Table of Contents Introduction I. General Information II. Master's Degree Programs III. Doctoral Degree Program IV. Departmental Policies Introduction The purpose of this handbook is to provide information to graduate students of mathematics at the North Dakota State University. It does not supersede any material found in the Graduate Bulletin or the Graduate School News. The Mathematics Department (300 Minard Hall), and the Graduate School (201 Old Main) are good sources of additional information. I. General Information The Department of Mathematics offers graduate study leading to the degrees of Master of Science (M.S.) and Doctor of Philosophy (Ph.D.). To obtain a graduate degree, a student must fulfill requirements of both the Graduate School and the Mathematics Department. Graduate School requirements for advanced degrees may be found in the Graduate Bulletin (pp. 183 - 188). Departmental requirements for each degree are summarized below and discussed in greater detail in subsequent sections of this handbook II. Master's Degree Programs The Master of Science degree is offered in two options: the Thesis Option or the Comprehensive Study Option. The Thesis Option emphasizes research and preparation of a scholarly thesis, whereas the Comprehensive Study Option emphasizes a broader understanding of a major area of mathematics. A. Departmental Requirements 1. A total of 30 credit hours in approved graduate-level mathematics course work, depending on the degree option (see below). Subject to the approval of the supervisory committee, at most 6 of these 30 credits may be earned in 600-level mathematics courses (but NOT Math 620, 621, 650, or 651) or in courses in fields other than mathematics. Thesis option: A total of 6 to 10 credit hours of Math 798 (Master's Thesis), in addition to 18 credit hours in courses numbered 700 - 789. These must include the two-semester sequences in Algebra (Math 720, 721) and Real Analysis (Math 750, 751). Comprehensive Study option: A total of 2 to 4 credit hours of Math 797 (Master's Paper), in addition to 24 credit hours in courses numbered 700 - 789. These must include the two-semester sequences in Algebra (Math 720, 721) and Real Analysis (Math 750, 751). 2. A passing grade in preliminary examinations in Algebra and Real Analysis. Each exam may be taken twice (a third time only with the chair's permission). 3. Demonstrated proficiency in a computer programming language. 4. A thesis or expository paper written under the supervision of a faculty member and defended at an oral examination administered by the student's supervisory committee. The purpose of the thesis or expository paper is to give the student an opportunity to study an area of mathematics and to organize and present these findings in writing. B. Comments Candidates have six calendar years from the time of enrollment in the Graduate School to complete the Master's degree. Students who change degree programs during this six-year period may be granted an extension after review and approval by the Graduate School. In any event, courses used toward the degree must have been taken within six years of graduation; courses older than this must be revalidated. III. Doctoral Degree Program The Doctor of Philosophy degree is awarded in recognition of high scholarly attainment as evidenced by a period of successful advanced study, the satisfactory completion of prescribed examinations, and the development of an acceptable dissertation covering some significant aspect of Mathematics. A. Departmental Requirements 1. A total of 90 credit hours in approved graduate-level mathematics course work, including: a. At least 42 credit hours in courses numbered 700 - 789 or as approved by the Director or Chair. These must include the two-semester sequences in Algebra (Math 720, 721) and Real Analysis (Math 750, 751), and four courses from the following list, which must be passed with a grade of B or higher: Math 728 (Linear Algebra), Math 746 (Topology), Math 752 (Complex Analysis), Math 754 (Functional Analysis), Math 756 (Dynamical Systems), Math 772 (Number Theory), Math 788 (Numerical Analysis). b. At least 3 credit hours of Math 790 (Graduate Seminar). c. At least 6 credit hours of Math 799 (Doctoral Dissertation). d. Subject to the approval of the supervisory committee, at most 12 credits may be earned in 600-level mathematics courses (but NOT Math 620, 621, 650, or 651) or in courses in fields other than mathematics. 2. A passing grade (PhD Pass) in preliminary examinations in Algebra and Real Analysis. Each exam may be taken twice (a third time only with the Chair's permission). 3. Demonstrated proficiency in one foreign language commonly used in the mathematical literature, normally French, German or Russian, as well as a demonstrated proficiency in a computer programming language. This requirement must be met prior to the preliminary oral examination. A student's supervisory committee may require a second foreign language. 