PhD in Mathematics - Inverse Problems and Imaging in Irvine United States | University of California Irvine

The Mathematics Department faculty at UC Irvine are distinguished scholars dedicated to teaching, conducting groundbreaking research in both theoretical and practical mathematics, and serving the community through STEM outreach initiatives. With 34 permanent faculty members and 4 adjunct instructors, the department is further enriched by postdoctoral researchers, lecturers, and visiting professors who contribute significantly to both education and research. Established in 1965, UC Irvine blends top-tier academic research with an ideal Southern California 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 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 Ph.D. qualifying exams, candidacy reviews, and dissertation work. By their second year, students must pass at least two M.S.-level exams in Real Analysis, Complex Analysis, or Algebra. By year three, they must pass two Ph.D.-level exams in these subjects. Students can meet these requirements through Core Assessment Exams (held annually in spring) or Qualifying Exams (before fall quarter). Each subject exam may be attempted no more than three times. Passing a Qualifying Exam before taking the related course grants an exemption from that course.

Inverse Problems involve deducing hidden system parameters from external measurements—applied in medical imaging, geophysical exploration, industrial testing, and astrophysics. These challenges are central to modern science and technology, enabling advancements like detecting underground resources, improving material integrity assessments, optimizing designs, and modeling biological processes.