Office: 1150 Faculty/Administration Bldg.; 577-2479
Chairperson: Lowell J. Hansen
Associate Chairperson: Daniel Frohardt
Academic Services Officer: Mary Klamo
Website: http://www.math.wayne.edu
Gregory F. Bachelis, Robert D. Berman, Lawrence J. Brenton, Leon Brown (Emeritus), Robert R. Bruner, Pao-Liu Chow, William S. Cohn, Daniel S. Drucker, Daniel Frohardt, David H. Gluck, David Handel, Lowell J. Hansen, Chorng-Shi Houh (Emeritus), John M. Irwin (Emeritus), Steven M. Kahn, Rafail Z. Khasminskii (Distinguished Professor), John Klein, Alexander Korostelev, Tachen Liang, Guozhen Lu, Kay Magaard, Leonid Makar-Limanov, Peter Malcolmson, Jose L. Menaldi, Boris Mordukhovich, D. Clarence Morrow (Emeritus), Togo Nishiura (Emeritus), Frank Okoh, Jingyal Pak (Emeritus), Choon-Jai Rhee, Claude L. Schochet, Bertram M. Schreiber, Tze-Chien Sun, Martin T. Wechsler (Emeritus), Gang Yin, Zhimin Zhang
John C. Breckenridge, David W. Jonah, Harold T. Slaby (Emeritus), Stephen A. Williams
Po Hu, Daniel Isaksen, Catherine Lebiedzik, Sheng Zhang
The courses offered by the Department of Mathematics serve several purposes; they supply the mathematical preparation necessary for students specializing in the physical, biological or social sciences, in business administration, in engineering, and in education; they provide a route by which students may arrive at the level of research competency in any of several special mathematical areas; they allow students to prepare themselves for work as mathematicians and statisticians in industry and government; and they give an opportunity to all inquisitive students to learn something about modern mathematical ideas.
All course work must be completed in accordance with the regulations of the Graduate School and the College governing graduate scholarship and degrees; see Regulations of the University, Academic and Academic Regulations of the College of Science. Degree applicants are expected to inform themselves concerning these regulations and to take the responsibility of conforming to them. Additional requirements for specific graduate degrees in mathematics are explained below.
Admission to these programs is contingent upon admission to the Graduate School; see Admission, Regular.
Except for the program leading to the degree of Master of Arts in Applied Mathematics, the entrance requirements for the master's programs in mathematics and statistics include successful completion of twelve semester credits in mathematics beyond sophomore calculus (equivalent to MAT 2010, 2020, 2030, 2250, and 2350); this course work should include advanced calculus and linear or modern algebra. Credit accrued in courses such as the history of mathematics or the teaching of mathematics, in which the study of mathematics itself is not the primary purpose will not be counted toward this requirement. As preparation for graduate study, the Mathematics Department strongly recommends undergraduate course work along the line of option A, described under Bachelor's Degrees in the undergraduate bulletin.
DEGREE REQUIREMENTS: The Master of Arts with a Major in Mathematics is offered under the following options:
Plan A: Twenty-four credits in course work plus an eight credit thesis.
Plan B: Twenty-seven credits in course work plus a three credit essay.
Plan C: Thirty credits in course work.
Completion of these plans must satisfy the following criteria:
1. At least twenty-four credits must be earned in course work from the Mathematics Department. Credits earned toward a thesis or essay in accordance with Plan A or Plan B may be included among these twenty-four credits.
2. Election of Mathematics 5420, 5430, 5600 and 5610, if not previously completed. Election of Mathematics 6500 or 6600, if not previously completed.
3. Election of at least two of the following, if not previously completed: Mathematics 5100, 5220, 5230, 5410, 5530, 5700, 5770, 5800, 5870. These courses represent several areas of applied mathematics.
4. Election of at least one additional mathematics course numbered 6000, or higher, with the exception of Mathematics 7999, 8999 and teacher preparation courses.
5. By the time twelve credits have been earned a Plan of Work, approved by a departmental adviser, should be submitted to the director of the master's program in mathematics. At this time, the Graduate Committee will act on the application for candidacy. The student will not be allowed to take more than twelve credits in the master's program unless candidacy has been established.
6. In the Plan of Work the student will state his or her choice of one of the plans A, B, or C. The choice of plan must be approved by the Graduate Committee.
7. There is a final oral examination for the master's degree. All students in Plan C are required to take this examination. Students in Plan A or B may, upon recommendation of the thesis or essay adviser, be excused from the final oral examination by the Graduate Committee.
8. It is required that the thesis or essay of each student in Plans A or B be presented in a public lecture.
NOTE: Candidates for the Master of Arts degree with a major in mathematics or in mathematical statistics are exempt from the requirement of the Graduate School that six credits in the major field must be in courses numbered 7000 and above.
The requirements for this degree differ from those for the Master of Arts with a major in mathematics (see above) only in that the three requirements 2, 3, and 4 are replaced by a single one:
2. Election of Mathematics 5420, 5430, 5600, 5610, 5700, 5710, and 5800, if not previously completed. Election of two courses from the group: MAT 5030, 5770, 5830, 5870, 6830, 6840, 6500 or 6600. Mathematics 7700 is recommended.
It is stressed that all other requirements (1, 5, 6 and 7 above) are the same, except that the essay under Plan B must be written in the area of mathematical statistics.
