PhD in Mathematics - Analysis and Partial Differential Equations 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 full-time professors and 4 adjunct instructors, the department is further enriched by postdoctoral fellows, 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, diverse campus. Our programs equip undergraduate and graduate students with professional expertise in teaching, mathematical research, or applied fields, while also delivering essential math courses to the broader UCI student body. The department serves roughly 110 graduate students, more than 615 undergraduate majors, and many others pursuing minors or specialized studies.

Doctoral candidates follow a structured path of coursework, seminars, and independent study to prepare for their Ph.D. qualifying exams, candidacy review, and dissertation. 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 the same subjects by year three. These requirements can be met through either annual Core Assessment Exams or fall Qualifying Exams, with a maximum of three attempts per subject. Students who pass a Qualifying Exam before taking the related course receive an exemption from that course.

Faculty research spans diverse areas, including multivariable complex function theory, harmonic analysis, critical point theory, dynamical systems, quantum mechanics applications, and nonlinear PDE analysis—covering fluid dynamics, diffusion processes, boundary value problems, and advanced mathematical physics.