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Graduate Studies Catalog 2007-2009

Department of Mathematics

200 Albert W. Brown Building
Phone: (585) 395-2036; Fax: (585) 395-2304
www.brockport.edu/math

Chairperson and Associate Professor: Mihail Barbosu, PhD, Paris Observatory and Paris VI University; Professor: Sanford S. Miller, PhD, University of Kentucky; Associate Professors: Dawn M. Jones, PhD, Western Michigan University; Gabriel T. Prajitura, PhD, University of Tennessee-Knoxville; Howard J. Skogman, PhD, University of California at San Diego; Charles J. Sommer, PhD, SUNY Buffalo; Assistant Professors: Jason R. Morris, PhD, University of Pittsburgh; Bogdan Petrenko, PhD, University of Illinois at Urbana-Champaign; Rebecca Smith, PhD, University of Florida; Pierangela Veneziani, PhD, Rutgers University; Ruhan Zhao, PhD, University of Joensuu, Finland.

The mission of the Master of Arts in Mathematics program is to provide students with a solid foundation in the major areas of mathematics, an appreciation for the structures and theories of advanced mathematics, and a deeper understanding of the role of mathematics in applications. The department strives to produce graduates who exhibit knowledge, comprehension and creativity in the practice of mathematics as they pursue their careers in college/high school teaching, business or government, or as they pursue doctoral studies.

The program is designed to meet the needs of a broad range of students, including mathematics teachers at the secondary and college levels, industrial mathematicians, computer professionals, and prospective candidates for a PhD in mathematics. For example, individuals seeking permanent or professional certification in secondary mathematics may, following consultation with their advisors, develop an appropriate Plan of Study within the MA program. The Master of Arts in Mathematics program is quite flexible. The degree candidate chooses a core course in each of three areas: algebra, analysis and applied mathematics or statistics, and chooses seven other courses with the approval of the Mathematics Graduate Committee.

Please note that the information in this document is subject to change. For the latest information on our courses, please contact the department.

Admission
The applicant must possess a baccalaureate degree from an accredited institution (see the Graduate Admissions section in this catalog for further details) and have completed the equivalent of an undergraduate major in mathematics. (This usually means a minimum of 24 credits beyond calculus with an average of “B” or better. Deficiencies can be removed by taking remedial coursework, but these credits will not contribute to a student’s graduate Plan of Study.) The applicant must submit to the Office of Graduate Admissions a completed self-managed application for admission as a matriculated student that includes official transcripts of all undergraduate and graduate studies and two letters of recommendation from persons who can attest to the applicant’s qualifications for graduate study.

Financial Assistance
A limited number of graduate assistantships are available. These carry a stipend and scholarship for up to 18 credits of tuition per academic year. To be eligible for a graduate assistantship, students must be full-time (i.e., registered for a minimum of nine credits a semester). Assistantship duties require 15 hours of work per week. Additional information may be obtained from the department office and the Office of Graduate Studies, (585)395-2525.

Student Advisement
Each student admitted to the Master of Arts in Mathematics program selects an advisor or is assigned one by the Graduate Committee. The student and advisor constitute the Advisory Committee for the student.

Plan of Study
The Advisory Committee has the responsibility of planning the student’s program and submitting a Plan of Study to the Graduate Committee for approval during the student’s first semester in the program.

The Plan of Study must include 30 credits of course work, with a minimum of 15 credits of mathematics at the 600 level or above. Of the 30 credits, a minimum of 21 credits must be in mathematics, as follows:

  1. three core courses: algebra (MTH 621 or 629), analysis (MTH 651 or 659), applied mathematics or statistics (MTH 641 or 669); and
  2. at least four additional approved graduate mathematics courses (which may include CSC 583).

The remaining credits are to be approved electives at the 500 level or above. These may be courses in mathematics, computer science, economics, education or other mathematics-related fields. Credit is not allowed for any course that substantially duplicates a course taken as an undergraduate or intended for graduate students in other disciplines.

Requirements for the Degree
Requirements for the Master of Arts in Mathematics include:

  1. Course Work: 30 credits in an approved Plan of Study, as described above. Ordinarily, no more than six transfer credits are accepted. A cumulative grade point average of 3.0 is required for the courses in the Plan of Study.
  2. Comprehensive Examination: After completing 24 or more credits of the courses included in the Plan of Study, the student must pass a comprehensive examination.

Satisfactory Progress
Students in the MA program in mathematics are expected to make satisfactory progress toward completion of their degree. Those who do not are subject to academic probation and dismissal. Please refer to the College’s policy concerning academic probation and dismissal as published in this catalog.