This degree is designed for students who are interested in applied mathematics or are interested in applying mathematics to areas outside of mathematics (e.g., biology, chemistry, computer science, economics, engineering, geology, medical science, physics, psychology, social science). The program is flexible in that it does not represent the teaching of any fixed body of knowledge. It does require two areas of concentration, one of these being the major in mathematics (pure and applied) with emphasis on the applicable subjects. The minor area is to be either in applied mathematics or in an area outside of mathematics (such as the above) to which the student is interested in applying mathematics. Mathematical methods are emphasized.
Admission to this program is contingent upon admission to the Graduate School; see Admission, Regular. Applicants for the program leading to the degree of Master of Arts in Applied Mathematics must have either twelve credits beyond the calculus sequence or knowledge equivalent to Mathematics 2010-2030, 2250, 2350, 5070, 5420, Computer Science 2110 and a good background in some area in which he or she is planning to apply mathematics. A bachelor's degree in mathematics is not required.
DEGREE REQUIREMENTS: This program is usually offered as a Plan B master's degree option requiring twenty-nine credits of course work plus a three credit essay. However, other master's degree options (see Mathematics (M.A. Program)) may be elected with the approval of the Departmental Graduate Committee. Specific requirements for the degree are as follows:
1. A minimum of thirty-two credits.
2. A minimum of twenty credits in mathematics courses not previously completed and numbered 5030 or above (except courses for teachers). At least four of these credits must be elected from the courses listed in requirement 3 for mathematics major cited above.
3. Each student must declare a minor (e.g., one of the areas mentioned above) in which he or she is planning to apply mathematics, and have at least eight credits in that area in addition to those required above.
4. The entire program of study must be a coordinated one that meets with the approval of the student's academic adviser, who will be assigned upon admission.
Each student in this program will ordinarily be required to write a project-type essay for three credits under the direction of a supervisor in the Mathematics Department and an essay adviser from some department related to the minor area, both of whom must approve the essay. (If the chosen minor area is in applied mathematics, the adviser in the major area can be the same as the adviser in the minor area.) The selection of advisers and topics must be approved by the Graduate Committee of the Mathematics Department.
All applicants for the degree of Doctor of Philosophy with a major in mathematics are urged first to study the general University requirements for this degree and to plan their programs so that all those requirements are fulfilled in the proper order and at the proper times. Listed below are the major steps in earning this degree. Specific requirements of the Mathematics Department are included.
Admission to this program is contingent upon admission to the Graduate School; see Admission, Regular. Doctoral applicants must have completed a master's degree in mathematics or reached an equivalent level of advancement. The Department Graduate Committee may make exceptions to this rule in cases where unusual ability has been demonstrated. Admission to the doctoral program will be granted only to those whose records indicate an ability to succeed in advanced study and research.
DEGREE REQUIREMENTS: Candidates for the doctoral degree must complete ninety credits in course work beyond the bachelor's degree, including thirty credits of dissertation direction. The thirty credit dissertation registration requirement is fulfilled in one of two ways: 1) Students who have accumulated credits in the course numbered 9999 (Doctoral Dissertation Research and Direction) register for a total of thirty credits in 9999; or 2) Students who have not accumulated any credits in the course numbered 9999 and who attain Candidacy after Summer semester 2001 register for the courses 9991, 9992, 9993, and 9994 (Doctoral Dissertation Research and Direction I, II, III, and IV, respectively), in consecutive academic year semesters. Additional specific requirements for this degree in mathematics are as follows:
Preliminary Examinations are two two-hour written tests, covering undergraduate level material in analysis and algebra (from a sophisticated point of view). A student who is admitted to the Ph.D. program must take the Preliminary Examination within the first two scheduled examination sessions after the date of admission. Any delay in taking the examinations must be approved in advance by the Graduate Committee.
Language Examinations: Students are expected to show proficiency, at the level of translating mathematical literature, in two modern languages other than English. Examiners and exam format will be determined on an individual basis by the Graduate Committee. One language exam must be in French, German, or Russian, and this examination must be passed before completion of the written qualifying examinations. The second language may be any language in which there is a substantial body of modern mathematical literature, including computer languages. The second language exam must be passed before the Defense of Dissertation is scheduled.
Course Requirements: In addition to the examinations described above, before advancement to candidacy every student in the Ph.D. program must complete each of the following four courses with a grade of 'B' or better: MAT 7400, 7500, 7600, and 6600.
QUALIFYING EXAMINATIONS consist of two sections, a written and an oral examination. A student must begin the written qualifying examination by the end of the third year in the Ph.D. program, and must pass all parts of the examination by the end of the fourth year in the Ph.D. program. All parts of the examination must be passed before a student can advance to Candidacy Status.
Written Qualifying Examinations consist of two 3-hour parts, a major and a minor area exam. The examination committee will give the student a list of topics in the student's area of specialization. These topics should both reflect the student's particular research interest and be of sufficient breadth to cover the entire area. The committee will also designate a minor area on which the student will be examined. The minor area is to be supportive of the major area but sufficiently different to avoid compromising the diversity of the total two-part exam.
Oral Qualifying Examinations: By University regulations, after passing the written Qualifying Examinations, a student must take an oral Qualifying Examination within thirty days after certification of passing the written exam. The oral examination committee consists of the written examination committee, and a representative of the Graduate Committee. The oral examination will normally cover material similar to that of the written examinations, but may also include material outside the written examination areas which is deemed relevant to the student's research work.
Defense of Dissertation: Candidates must pass a final oral examination covering their research after the candidate's adviser has approved the completed dissertation.
General sources of financial aid for graduate students may be found in the section on Graduate Financial Assistance; see Financial Assistance .
A number of graduate assistantships and research fellowships are available for graduate students. Requests for information should be addressed to the Chairperson of the Department of Mathematics.