PhD in Mathematics - Probability in Irvine United States | University of California Irvine

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 tenured professors and 4 adjunct instructors, the department is further strengthened by postdocs, lecturers, and visiting professors who contribute significantly to both education and research. Established in 1965, UC Irvine merges top-tier academic research with Southern California's ideal setting, featuring excellent climate and a vibrant campus culture. Our programs equip undergraduate and graduate students with expertise for careers in teaching, mathematical research, or applied fields, while also delivering essential math courses to the broader UCI student body. The department serves about 110 graduate students, more than 615 undergraduate majors, and many others pursuing minors or specialized tracks.

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. By year three, they must clear two Ph.D.-level exams in these subjects. Students can fulfill these requirements through either annual Core Assessment Exams or fall-quarter Qualifying Exams, with a maximum of three attempts per subject. Those passing a Qualifying Exam before taking the related course receive an exemption from that course requirement.