Irvine,
CA,
United States
Type
Public
Degrees offered
Bachelor's Degree
PhD in Mathematics - Algebra and Number Theory in Irvine United States | University of California Irvine
University of California Irvine
|
Irvine United States
Visit institution website
for more information
Qualification
Doctor of Philosophy
Languages
English
Delivery Mode
On-Campus
Tuition (2025)
USD
26,802
Attendance
Full-time
Full-time Duration
72 months
The Mathematics Department at UC Irvine boasts distinguished faculty who excel in teaching, conducting groundbreaking research across pure and applied mathematics, and supporting the community through STEM outreach initiatives. With 34 permanent faculty members and 4 adjunct instructors, the department is further strengthened by postdoctoral researchers, lecturers, and visiting professors who contribute significantly to both teaching and research. Established in 1965, UC Irvine merges top-tier research opportunities with Southern California's ideal setting, featuring excellent climate and a vibrant, diverse campus. Our programs equip undergraduate and graduate students with professional expertise in teaching, mathematical research, or applied fields, while also delivering essential mathematics courses to the broader UCI student body. The department serves around 110 graduate students, more than 615 undergraduate majors, and many others pursuing minors or specialized concentrations.
Doctoral candidates follow a structured path of coursework, seminars, and independent study to prepare for Ph.D. qualifying exams, candidacy reviews, and dissertation work. First-year students must pass two out of three M.S.-level exams in Real Analysis, Complex Analysis, and Algebra by their second year, followed by two Ph.D.-level passes in these subjects by year three. Students can fulfill these requirements through either annual Core Assessment Exams or fall Qualifying Exams, with a maximum of three attempts per subject. Passing a Qualifying Exam before taking the related course grants exemption from that course.
UCI's Algebra and Number Theory group explores diverse fields such as coding theory, cryptography, elliptic curves, Iwasawa theory, noncommutative geometry, L-functions, and finite field varieties. Regular seminars cover Number Theory, Cryptography, and Algebra topics.
Destination of Study
Subjects of Study
Language Requirements
English
IELTS 7.0
Qualification Requirements
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.
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.
Tuition
USD
26,802