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Graduate Catalog

Department of Mathematics

(585) 395-2194

Chairperson and Associate Professor: Charles J. Sommer, PhD, SUNY Buffalo. Professors: Joseph B. Harkin, PhD, Illinois Institute of Technology; John G. Michaels, PhD, University of Rochester; Sanford S. Miller, PhD, University of Kentucky. Associate Professors: Richard T. Mahoney, PhD, Washington University. Assistant Professors: Mihail Barbosu, PhD, Paris Observatory and Paris VI University, PhD, "BABES-Bolyai" University; Dawn Jones, PhD, Western Michigan University; Gabriel Prajitura, PhD, University of Tennessee-Knoxville; Howard Skogman, PhD, University of California at San Diego. Lecturer: Cynthia P. Burke, MA, SUNY College at Brockport.

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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 further 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 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.

Admission
The applicant must possess a baccalaureate degree from a regionally accredited institution 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, but without credit.) 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 remission of up to 18 credits of tuition per academic year. 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

  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 index of 3.0 is required for the courses in a 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 found on p.58 of 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 student may elect (subject to Graduate Committee approval) either of the following examinations:

  1. a six-hour sit-down exam, made up of three two-hour exams to be given during one week.
  2. 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.

Both types of exams are 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.

Math Courses

MTH 512 History of Mathematics. Prerequisite: MTH 203. Covers the history and development of mathematical ideas from primitive origins to today. Includes topics such as arithmetic, number theory, geometries, algebra, calculus, and selected advanced topics. 3 Cr. Spring

MTH 521 Number Theory. Prerequisites: MTH 202 and 281. Covers mathematical induction, divisibility, primes, arithmetic functions, congruences, Diophantine problems, Gaussian primes, Euler's generalization of Fermat's theorem, and selected advanced topics. 3 Cr. Fall

MTH 532 College Geometry. Prerequisite: MTH 424. 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. Fall

MTH 541 Statistical Methods I. Prerequisite: MTH 346 or 243 or an equivalent introductory statistics course. Covers estimation, hypothesis testing, simple regression, categorical data, and non-parametric methods. Requires the use of computer statistical analysis packages, e.g. MINITAB and SPSS. 3 Cr. Fall. (May not be included as pa

MTH 542 Statistical Methods II. Prerequisite: MTH 541 or instructor's permission. Covers one- and two-way analysis of variance, multiple regression, experimental design, and linear models. Requires the use of computers for data analysis. 3 Cr. Spring

MTH 546 Probability and Statistics II. Prerequisites: MTH 203 and 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. Every Semester

MTH 551 Advanced Calculus. Prerequisite: MTH 203. Covers vector differential calculus, Inverse Function Theorem, Implicit Function Theorem, line integrals including Green's theorem, independence of path, and surface integrals with Gauss' and Stokes' theorems. 3 Cr.

MTH 552 Applied Analysis. Prerequisite: MTH 203. Presents a survey of mathematical methods used in the physical sciences. Includes topics such as vector analysis, linear algebra, partial differentiation, multiple integration, Fourier series, and complex analysis. 3 Cr.

MTH 555 Differential Equations. Prerequisite: MTH 202. Covers differential equations of first and second orders and their applications, linear equations, series solutions, approximate solutions, and the Laplace transform. 3 Cr. Fall

MTH 557 Real Analysis. Prerequisites: MTH 203 and 424. Provides a study of functions of a real variable. Emphasizes theory, proof techniques, and writing skills. Includes: real numbers, denseness of the rational numbers, convergence of sequences of real numbers, Cauchy sequences, Bolzano-Weierstrass theorem, continuous functions, uniform continuity, differentiable functions, and integrable functions. Enhances understanding of the topics through a series of required writing tasks. 3 Cr. Every Semester

MTH 561 Mathematical Models for Decision Making I. Prerequisite: MTH 245 or 281. Covers linear programming, transportation and assignment models, network models, and dynamic programming. 3 Cr. Fall

MTH 562 Mathematical Models for Decision Making II. Prerequisite: MTH 346. Covers probability models, decision theory, inventory and queuing models, and Markov analysis. 3 Cr. Spring

MTH 571 Numerical Analysis. Prerequisites: MTH 203 and CSC 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. 3 Cr.

MTH 581 Discrete Mathematics II. Prerequisites: MTH 201 and 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. Every Semester

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

MTH 612 History of Contemporary Mathematics. 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 In Mathematical Modeling. Designed for secondary school mathematics teachers. Focuses on the use of the computers 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. 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. Prerequisite: MTH 425 or an equivalent abstract algebra course. 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. 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. Prerequisite: MTH 424. 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. Prerequisite: 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. Prerequisite: MTH 557. Includes topics such as limits and continuity of functions, uniform continuity and the Weierstrass Approximation Theorem, theory of differentiation and the Riemann integral, convergence of sequences of functions, uniform convergence of series of functions, functions of bounded variation, and Riemann-Stieltjes integration. 3 Cr.

MTH 659 Topics in Analysis. 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. 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. To be defined in consultation with the instructor sponsor prior to registration. 1-3 Cr.

  The information in this publication was current as of December 2002 when the text was compiled. Changes, including but not restricted to, tuition and fees, course descriptions, degree and program requirements, policies, and financial aid availability may have occurred since that time. Whether or not a specific course is scheduled for a given term is contingent on enrollment, budget 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 purpose 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. Inquiries on the current status of requirements can be addressed to the appropriate College department of office. Also refer to the Brockport Web site home page at www.brockport.edu for current information.

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