Qualifier Examination Information

All Ph.D. students must pass three examinations in different areas of advanced mathematics or statistics. Following is the relevant part of the Ph.D. program description:

Students must pass three written examinations. Two of these will be chosen from the areas Algebra, Combinatorics and Real Analysis. The third will be chosen from the areas Mathematical Modeling, Applied Statistics and Probability & Mathematical Statistics. Normally, these will be taken within a year of completion of the core coursework. These examinations need not be taken together. Usually, at most two attempts at passing this examination will be permitted. Students who wish to make a third attempt must petition the Graduate Studies Committee of the department for permission to do so.

Every year, the exams will be given in January and August. Each exam will be 3 1/2 hours long. 

Topics students are expected to know for each exam are listed below. Past exams and tips are available.


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Suggested References

Also useful are the following Schaum's Outlines:

Mathematical Modeling

Suggested References


Suggested References

[1] Billingsley, Patrick. Probability and Measure.  Wiley, Anniversary Edition, 2012.

Real Analysis

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Another book that contains more elementary background information is the following.


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Mathematical Physics

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