Comprehensive Examination
The Comprehensive Examination is given two weeks after the fall semester ends, two weeks after the spring semester ends, or in August. It is based on the three core courses in algebra, analysis and applied mathematics/statistics included in the student’s Plan of Study.

The candidate will take a set of three take-home exams. The student has two weeks to complete the exams, which may include in-depth problems that require the use of reference materials.

The exam is subject to these rules:

  1. an oral follow-up exam may be required in the case of inconclusive results, and
  2. the exam may be taken only twice.

MATHEMATICS COURSES

MTH 512 History of Mathematics (A). Prerequisites: MTH 202 and MTH 245 or MTH 281. Covers the history and development of mathematical ideas from primitive origins to the present. Includes topics such as arithmetic, number theory, geometries, algebra, calculus and selected advanced topics. 3 Cr.

MTH 520 Mathematics for Adolescence Teachers (A). Prerequisite: MTH 432. Analyzes the adolescence mathematics curriculum (grades 5-12) from an advanced prospective. Topics include algebra, geometry, data analysis, statistics, trigonometry, discrete mathematics, calculus. Students will examine their own understanding of these topics as well as examine the theoretical underpinning of each. 3 Cr.

MTH 521 Number Theory (A). Prerequisites: MTH 281 and instructor’s permission or MTH 425. Topics include but are not limited to: mathematical induction, divisibility, primes, arithmetic functions, congruencies, modular arithmetic, Diophantine problems and the distribution of primes. 3 Cr.

MTH 530 Topology (A). Prerequisites: MTH 281 and either instructor’s permission or MTH 425 or MTH 457. Provides a study of topologies on various spaces. Emphasizes theory, abstraction, proof techniques and clarifies these by means of many specific examples. Bridges topics such as geometry, analysis and algebra. Topics include, but are not limited to set theory, continuous functions, connectedness, compactness and separation. 3 Cr.

MTH 532 College Geometry (A). Prerequisite: MTH 324. Studies geometry from the synthetic, analytic, transformational and vector viewpoints. Includes these topics: axiomatic systems, finite geometries, absolute geometry, Euclidean geometry, non-Euclidean geometries, geometric transformations and projective geometry. 3 Cr.

MTH 541 Statistical Methods I (A). Prerequisite: MTH 243 or MTH 346. Covers estimation, hypothesis testing, simple regression, categorical data and non-parametric methods. Uses statistical analysis software. 3 Cr.

MTH 542 Statistical Methods II (A). Prerequisite: MTH 541 or instructor’s permission. Covers one and two-way analysis of variance, multiple regression, experimental design and linear models. Uses statistical analysis software. 3 Cr.

MTH 546 Probability and Statistics II (A). Prerequisites: MTH 203 and MTH 346. Covers the Central Limit Theorem, maximum likelihood estimation, method of moments, unbiased and sufficient statistics, minimum variance, Cramer-Rao lower bound, confidence intervals, Neyman-Pearson Lemma, power calculations, likelihood ratio tests. 3 Cr.

MTH 556 Advanced Differential Equations (A). Prerequisites: MTH 255, MTH 324 or exposure to matrix theory. Covers series solutions about singular points, systems of linear first-order differential equations, plane autonomous systems, Fourier series, Sturm Liouville problems, partial differential equations of physics including the heat, wave and Laplace equation. 3 Cr.

MTH 561 Deterministic Mathematical Models (A). Prerequisites: either MTH 245 or MTH 281 or instructor’s permission. Teaches applied mathematics techniques to be used in engineering, business, finance and other management fields. Includes linear programming, sensitivity analysis, the simplex method, shortest path method, integer linear programming and network models. 3 Cr.

MTH 562 Stochastic Mathematical Models (A). Prerequisite: MTH 346. Teaches applied mathematic techniques to be used in engineering, business, finance and other management fields. Includes project scheduling, decision theory, simulation, risk analysis, multicriteria decision problems, inventory and queuing models, forecasting, dynamic programming and Markov analysis. 3 Cr.

MTH 563 Graph Theory (A). Prerequisite: MTH 324 or instructor’s permission. An introduction to graph theory, including distance concepts, symmetry and structure, trees and connectivity, Eulerian and Hamiltonian Graphs, planar graphs and imbeddings and applications of graphs. 3 Cr.

MTH 565 Combinatorics (A). Prerequisite: MTH 324. Gives an introduction to combinatorics including basic counting techniques involving permutations, combinations, compositions and partition; binomial coefficients; the twelvefold way; recursions and generating functions. Other topics may include a more advanced study of permutations, sequences in combinatorics, magic squares, the probabilistic method, etc. 3 Cr.

