Preliminary & Qualifying Exams


The preliminary examination covers two of the three foundational course sequences, MAT 601-602 (Fundamentals of Analysis), MAT 631-632 (Introduction to Algebra), and MAT 651-652 (Probability and Statistics). It consists of four 2-hour written examinations, two over each sequence. These exams are given as the comprehensive final exams at the end of each semester. The possible outcomes for each exam are Pass, Superior Pass, and Fail. Students must receive three grades of Superior Pass and one Pass or Superior Pass, in the four exams covering two sequences. In each of the four courses, the course grade and the outcome of the Preliminary Examination are two separate decisions.

Students who wish to continue in the Ph.D. program must pass these examinations before their second year of graduate study. Only two attempts at each of these examinations are permitted. A second try at each exam will be offered in August before the student’s second year. The exact date will be announced at least a month ahead of time.

Students who enter the Mathematics Graduate Program with extensive preparation in mathematics may attempt the Preliminary Examinations upon entering the Program. This attempt will not be counted as one of the two attempts at the Preliminary Examinations.

Students may petition the Mathematics Graduate Committee to postpone the Preliminary Examinations until their second year of graduate study.

Qualifying Exams

The Qualifying Examination consists of two written tests, each covering one of the following two-course sequences.

  • Algebra: MAT 731, 732
  • Analysis I: MAT 701, 712
  • Analysis II: MAT 701, 721
  • Combinatorics: MAT 645, 646
  • Numerical Analysis: MAT 683, 684
  • Statistics: MAT 654, 755
  • Topology: MAT 661, 761

The student should choose the qualifying exams in consultation with their anticipated PhD advisor. The approved combinations for the two qualifying exams are

  • Applied Math: Numerical Analysis and Analysis I
  • Statistics: Statistics and Analysis II
  • Pure Math: Any combination of Algebra, Analysis I, Analysis II, Combinatorics, and Topology such that the course sequences are disjoint.

Each part of the Qualifying Examination lasts four hours. The parts may be taken separately. There are only two outcomes on each part, Pass or Fail. These examinations will be given twice a year, before or near the beginning of each semester. The exact dates will be announced at least a month ahead of time.

Students must either pass the coursework on which a Qualifying Exam is based before taking it, or petition the Graduate Committee. Students should take the qualifying exam as soon as possible after finishing the corresponding coursework. Students must pass one qualifying exam by the August preceding their fourth year of graduate study and pass both exams no later than January during their fourth year of graduate study.

With the approval of the Mathematics Graduate Committee, students who postpone taking one or both of their Preliminary Examinations until their third year of graduate study may also postpone the Qualifying Examinations, in the same area, until their fourth year of graduate study.

Exam Resources

A number of study materials compiled by the graduate students at Syracuse University have been scanned an uploaded to the MGO website for student use. All these resources can be found at the link below:

Other Graduate Preliminary & Qualifying Exams

While the above links should be the primary reference source for problems while preparing for your graduate mathematics exams at Syracuse University, qualifying exams from other universities can serve as an additional source of problems for review.

Written Exams

SUNY Albany
UC Berkeley
Boston University
University of Colorado Boulder
University of Connecticut
UC Davis
University of Florida
University of Georgia (Qualifying Exams are at this link)
University of Illinois
Indiana University
University of Iowa
Johns Hopkins University
Kansas State University
Louisiana State University
University of Maryland
University of Massachusetts Amherst
University of Michigan
University of Minnesota
University of Missouri
University of Nebraska-Lincoln
University of New Mexico
Northeastern University
Northwestern University
Ohio State University
University of Oklahoma
Penn State University
University of Pittsburgh
Purdue University
University of Rochester
Rutgers State University
University of South Carolina
Stanford University
Temple University
Texas A&M University
University of Utah
University of Washington
University of Wisconsin-Madison

Oral Examinations

Princeton University

University of Cambridge