Each student must pass, or demonstrate a knowledge of, six of the eight core courses. These consist of two-course sequences in

- algebra (593, 594)
- analysis (596, 597)
- applied analysis (556, 572)
- geometry/topology (591, 592)

Each student must pass the Qualifying Review. This consists of written examinations, based on the same syllabuses as the core courses, a course requirement, and a survey by the Doctoral Committee of the student’s record as a graduate student in the Department. The purpose of the Review is to ensure that students have a good knowledge of core graduate mathematics and to evaluate the chances that a student will be able to complete a Ph.D. degree.

The Qualifying Review is conducted three times a year, and should be taken as soon as the student feels ready. It can be taken as many times as necessary with the only stipulation that a student must pass the exams in one area by the beginning of the fourth term in the program, and must complete the entire Review by the beginning of the sixth.

Students are required to take six courses beyond those needed for the Qualifying Review, distributed among at least three of five areas of mathematics.

To ensure greater intellectual breadth, the Graduate School requires that every student must successfully complete four hours of cognate courses before achieving Candidacy. For students in most departments, these must be taken outside the student’s home department, but mathematics students are allowed to take courses within the Mathematics Department under certain restrictions and with Advisor or Doctoral Committee approval. Cognate courses can be taken at any time.

The course requirements listed above should be regarded as the absolute minimum. The Department expects that most students will take more courses distributed so that they achieve a broad background in their specialty and related areas. Students should also participate actively in the Departmental Seminars offered in their area of interest and attend Colloquia since it is there that they can learn about the latest developments and open problems.

**Schedule** (doc)

Syllabi

Algebra

Algebra I Syllabus (PDF)

Algebra II Syllabus (PDF)Analysis

Complex Analysis Syllabus (PDF)

Real Analysis Syllabus (PDF)Applied Analysis

Methods of Applied Analysis Syllabus

Page 1, Page 2 (PDF)

Numerical Methods Applied Analysis Syllabus (PDF)Topology

Algebraic Topology Syllabus (PDF)

General Topology Syllabus (PDF)

**Past Exams**

Algebra

QR Exam (Sept 2009) (PDF)

QR Exam Solutions (Sept 2009) (PDF)

QR Exam (May 2009) (PDF)

QR Exam Solutions (May 2009) (PDF)

QR Exam (Jan 2009) (PDF)QR Exam Solutions (Jan 2009) (PDF)

QR Exam (Sept 2008 ) (PDF)

QR Exam Solutions (Sept 2008 ) (PDF)

QR Exam (May 2008 ) (PDF)

QR Exam Solutions (May 2008 ) (PDF)

QR Exam (Jan. 2008 ) (PDF)

QR Exam Solutions (Jan, 2008 ) (PDF)QR Exam (Sept. 2007) (PDF)

QR Exam Solutions (Sept, 2007) (PDF)

QR Exam (May, 2007) (PDF)

QR Exam Solutions (May, 2007) (PDF)

QR Exam (Jan, 2007) (PDF)

QR Exam Solutions (Jan, 2007) (PDF)QR Exam (Sept, 2006) (PDF)

QR Exam Solutions (Sept, 2006) (PDF)

QR Exam (May, 2006) (PDF)

QR Exam (Jan, 2006) (PDF)QR Exam (Sept, 2005) (PDF)

QR Exam Solutions (Sept, 2005) (PDF)

QR Exam (May, 2005) (PDF)

QR Exam Solutions (May, 2005) (PDF)

QR Exam (Jan, 2005) (PDF)

QR Exam Solutions (Jan, 2005) (PDF)

Analysis (Real and Complex)

Analysis QR Exam (Sept 2009) (PDF)

Analysis QR Exam (Jan 2009) (PDF)Analysis QR Exam (Sept 2008 ) (PDF)

Analysis QR Exam (May 2008 ) (PDF)

Analysis QR Exam (Jan, 2008 ) (PDF)Analysis QR Exam (Sept, 2007) (PDF)

Analysis QR Exam (May, 2007) (PDF)

Analysis QR Exam (Jan, 2007) (PDF)Analysis QR Exam (Sept, 2006) (PDF)

Analysis QR Exam (May, 2006) (PDF)

Analysis QR Exam (Jan, 2006) (PDF)Analysis QR Exam (Sept, 2005) (PDF)

Analysis QR Exam (May, 2005) (PDF)

Analysis QR Exam (Jan, 2005) (PDF)

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