Graduate Program: Preliminary Examination
Preliminary examinations may be attempted before the start of the first year of graduate study, but the usual time to take them is at the start of the second year of graduate study. They are offered in several different subjects (algebra, analysis, topology etc.) and the requirement is to pass the examinations in three of these subjects (or earn sufficient partial credit in more subjects).
The purpose of the examinations is to make sure that the student acquired the minimal background necessary to even think of doing original research. Accordingly, well-prepared students may find that they know the material from some of the subject examinations already upon arrival. In this case the examinations can be taken in the September, in the week before new student week.
To help the students prepare for the preliminary examinations, the department has set up several first-year courses which cover the topics in a systematic fashion. The corresponding course numbers are given after each subject in the list below.
To help the graduate students (including incoming and prospective students) better prepare for the exams, we provide here some sets of problems from past years. Trying to solve these problems is an excellent way to find out in which areas more work is needed. We encourage prospective graduate students to study books and audit courses related to the material of these exams while still in college.
Previous Exams
Algebra (470)
- Syllabus: page 1, page 2, page 3,
- Algebra Preliminary Examination, Fall 1991 (pdf)
- Algebra Preliminary Examination, Fall 1996 (pdf)
- Algebra Preliminary Examination, Fall 1997 (pdf)
- Algebra Preliminary Examination, Fall 1999 (pdf)
- Algebra Preliminary Examination, Fall 2000 (pdf)
- Algebra Preliminary Examination, Fall 2001 (pdf)
- Algebra Preliminary Examination, Fall 2002 (pdf)
- Practice Algebra Preliminary Examination, Fall 2003 (pdf)
- Algebra Preliminary Examination, Fall 2003 (pdf)
- Algebra Preliminary Examination, Fall 2006 (pdf)
- Algebra Preliminary Examination, Fall 2007 (pdf)
Algebraic Topology (460)
- Syllabus for Part 1, Differential Topology
- Syllabus for Part 2, Algebraic Topology
- Topology Preliminary Examination, Fall 1995 (pdf)
- Topology Preliminary Examination, Fall 1996 (pdf)
- Topology Preliminary Examination, Winter 1997 (pdf)
- Topology Preliminary Examination, Fall 1997 (pdf)
- Topology Preliminary Examination, Fall 1998 (pdf)
- Topology Preliminary Examination, Winter 1999 (pdf)
- Topology Preliminary Examination, Fall 2000 (pdf)
- Topology Preliminary Examination, Fall 2002 (pdf)
- Topology Preliminary Examination, Fall 2003 (pdf)
- Topology Preliminary Examination, Fall 2005 (pdf)
- Topology Preliminary Examination, Fall 2006 (pdf)
- Topology Preliminary Examination, Fall 2007 (pdf)
Analysis (Real and Complex) (410)
- Syllabus
- Analysis Preliminary Examination, Fall 1994 (pdf)
- Analysis Preliminary Examination, Fall 1995 (pdf)
- Analysis Preliminary Examination, Winter 1996 (pdf)
- Analysis Preliminary Examination, Winter 1997 (pdf)
- Analysis Preliminary Examination, Fall 1997 (pdf)
- Analysis Preliminary Examination, Winter 1998 (pdf)
- Analysis Preliminary Examination, Fall 1998 (pdf)
- Analysis Preliminary Examination, Fall 1999, Page 1 (pdf), Page 2
- Analysis Preliminary Examination, Fall 2000 (pdf)
- Analysis Preliminary Examination, Fall 2002 (pdf)
- Analysis Preliminary Examination, Fall 2003 (pdf)
- Analysis Preliminary Examination, Fall 2004 (pdf)
- Analysis Preliminary Examination, Fall 2005 (pdf)
- Analysis Preliminary Examination, Fall 2006 (pdf)
- Analysis Preliminary Examination, Fall 2007 (pdf)
Differential Geometry (440)
- Syllabus for Part 1, Differential Topology
- Differential Geometry Preliminary Examination, Fall 1993 (pdf)
- Differential Geometry Preliminary Examination, Fall 1997, Page 1 (pdf), Page 2
- Differential Geometry Preliminary Examination, Fall 1998, Page 1 (pdf), Page 2
- Differential Geometry Preliminary Examination, Spring 2000 (pdf)
- Differential Geometry Preliminary Examination, Fall 2000 (pdf)
- Differential Geometry Preliminary Examination, Fall 2003 (pdf)
- Differential Geometry Preliminary Examination, Fall 2007 (pdf)
Dynamical Systems (430)
- Syllabus
- Dynamical Systems Preliminary Examination, Fall 1988 (pdf)
- Dynamical Systems Preliminary Examination, Fall 1991 (pdf)
- Dynamical Systems Preliminary Examination, Summer 1994 (pdf)
- Dynamical Systems Preliminary Examination, Fall 1995 (pdf)
- Dynamical Systems Preliminary Examination, Winter 1996 (pdf)
- Dynamical Systems Preliminary Examination, Fall 1996 (pdf)
- Dynamical Systems Preliminary Examination, Fall 2000 (pdf)
- Dynamical Systems Preliminary Examination, Fall 2001 (pdf)
- Dynamical Systems Preliminary Examination, Fall 2002 (pdf)
- Dynamical Systems Preliminary Examination, Fall 2003 (pdf)
- Dynamical Systems Preliminary Examination, Fall 2004 (pdf)
Partial Differential Equations (420)
- Syllabus
- PDE Preliminary Examination, Winter 2000 (pdf)
- PDE Preliminary Examination, Fall 2000 (pdf)
Probability (450)
- Syllabus
- Probability Preliminary Examination, Fall 1996 (pdf)
- Probability Preliminary Examination, Fall 1997 (pdf)
- Probability Preliminary Examination, Fall 1998 (pdf)
- Probability Preliminary Examination, Fall 2000 (pdf)
- Probability Preliminary Examination, Fall 2005 (pdf)
- Probability Preliminary Examination, Fall 2006 (pdf)
