The qualifying exam in mathematics is designed to measure the breadth of a student’s knowledge in mathematics. The exam may identify those areas in which a student’s knowledge is weak. Passing the exam is an indication that a student is ready to begin more specialized study leading to research work.
The exam is given at the very start of each semester. A student may take the exam as often as (s)he likes. There is absolutely no stigma attached to `failing’ the exam. `Failing’ it may well provide more useful information than `passing’ it. `Passing’ the exam early is mainly an indication that a student has been an undergraduate at a university with a broad undergraduate program in mathematics. It is not a good predictor of the quality of the eventual PhD thesis.
Students are strongly encouraged to first take the exam no later than their second semester. Before passing the qualifying exam, students should take three beginning 200 level (or 100 level) math courses each semester. In a semester in which they are teaching they need only take two such courses. After passing the qualifying exam students are usually excused from grades in any math courses they take. Students are expected to pass the qualifying exam by the end of their second year.
The exam consists of three three hour papers on three consecutive days. Each paper typically has 6 questions covering a broad range of mathematics. The questions aim to test your ability to solve concrete problems by identifying and applying important theorems. They should not require great ingenuity. In any given year the exam may not cover every topic on the syllabus, but it should cover a broadly representative set of quals/topics and over time all quals/topics should be examined.
Some Old Qualifying Exams
|Some old departmental qualifying exams are available here:||Some PDF files of questions arranged by topics.||Collected by Danny Calegari and Tom Coates source.|