4. A passing grade in a preliminary oral examination administered by the student's supervisory committee after the language requirements and all didactic coursework have been completed. Upon passing the oral examination, the student advances to candidacy for the Ph.D. 5. A dissertation consisting of a written presentation of original and significant research completed by the student under the supervision of a faculty member and defended at a final oral examination administered by the candidate's supervisory committee. B. Comments 1. Credits used to satisfy the requirements for a Master's degree at NDSU may be included in the total 90 credits required for the Ph.D. 2. Students entering the doctoral program with a Master's degree from another institution need only complete 60 credit hours, including: a. At least 30 credit hours in courses numbered 700 - 789 (but NOT Math 720, 721, 750, or 751). b. Subject to the approval of the supervisory committee, at most 6 credits may be earned in 600-level mathematics courses (but NOT Math 620, 621, 650, or 651) or in courses in fields other than mathematics. All other requirements must be satisfied as above. 3. All students must advance to candidacy no later than the start of their seventh year in the graduate program in Mathematics. Graduate credit for any coursework that is more than ten calendar years old at the time of the dissertation defense cannot be used to satisfy degree requirements. IV. Departmental Policies A. Supervisory Committee The Graduate Student Advisory Committee (GSAC) will advise most entering graduate students in mathematics for the first two semesters of their programs. The GSAC is formed by the Department Chair, the Graduate Program Director, the First Year Graduate Advisor, and other faculty members of the Mathematics Department. At the end of the second semester of the student's program, the GSAC will consult with the student and faculty involved to help select a supervisory committee of faculty members and other qualified experts in the field. The committee will be chaired by a major advisor, who will be in charge of the student's plan of study and supervise the student's research and preparation of the disquisition. A supervisory committee may be appointed later than the student's second semester if doing so is deemed to be in the best interest of the student. B. Plan of Study A plan of study will be prepared by the student and the major advisor no later than the semester immediately after the student's committee is formed. The plan of study must be approved by the student's committee, Graduate Program Director, Department Chair, Academic Dean, and the Dean of the Graduate School. Official plan of study forms may be downloaded from the Graduate School webpage. As students develop their plan of study under the supervision of their committee, they should include courses from the catalog which they plan to take in the future, with the understanding that, whenever possible, these courses will be offered as needed. Each year, the GSAC will suggest to the Department Chair a list of graduate courses to be offered the following year based on the proposed coursework in the Plans of Study which have been filed. The date in the plan of study for those courses to be taken in the future should read "pending." The Graduate Program Director and the Department Chair must be informed promptly by the student of any changes in the student's program, including all courses dropped and added, and all changes of hours or type of credit. A copy of each student scan form and request for registration changes must be given to the Director or Chair. After a student's committee has been formed, the committee's approval must also be obtained before each of these changes. C. Language Requirement Doctoral students must demonstrate, in a written examination, their proficiency in a foreign language commonly used in the mathematical literature. Acceptable languages include French, German, and Russian. Once a student selects an approved language and prepares appropriately, the student's advisor selects three mathematics papers that are written in the chosen language. The student translates these papers on his or her own, and then schedules an initial meeting with a language expert from the Modern Languages Department who can gauge if the student is ready for a more rigorous translation test. If the student's preparation is deemed adequate, the language expert selects a portion of the papers for the student to translate (with the aid of a dictionary) to the expert's satisfaction. Additionally, Doctoral and Master's students must demonstrate their proficiency in a computer programming language. This can be accomplished either by passing Math 660 (Intensive Mathematica) or another NDSU computer programming course with a grade of B or higher, or by passing completing a programming examination given by the Graduate Program Director. D. Preliminary Examinations There are three preliminary examinations required for advancement to candidacy for the Ph.D. They consist of two written examinations (in the subjects of Algebra and Real Analysis) and one oral examination. Passing grades in the written preliminary examinations are also required for the Master's degree. The examinations in Algebra and Real Analysis are scheduled in early January and immediately before the Fall Semester every year. Each exam may be taken twice (a third time