Master of Arts in Teaching College Mathematics

Doctor of Philosophy with a major in Mathematics and specializations in pure mathematics, applied mathematics and mathematical statistics

All graduate degrees are governed by general University regulations. Information concerning these may be found in the Liberal Arts Academic Procedures section (pages 192-194) and also in the Graduate School section (pages 2-30) of the graduate bulletin. 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.

Master of Arts Degrees in Mathematics

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 201, 202, 203, 225, and 235); this course work should include advanced calculus and linear or modem 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 Bachelors Degrees in the undergraduate bulletin.

Master of Arts with a Major in Mathematics

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.

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 542, 543, 560 and 561, if not previously completed. Election of Mathematics 650 or 660, if not previously completed.
3. Election of at least two of the following, if not previously completed: Mathematics 522, 523, 541, 553, 570, 577, 582, 586 and Computer Science 661. These courses represent several areas of applied mathematics.
4. Election of at least one additional mathematics course numbered 600, or higher, with the exception of Mathematics 799, 899 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 masters 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. Students in Plan A or B are required to present their thesis or essay in a public lecture.

Computer Science Cognates: For students interested in computer science, suitable cognates are: CSC518, CSC661, and CSC6O2.

Secondary Teaching Option: To exercise this option a student should declare specialization in secondary teaching on the Plan of Work. The student should also have, or be in the process of obtaining, a certificate to teach in the secondary schools. Once approved for this option, the student may, if desired, modify the requirements for the

Master of Arts degree in any or all of the following ways:

• substitute Mathematics 616 for 542 in satisfying requirement two.
• substitute Mathematics 615 for 570 in satisfying requirement three.
• add Mathematics 614 to the list of optional courses used in satisfying requirement four.

Master of Arts with a Major in Mathematical Statistics

2. Election of Mathematics 542, 543, 560, 561, 570, 582 and 780, if not previously completed. Election of Mathematics 650 or 660, if not previously completed. Mathematics 760 is recommended.

Master of Arts in Teaching College Mathematics

1. a total of thirty-two credits is required.
2. requirements 3 and 4 are replaced by the election of at least three courses to be determined in consultation with the director of the master's program.
3. only Plan B (see above) is permitted.

Master of Arts in Applied Mathematics

Admission to this program is contingent upon admission to the Graduate School; for requirements, see page 14 of the graduate bulletin. 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 201-203, 225, 235, 507, 542, Computer Science 203 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 masters degree options (see above under Major in Mathematics) 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 sixteen credits in mathematics courses not previously completed and numbered 507 or above (except courses for teachers).
3. At least four additional credits in mathematics courses as outlined in (2), above, or in Computer Science 661, 662.
4. 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.
5. 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.

Doctor of Philosophy with a Major in Mathematics

Admission to this program is contingent upon admission to the Graduate School; for requirements, see page 14 of the Graduate Bulletin. 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. Additional specific requirements for this degree in mathematics are as follows

Preliminary Examinations are two 2-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.

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.

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. Further, the first language examination must be passed before completing the Qualifying Examinations.

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, a representative of the Graduate Committee, and, per University regulations, a representative of the Graduate Dean. 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.

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 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 four courses with a grade of 'B' or better: MAT 740, 750, 760, and 660.

Defense of Dissertation: Candidates must pass a final oral examination covering their research after the candidate's adviser has approved the completed dissertation.

Fellowships, Assistantships, and Scholarships

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.