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.<br><br>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.<br><br>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.