## Degree Requirements

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.

C) Theoretical Physics, Classical Mechanics, Classical Electicity and Magnetism, Quantum Mechanics, Adv. Quantum Mechanics, Methods in Experimental Physics, Applied Regression Analysis, and two Physics specialty subject classes form the four following classes: Phys 871, 876, 881, 895.

*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.