PhD Entrance Exam(MS Advanced Exam)

Ph.D. Entrance Exam (M.S. Advanced Exam)

For more information about the Ph.D. Entrance Exam, see the Graduate Handbook.

List of Exam Topics and Their Examiners

1. Real Analysis: This exam covers, basically speaking, Lebesgue Measure and associated topics through the Lp spaces as are found in the standard text "Real Analysis" by Royden. Questions from advanced calculus (e.g. Math 451-452) also form a significant part of the exam, for which the course textbook by Ross is a suitable reference.

Here is a detailed Syllabus.

Examples of exams from previous years may be viewed by here. Note however, that these problems and similar sample problems are intended only as a general indication of problem topics and type.



2. Algebra:This examination is based on topics outlined here, not on any specific texts or contents of any specific course taught at WVU. Various old exams can be found here and here.



3. Topology: This exam cover topological spaces, separation axioms, metric space topology, continuity, connected spaces, and compactness. For more information on the topics and covered and some old exams, please look here.



4. Differential Equations: This exam covers intermediate ordinary differential equations at about the level of Brauer and Nohel. An outline of the topics covered can be found here. For more information about the exam, look here.


Please send any questions or comments to