Contents

## Preliminary & Qualifying Exams

### Prelims

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 studentâ€™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 Links

- Algebra Prelim Exam
- Algebra Qualifying Exam
- Analysis Prelim Exam
- Analysis Qualifying Exam
- Topology Qualifying Exam
- Statistics Qualifying Exam
- Numerical Analysis Qualifying Exam
- Combinatorics & Graph Theory Qualifying Exam

### 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)

Harvard

University of Illinois

Indiana University

University of Iowa

Johns Hopkins University

Kansas State University

UCLA

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