fields. There are seminars in Number Theory, Cryptography, and Algebra.

Hold a bachelor's degree (or equivalent) from a recognized academic institution with degree standards equivalent to those of the University of California
Have a minimum cumulative undergraduate GPA of 3.0
Transcripts Applicants must upload unofficial transcripts for all institutions attended since high school. If an applicant is admitted, official transcripts will be requested only from the institutions were a degree was earned. Foreign applicants must provide transcripts converted to English, and a calculated US GPA
Personal History Statement This will be required by all students, please see the Graduate Division website for more information.
Letters of Recommendation We require three letters of recommendation. Letters must be uploaded digitally, paper LORs will not be accepted.
GRE Official scores are required for the General and Subject GRE exam taken within the last five years for MS & PhD applicants. Subject GRE scores are mandatory for all PhD applicants. PhD applications will not be reviewed without Subject GRE scores. MS applications will be reviewed, however, priority will be given to applicants with Subject GRE scores. No minimum score requirement. International Students - International and permanent resident graduate students who are not citizens of countries where English is either the primary or dominant language (as approved by the UC Irvine Graduate Council) who wish to be considered for appointment as a Teaching Assistant (TA) must have a score of at least 26 in the speaking component of TOEFL iBT or a score of 8 or higher on the speaking module of the IELTS exam. This is a university requirement, the department cannot make exceptions for scores below 26 or 8, respectively.
TOEFL iBT minimum score of 80
IELTS - An overall minimum score of 7.0 for admission, with a score of no less than 6.0 on any individual module.