only with the chair's permission). To help the student prepare for the written examinations, the faculty has compiled lists of topics and references that may be obtained from the departmental office. Copies of previous examinations also may be obtained in the departmental office. The oral examination is administered by the student's supervisory committee after the written examinations, language requirements and all didactic coursework have been completed. At the oral examination, the student describes the plans for the dissertation and answers questions on the material from four semester courses selected by the student and the supervisory committee at least a month before the exam. A request to schedule must be sent to the Graduate School at least two weeks prior to the exam. Upon passing the oral examination, the student advances to candidacy for the Ph.D. E. Disquisitions Writing and defending the disquisition is the capstone experience of a student's graduate career. At the Doctoral level, the disquisition is called a dissertation. A dissertation must show originality and demonstrate the student's capacity for independent research; it must embody results of research which constitute a definitive contribution to knowledge. At the Master's degree, two types of disquisition are possible: a thesis or an expository paper. A thesis emphasizes original research and abilities to analyze data, whereas an expository paper emphasizes a broader understanding of Mathematics. Disquisitions reflect the work product of our graduate program. As such, they should be mathematically correct, utilize proper grammar and syntax, and adhere to the style format accepted by the Graduate School. The approved style for disquisitions is described in the booklet Guidelines for the Preparation of Disquisitions . A LaTeX document style which meets the criteria of the Graduate School is also available for download from the Math Department website. Any student wishing to write a disquisition under the direction of someone who is not a regular faculty member of the Mathematics Department at the rank of assistant professor or above must first obtain approval from the Graduate Student Advisory Committee and the Graduate School. The student must have successfully completed the written preliminary examination requirements and the foreign language requirement before requesting approval. To support the request for approval, the student must provide to the GSAC a written statement describing the proposed dissertation area and the reason(s) for (i) working with someone from outside the department and (ii) not working with a member of the department. The proposed dissertation advisor's curriculum vitae also must be provided. The GSAC may request additional information or actions to assist its consideration of the matter. If the request is approved, then to assure appropriate and substantial mathematical content in the student's dissertation, the student's Ph.D. committee must include at least two faculty members of the Mathematics Department, at least one of whom is approved to direct doctoral dissertations. F. Colloquia The Mathematics Department regards the colloquium lectures as a part of a student's graduate education, and graduate students are expected to attend these lectures. Speakers at the Mathematics Colloquia include mathematicians from outside the university, our own staff, and other members of the university community. Most talks are based on the speaker's current research interests, or are expository talks on advanced topics. They are general in nature, with technical details left to specialized seminars. G. Graduate Minor Degree Graduate students pursuing a degree in another department may, concurrently, obtain a graduate minor degree from the Mathematics Department. The minor degree is awarded at the time that the student completes his major degree. Graduate minor students must choose a faculty member from the Mathematics Department to serve in their supervisory committee as minor advisor and to help select the appropriate courses. Course work must include a total of 12 credit hours in mathematics courses numbered 601 - 789 or 700 - 789, including a two-semester 700-level sequence. These courses must be passed with a grade of B or higher. H. Academic Honesty Each graduate student in the Mathematics Department is expected to conform to the highest standards of academic honesty in all classwork, homework, examinations, research and writing, and to the highest standards of professional behavior in teaching. Any violation of this policy, such as plagiarism or other forms of academic dishonesty, will result in penalties, such as lowered grades, loss of financial support, and/or expulsion from a degree program. A letter to the Department describing the violation and the penalty assigned must document each punitive action taken by the Department or any of its professors against a student. A copy of the letter must be sent to the affected student. Each punitive action taken may be appealed through the following channels, successively: Graduate Student Advisory Committee, Department Chair, Academic Dean, and Dean of the Graduate School. [Adobe PDF Printable Version]