## Preliminary Examination

All students must pass the Preliminary Examination in order to continue with the program.

The Preliminary Examination consists of written examinations in the following three subjects: algebra, analysis, and geometry/topology.

Incoming students are strongly encouraged to take the Preliminary Examination upon entrance. There is no penalty for failing to pass a preliminary examination taken upon entrance to the program.

Incoming students are required to take each of the first-year courses (Algebra, Analysis, and Geometry-Topology) for which they do *not* pass the preliminary exam.

The rules for the Preliminary Examination are posted here.

The Preliminary Examination is given during New Student Week in September and at the end of the academic year (typically June). Graduate students must take the Preliminary Examination in all three subjects by the end of their first academic year. Students who do not pass the Preliminary Examination by the end of their first year must pass a make-up examination in September of their second year in order to continue in the program beyond the first quarter of the second year.

An award is offered at the end of each academic year to the student who has achieved the best performance in the Preliminary Examination. The award is accompanied by a monetary prize when sufficient funds are available.

Students who do not pass the Preliminary Examination by the end of their first year must pass a make-up examination in September of their second year in order to continue in the program beyond the first quarter of the second year. This rule may be waived with the permission of the instructor and the approval of the Graduate Committee.

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
- Algebra Preliminary Examination, Fall 1991
- Algebra Preliminary Examination, Fall 1996
- Algebra Preliminary Examination, Fall 1997
- Algebra Preliminary Examination, Fall 1999
- Algebra Preliminary Examination, Fall 2000
- Algebra Preliminary Examination, Fall 2001
- Algebra Preliminary Examination, Fall 2002
- Practice Algebra Preliminary Examination, Fall 2003
- Algebra Preliminary Examination, Fall 2003
- Algebra Preliminary Examination, Fall 2006
- Algebra Preliminary Examination, Fall 2007
- Algebra Preliminary Examination, Fall 2009
- Algebra Preliminary Examination, Spring 2011
- Algebra Preliminary Examination, Fall 2011
- Algebra Preliminary Examination, Spring 2012
- Algebra Preliminary Examination, Spring 2014
- Algebra Preliminary Examination, Spring 2015
- Algebra Preliminary Examination, Fall 2015
- Algebra Preliminary Examination, Spring 2016
- Algebra Preliminary Examination, Fall 2016

#### Analysis (Real and Complex) (410)

- Syllabus
- Analysis Preliminary Examination, Fall 1994
- Analysis Preliminary Examination, Fall 1995
- Analysis Preliminary Examination, Winter 1996
- Analysis Preliminary Examination, Winter 1997
- Analysis Preliminary Examination, Fall 1997
- Analysis Preliminary Examination, Winter 1998
- Analysis Preliminary Examination, Fall 1998
- Analysis Preliminary Examination, Fall 1999, Page 1 , Page 2
- Analysis Preliminary Examination, Fall 2000
- Analysis Preliminary Examination, Fall 2002
- Analysis Preliminary Examination, Fall 2003
- Analysis Preliminary Examination, Fall 2004
- Analysis Preliminary Examination, Fall 2005
- Analysis Preliminary Examination, Fall 2006
- Analysis Preliminary Examination, Fall 2007
- Analysis Preliminary Examination, Fall 2009
- Analysis Preliminary Examination, Spring 2010
- Analysis Preliminary Examination, Spring 2011
- Analysis Preliminary Examination, Fall 2011
- Analysis Preliminary Examination, Spring 2012
- Analysis Preliminary Examination, Spring 2013
- Analysis Preliminary Examination, Spring 2014
- Analysis Preliminary Examination, Spring 2015
- Analysis Preliminary Examination, Fall 2015
- Analysis Preliminary Examination, Spring 2016
- Analysis Preliminary Examination, Fall 2016

#### Geometry and Topology (Pre-2009)

Prior to Fall 2009, Topology and Geometry were courses with separate examinations; these examples should be used only as a source of problems, not as guidelines to the syllabus for or the structure of current exams. The current syllabus is below under Geometry/Topology (440).

- Topology Preliminary Examination, Fall 1995
- Topology Preliminary Examination, Fall 1996
- Topology Preliminary Examination, Winter 1997
- Topology Preliminary Examination, Fall 1997
- Topology Preliminary Examination, Fall 1998
- Topology Preliminary Examination, Winter 1999
- Topology Preliminary Examination, Fall 2000
- Topology Preliminary Examination, Fall 2002
- Topology Preliminary Examination, Fall 2003
- Topology Preliminary Examination, Fall 2005
- Topology Preliminary Examination, Fall 2006
- Topology Preliminary Examination, Fall 2007
- Differential Geometry Preliminary Examination , Fall 1993
- Differential Geometry Preliminary Examination, Fall 1997, Page 1 , Page 2
- Differential Geometry Preliminary Examination, Fall 1998, Page 1 , Page 2
- Differential Geometry Preliminary Examination, Spring 2000
- Differential Geometry Preliminary Examination, Fall 2000
- Differential Geometry Preliminary Examination, Fall 2003
- Differential Geometry Preliminary Examination, Fall 2006
- Differential Geometry Preliminary Examination, Fall 2007
- Algebraic Topology Preliminary Examination, Fall 2009
- Algebraic Topology Preliminary Examination Spring 2009
- Geometry Preliminary Examination, Spring 2009

#### Geometry/Topology (440)

- Syllabus
- Geometry/Topology Preliminary Examination, Fall 2009
- Geometry/Topology Preliminary Examination, Spring 2010
- Geometry/Topology Preliminary Examination, Fall 2010
- Geometry/Topology Preliminary Examination, Spring 2011
- Geometry/Topology Preliminary Examination, Fall 2011
- Geometry/Topology Preliminary Examination, Spring 2012
- Geometry/Topology Preliminary Examination, Spring 2013
- Geometry/Topology Preliminary Examination, Spring 2014
- Geometry/Topology Preliminary Examination, Fall 2014
- Geometry/Topology Preliminary Examination, Spring 2015
- Geometry/Topology Preliminary Examination, Fall 2015
- Geometry/Topology Preliminary Examination, Spring 2016
- Geometry/Topology Preliminary Examination, Fall 2016