# PhD Qualifying Exams

## General Comprehensive Exams

A student must pass the general comprehensive examination (GCE) in order to become a PhD candidate. The purpose of the GCE is to determine whether a student possesses the fundamental knowledge and skills necessary for study and research at the PhD level. It is a written examination offered three times a year, once each in January, May, and August. A student must pass by January of their second year if they enter in the fall and May of their second year if they enter in the spring.

## Past Qualifying Exams

### Linear Algebra - 502

- Linear Algebra GCE August 2014 (PDF)
- Linear Algebra GCE August 2015 (PDF)
- Linear Algebra GCE August 2016 (PDF)
- Linear Algebra GCE August 2017 (PDF)
- Linear Algebra GCE January 2015 (PDF)
- Linear Algebra GCE January 2016 (PDF)
- Linear Algebra GCE January 2017 (PDF)
- Linear Algebra GCE May 2015 (PDF)
- Linear Algebra GCE May 2016 (PDF)
- Linear Algebra GCE May 2017 (PDF)
- Linear Algebra GCE January 2018 (PDF)
- Linear Algebra GCE May 2018 (PDF)
- Linear Algebra GCE August 2018 (PDF)
- Linear Algebra GCE January 2019 (PDF)
- Linear Algebra GCE May 2019 (PDF)
- Linear Algebra GCE January 2020 (PDF)
- Linear Algebra GCE May 2020 (PDF)
- Linear Algebra GCE August 2020 (PDF)
- Linear Algebra GCE January 2021 (PDF)

### Analysis - 503

- Analysis GCE August 2014 (PDF)
- Analysis GCE August 2015 (PDF)
- Analysis GCE August 2016 (PDF)
- Analysis GCE August 2017 (PDF)
- Analysis GCE January 2015 (PDF)
- Analysis GCE January 2016 (PDF)
- Analysis GCE January 2017 (PDF)
- Analysis GCE May 2015 (PDF)
- Analysis GCE May 2016 (PDF)
- Analysis GCE May 2017 (PDF)
- Analysis and Measure Theory 503 GCE May 2018 (PDF)
- Analysis GCE August 2018 (PDF)
- Analysis GCE January 2019 (PDF)
- Analysis GCE May 2019 (PDF)
- Analysis GCE January 2020 (PDF)
- Analysis GCE May 2020 (PDF)
- Analysis GCE August 2020 (PDF)
- Analysis GCE January 2021 (PDF)

### Probability - 540

- Probability 540 GCE August 2012 (PDF)
- Probability 540 GCE August 2013 (PDF)
- Probability 540 GCE August 2016 (PDF)
- Probability 540 GCE August 2017 (PDF)
- Probability 540 GCE January 2014 (PDF)
- Probability 540 GCE January 2017 (PDF)
- Probability 540 GCE May 2008 (PDF)
- Probability 540 GCE September 2009 (PDF)
- Probability 540 GCE Spring 2012 (PDF)
- Probability 540 GCE Spring 2013 (PDF)
- Probability 540 GCE May 2018 (PDF)
- Probability 540 GCE August 2018 (PDF)
- Probability 540 GCE January 2019 (PDF)
- Probability 540 GCE May 2019 (PDF)
- Probability 540 GCE January 2020 (PDF)
- Probability 540 GCE August 2020 (PDF)

### Statistics - 541

**GCE Syllabus - Mathematical Statistics**

- Statistics 541 GCE August 2016 (PDF)
- Statistics 541 GCE August 2017 (PDF)
- Statistics 541 GCE January 2012 (PDF)
- Statistics 541 GCE January 2013 (PDF)
- Statistics 541 GCE January 2014 (PDF)
- Statistics 541 GCE January 2017 (PDF)
- Statistics 541 GCE May 2017 (PDF)
- Statistics 541 GCE Spring 2012 (PDF)
- Statistics 541 GCE January 2018 (PDF)
- Statistics 541 GCE August 2018 (PDF)
- Statistics 541 GCE January 2019 (PDF)
- Statistics 541 GCE May 2019 (PDF)
- Statistics 541 GCE January 2020 (PDF)
- Statistics 541 GCE August 2020 (PDF)
- Statistics 541 GCE January 2021 (PDF)