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DEPARTMENT OF MATHEMATICS
Chairperson: Vacant at time of publication; Professors: John G. Michaels, PhD, University of Rochester; Sanford S. Miller, PhD, University of Kentucky; Associate Professors: Mihail Barbosu, PhD, Paris Observatory and Paris VI University, PhD, BABES-Bolyai University; Charles J. Sommer, PhD, SUNY Buffalo; Assistant Professors: Dawn Jones, PhD, Western Michigan University; Izuro Mori, PhD, University of Washington; Gabriel Prajitura, PhD, University of Tennessee-Knoxville; Howard Skogman, PhD, University of California at San Diego; 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 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.
The applicant must possess a baccalaureate degree from an accredited institution (see Chapter 3 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, 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.
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.
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:
- three core courses: algebra (MTH 621 or 629), analysis (MTH 651 or 659), applied mathematics or statistics (MTH 641 or 669); and
- 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.
- 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 the Plan of Study.
- Comprehensive Examination: After completing 24 or more credits of the courses in- cluded in the Plan of Study, the student must pass a comprehensive examination.
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.
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:
- an oral follow-up exam may be required in the case of inconclusive results, and
- the exam may be taken only twice.
MTH 512 History of Mathematics (A). 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 (A). Prerequisites: MTH 202 and MTH 281. Covers mathematical induction, divisibility, primes, arithmetic functions, congruencies, Diophantine problems, Gaussian primes, Euler's generalization of Fermat's theorem and selected advanced topics. 3 Cr. Fall
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. Every Semester
MTH 541 Statistical Methods I (A). Prerequisites: MTH 243 or MTH 346 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
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. Requires the use of computers for data analysis. 3 Cr. Spring
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. Every Semester
MTH 551 Advanced Calculus (A). 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 (A). 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 556 Advanced Differential Equations (A). Prerequisites: MTH 255, MTH 324 or some 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. Spring
MTH 557 Real Analysis (A). Prerequisites: MTH 203 and MTH 324. Provides a study of functions of a real variable. Emphasizes theory and proof techniques. 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 Deterministic Mathematical Models (A). Prerequisite: either MTH 245 or MTH 281. 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. Fall
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. Spring
MTH 563 Graph Theory (A). Prerequisite: MTH 281. 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. Spring
MTH 571 Numerical Analysis I (A). 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. 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. Every Semester
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: Mathematics major as an undergraduate. 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. Fall
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). 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 (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 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 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 (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.