An PhD degree in mathematics requires 84 hours of graduate credit.

PhD Program in Applied Mathematics

To complete the PhD program in applied mathematics the student must satisfy the course, language and residency requirements given below; pass the qualifying and preliminary examinations; write a dissertation containg original research in applied mathematics.

*Course Requirements:* A total of at least 84 hours of graduate credit is required. Math 757-758 and mathematics or statistics courses numbered below 700 may not be included. At least 36 hours must be in mathematics and statistics courses numbered above 800 (exclusive of PhD Dissertation). Courses used toward a master's degree may be included. A maximum of 36 hours may be transferred from another university at the discretion of the student's committee. Real Analysis I and II and Numerical Linear Algebra are required of all students. In addition a student must complete one of the following two sets of requirements:

A) Complex Analysis I and II, Partial Differential Equations I and II, Functional Analysis I and II, and either Numerical Analysis of Ordinary Differential Equations or Numerical Analysis of Partial Differential Equations.

B) Theory of Statistics I and II, Theory of Probability I and II, Theory of Statistical Inference I and II, Theory of Linear Models I and II.

*Language Requirements:* The student must demonstrate proficiency either in two foreign languages or in one foreign language and one high level computer language. The foreign languages are Chinese, French, German and Russian. The language proficiency will be demonstrated by passing an examination that consists of the translation, with the use of a dictionary, of one or more passages of mathematical text from the foreign language into English.

*Residency Requirement:* The student must complete at least one academic year in residence as a full-time student at WSU.

*Qualifying Exam:* The qualifying exam is a written exam administered near the middle of both the fall and spring semesters. The exam is a six- hour exam given on two different days within a one week period. The topics covered by the exam are real analysis, numerical analysis, advanced calculus and linear algebra. The exam should be taken at the first opportunity after completing Real Analysis I and II and Numerical Linear Algebra. A student who does not pass on the first
attempt may be permitted to take the exam a second time. A person who retakes the exam must retake the entire exam. The exam may be retaken only once.

*PhD Committee:* Upon the student passing the qualifying exam, the graduate coordinator, in consultation with the student, will recommend to the departmental PhD Advisory Committee a PhD Committee for the student. The student's PhD Committee will consist of the student's dissertation adviser as chair and four other members. At least one, but no more than two, of the committee members shall be from departments outside the Mathematics and Statistics. Within one semester after passing the qualifying exam the student should submit a Plan of Study to the committee for approval. This committee will serve as examining committee for both the preliminary and final exams.

*Preliminary Exam:* The preliminary exam covers specific topics relevant to the student's research area as determined by his or her PhD committee. The student will meet as soon as possible with the committee to set the topics to be covered. For full-time students, the exam should normally be taken about one year after passing the qualifying exam. Before the preliminary exam is taken all language requirements must be met. The preliminary exam should be passed before beginning work on the dissertation. A student who fails the preliminary exam may be permitted to retake the exam if the committee so determines.

*Dissertation and Final Exam:* Upon passing the preliminary exam the student becomes a candidate for the PhD degree. Soon thereafter the student must submit a written dissertation proposal to his or her committee for approval. While working on the dissertation the student should enroll for a total of at least 18 hours of PhD Dissertation. The student must be enrolled at the University during each semester after admission to candidacy until completion of the dissertation. After the dissertation is completed the student must present and defend it before the committee. This defense constitutes the final exam. The dissertation defense is open to the public.