MTH 571 Numerical Analysis I (A). Prerequisite: MTH 203. Covers the development of methods used to numerically approximate the solutions to mathematical problems, with consideration given to generation and propagation of round-off errors, convergence criteria and efficiency of computation. Includes these topics: roots of nonlinear equations, systems of nonlinear and linear equations, polynomial approximations, numerical differentiation and integration, and curve fitting. Mathematical software, such as MAPLE, will be used. 3 Cr.

MTH 581 Discrete Mathematics II (A). Prerequisites: MTH 201 and MTH 281. A second course in discrete mathematical structures. Includes these topics: algorithms and complexity, combinatorial techniques, recurrence relations, inclusion-exclusion principle, equivalence and partial-order relations, graph theory, Boolean algebra and normal forms, tree structures and traversals, languages, grammars and finite-state machines. 3 Cr.

MTH 599 Independent Study in Mathematics (A). To be defined in consultation with the instructor-sponsor prior to registration. 1-3 Cr.

MTH 605 Problem Solving in Mathematics (A). Prerequisite: Departmental permission. Develops problem-solving ability at the graduate level. Emphasis on meaning, strategies and written communication. Especially appropriate for adolescence mathematics teachers. 3 Cr.

MTH 612 History of Contemporary Mathematics (A). Covers the development of mathematics from the 17th century to its current form. Includes these topics: the development of calculus, number theory, abstract algebra, geometries and applied mathematics. Examines the works of outstanding mathematicians. 3 Cr.

MTH 619 Topics for Teachers I - Mathematical Modeling (A). Designed for secondary school mathematics teachers. Focuses on the use of the computer as a modeling device, and on mathematical models in the social and life sciences. Includes these topics: problem solving, algorithm design and the development of programming skills. 3 Cr.

MTH 621 Algebra (A). Prerequisite: MTH 425. Includes these topics: groups and subgroups, normal subgroups and quotient groups, permutation groups, finite Abelian groups, some special classes of rings, homomorphisms, ideals and quotient rings Euclidean rings and polynomial rings. 3 Cr.

MTH 628 Applications of Algebra (A). Prerequisites: MTH 425 and either MTH 621 or instructor’s permission. Applies group theory and ring theory to the solution of polynomial equations and to problems in number theory, geometry, coding theory, combinatorics and selected areas of computer science. 3 Cr.

MTH 629 Topics in Algebra and Number Theory (A). Introduces topics of current interest in research or topics not covered in other courses in algebra and number theory. An outline of selected topics will be announced before the course is offered. 3 Cr.

MTH 639 Topics in Geometry (A). Prerequisite: MTH 324. Introduces topics of current interest in research or topics not covered in other courses in geometry. An outline of selected topics will be announced before the course is offered. 3 Cr.

MTH 641 Mathematical Statistics (A). Prerequisite: MTH 446 or MTH 546. Allows for rigorous development of probability concepts in the sample space and models for discrete and continuous random variables. Introduces bivariate normal distribution, transformation of variables, statistics and sampling distributions, Central Limit Theorem, parametric estimation, Rao-Cramer inequality, hypothesis tests, power functions, Neyman-Pearson Theorem and both UMP and Likelihood Ratio tests. 3 Cr.

MTH 651 Real Analysis (A). Prerequisite: MTH 457. Includes topics such as uniform continuity and the Weierstrass Approximation Theorem, theory of differentiation and the Riemann integral, convergence of series of functions, uniform convergence of series of functions, functions of bounded variation, Riemann-Stieltjes integration, Lebesque measure and Lebesque integration. 3 Cr.

MTH 659 Topics in Analysis (A). Introduces topics of current interest in research or topics not covered in other courses in analysis. An outline of selected topics will be announced before the course is offered. 3 Cr.

MTH 669 Topics in Applicable Mathematics and Statistics (A). Introduces topics of current interest in research or topics not covered in other courses in applicable mathematics and statistics. An outline of selected topics will be announced before the course is offered. 3 Cr.

MTH 699 Independent Study in Mathematics (A). To be defined in consultation with the instructor-sponsor prior to registration. 1-3 Cr.

The information in this publication was current as of Summer 2007 when the text was compiled. Changes, including but not restricted to, tuition and fees, course descriptions, degree and program requirements, policies, and financial aid eligibility may have occurred since that time. Whether or not a specific course is scheduled for a given term is contingent on enrollment, budget support and staffing. The College reserves the right to make any changes it finds necessary and may announce such changes for student notification in publications other than the College catalogs. For the purposes of degree and program completion, students are bound by the requirements in effect as stated in the printed catalog at the time of their matriculation at SUNY Brockport. Students matriculated in summer are bound by the catalog in effect the following fall semester. Inquiries on the current status of requirements can be addressed to the appropriate College department or office. Also refer to the Brockport Web site home page at www.brockport.edu for current information. Printed Summer 2007