Mathematics

Overview

Key Features

Qualifying examinations are offered twice yearly, in August and in January, shortly before the beginning of Fall and Spring semesters. Students with prior preparation may attempt the examinations upon entrance to the program, or after one semester. Ideally a student will complete the qualifying examinations by the August following entrance to the Ph.D. program.  

Students who receive a failing grade twice on any one of the examinations will not be continued in the Mathematics degree from The University of Arizona. Students who do not complete the three examinations within five semesters and with a cumulative passing grade will not be continued in the Ph.D. program unless the Graduate Committee, upon review of the case, finds extenuating reasons to justify such continuation. 

Two year-long Mathematics course sequences that are not co-convened and are not part of the required core of algebra, real analysis, and geometry-topology are required. These two sequences must be in two of the three general areas: algebra and number theory, analysis and geometry, mathematical physics and applied mathematics. 

For most students one of the sequences will be Complex Analysis (Math 520A-B). At least six approved units outside of Mathematics are also required. There is a language requirement which can be satisfied in any two of the following: French, German, Russian, or computer programming. The principal component of the program is the completion of a dissertation involving original creative research.