Mathematical Sciences - Graduate
The department is committed to the idea that pure and applied mathematics are two faces of the same subject. The research of the faculty and the training of the students cover a wide variety of topics in pure mathematics, as well as statistics and computer science. The department offers a lively research atmosphere. Students are encouraged to take a broad range of courses. Teaching assistants are given varied assignments intended to increase their experience and employability. The distinguished research faculty offers considerable personal attention to graduate students.
The department offers the MA and PhD degrees. Research areas of faculty expertise include algebra, combinatorics, dynamical systems, geometry/topology, graph theory, probability and statistics.
The MA program is intended to give the student a solid professional basis either for proceeding to the PhD program or for work in government, industry or teaching at the community college level. The PhD degree prepares a student for university or college teaching and for higher-level employment in government and industry. Entering students having substantial graduate-level training may enter the PhD program, skipping the MA.
The department is noted for its method of graduate education. In first-year courses, the emphasis is on training the student to do mathematics in depth. Many students report that these courses are the formative experiences of their professional lives.
Teaching assistantships are available. They provide not only financial support but also valuable experience, either in teaching a variety of courses or assisting faculty in special courses. The aim is to enhance students’ training with actual experience helpful in obtaining employment.
Department members assist students in obtaining suitable employment and offer advice for career development.
The department cooperates with the Division of Education, which offers both the MAT (Master of Arts in Teaching) degree in Mathematics Adolescence Education and the MSEd (Master of Science in Education) degree in Adolescence Education in Mathematics.
Minors
Although there is no official requirement of a minor, the department supports the concept of suitable study outside the area of primary emphasis, particularly for doctoral students. Doctoral students in pure mathematics are encouraged to obtain expertise in an area of applied mathematics sufficient for competency in instruction in that area at the undergraduate level. Students in statistics and other applied areas naturally obtain appropriate training in pure mathematics in the regular course of study.
Note: A departmental graduate student handbook is available on the department Web pages at www.math.binghamton.edu/dept/grad/GraduateHandbook/index. html.
Requirements
Admission to Regular Standing
For admission to regular standing, a student should have a bachelor’s degree and have completed (with an average of at least 3.0) a set of mathematics courses approximately equivalent to those required for a bachelor’s degree at Harpur College with a specialization in mathematics. The department encourages submission of Graduate Record Examination scores for the aptitude and advanced tests that are useful in evaluating applicants.
Master of Arts Program
The official requirement for a master’s degree is a minimum of 30 credit hours at the graduate level. This requirement may technically be satisfied in three semesters. However, the 30-hour requirement is regarded as minimal, and most students take four semesters to complete the master’s degree. Each student’s program is worked out in consultation with an adviser, under the general supervision of the graduate committee. While it is possible for a student to fulfill up to eight hours of course requirements by writing a master’s essay, only in certain circumstances is this encouraged. Students writing a master’s essay must pass an oral examination covering the subject matter of the essay.
MA students who do not write master’s essays must pass an oral examination in the last semester of their MA program. For this purpose, a committee of three or more faculty members is appointed. Usually these are faculty members who have taught the student. The examination syllabus is arranged by the committee in consultation with the student; in general it covers 30 hours of the student’s coursework.
Master of Arts in Teaching and Master of Science in Education
The Department of Mathematical Sciences cooperates with the program in education, which offers both the MAT (Master of Arts in Teaching) degree, Grades 7-12, in Mathematics Adolescence Education, and the MSEd (Master of Science in Education) degree in Adolescence Education in Mathematics.
The MAT degree program is for those with an undergraduate degree in mathematics who are seeking provisonal certification to teach mathematics in grades 7-12. The MSEd degree program is for those who already hold provisional certification to teach in New York state, and leads to permanent certification in New York state to teach mathematics in grades 7-12. Requirements for these degrees are listed in this publication in the section on the School of Education and Human Development. Mathematics courses specifically designed for these programs are indicated by MAT/MSEd following the course title.
Inquiries about these programs should be directed to the Program in Education, School of Education and Human Development, Binghamton University, PO Box 6000, Binghamton, New York 13902-6000.
Doctor of Philosophy Program
A minimum of 14 courses at the graduate level (including those counted for the MA) is required. A total of five or six years of full-time graduate study (including study toward the MA) is normally required to complete the doctorate.
Admission to PhD candidacy begins with informal discussions among the student, the adviser and other members of the department on whether it is wise for the student to consider pursuing a doctorate. Such discussions generally take place early in the student’s fourth semester of graduate study, near the end of the master’s program, when department members are able to assess the student’s abilities. Then, or later, the student finds a prospective dissertation adviser who is an active and established researcher and who is willing (at least provisionally) to supervise the student’s doctoral dissertation.
At an appropriate time, the adviser presents to the graduate committee a format for the “admission to candidacy” examination of the student. This format, worked out in consultation with the student, may be one or several examinations, written or oral, in several areas; an oral presentation of research papers; or a combination of these. The adviser provides syllabi for the areas to be covered on the examination. The graduate committee either accepts the adviser’s recommendation or suggests alternatives; it then appoints an examining committee to carry out its instructions. The examining committee reports the results of its examination and its recommendations to the graduate committee. The graduate committee makes the final decision on the student’s admission to candidacy. A detailed explanation of this procedure is available in the department.
Dissertation
The student must, of course, do research and write a dissertation. It is the student’s responsibility to find an adviser willing to supervise the research and guide the student in writing the thesis. The graduate committee then appoints a guidance committee for the student. The dissertation must be defended in an oral examination.
Components in Mathematics and Statistics
Within the MA or PhD program there are two components or areas of emphasis. The flavor of these components may be indicated as follows:
Mathematics Component
The department is committed to the idea that the student whose primary interest is pure mathematics should also be acquainted with some applications. Thus, even students pursuing the PhD degree in mathematics are encouraged to take some courses in computer science and/or statistics. The department has special emphasis in algebra, combinatorics, dynamical systems, functional analysis, geometry/topology, graph theory, probability and statistics. The department has a tradition of developing intellectual independence in its graduate students. Much time is given to the education of graduate students, both individually and in small classes.
Statistics Component
The statistics component gives broad training. The master’s degree prepares students for jobs as statisticians and data analysts in government and industry. The PhD degree prepares students for university teaching and research, as well as consulting and research roles in industry and government. Students are given training in many diverse statistical methods used to analyze data, as well as the mathematical, statistical and probabilistic foundation.
Course Offerings: Undergraduate
For full course descriptions, refer to this location on the Web: bulletin.binghamton.edu/math.htm.
Note: Unless otherwise noted, all undergraduate courses carry four credits and are offered every year.
Course Offerings: Graduate
It should be noted that a substantial number of the department’s advanced graduate courses are offered in MATH 590, Topics in Modern Mathematics, and are therefore not listed here. This allows for flexibility and the offering of once-only courses on topics of current research interest. Recent topics have included algebraic K-theory, biologically inspired methods of computation, cohomology of groups, combinatorial group theory, convex polytopes, differential geometry, differential topology, ergodic theory of geodesic flows, geometric group theory, graph theory, homotopy theory, infinite simple groups, languages and molecular computation, lattice theory, Lie algebras, matroid theory and biased graphs, representation theory, surgery theory, theory of fiber spaces, topics in rings and algebras, topological aspects of oriented matroids, asymptotic theory, data analysis, reliability, risk processes, semiparametric models and survival analysis.