## Main Page Content

### 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; Kazumi Nakano, PhD, Wayne State University.

**Associate Professors:**
Norman J. Bloch, PhD, University of Rochester; Richard T. Mahoney, PhD,
Washington University.

**Assistant Professors:** Mihail Barbosu, PhD, Paris
Observatory and Paris VI University, PhD, "BABES-Bolyai" University;
Petros Hadjicostas, PhD, Carnegie Mellon University; Dawn Jones, PhD,
Western Michigan University. Lecturer: Cynthia P. Burke, MA, SUNY College
at Brockport

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 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.

### 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.

### 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:

- 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.

### Requirements for the Degree

- 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.
- Language Requirement: Knowledge of a computer language or a foreign language must be demonstrated to the department. A student may petition the Graduate Committee to waive this requirement.
- 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

Because of the requirement that an index of 3.0 be achieved by the student, satisfactory progress is necessary. A student is subject to dismissal from the program if, upon completion of 15 credits of the Plan of Study, the student's cumulative index is below 2.50.

### 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:

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

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

### Mathematics 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.

**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 538 Projective Geometry (A). **Prerequisite:
MTH 424. Covers axiomatic systems, projectivity, Desargues' theorem, collineations,
the cross ratio, homogeneous coordinates in a plane, finite projective
planes, conics, linear transformations, and subgeometries. 3 Cr.

**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 part of MA Plan
of Study.) 3 Cr.

**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 Markovanalysis. 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 605 Problem Solving in Mathematics.** Prerequisite:
Mathematics major as undergraduate. Develops problem-solving ability at
the graduate level. Emphasizes meaning, strategies and written communication.
Especially appropriate for secondary mathematics teachers. 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 614 Foundations of Mathematics.** Prerequisites:
MTH 425 and 457. Lays the foundation for selected mathematical concepts.
Starting with Peano's axioms for the integers, develops the real number
system by means of Cauchy sequences of rational numbers. Establishes the
arithmetic of transfinite cardinal numbers. Examines and applies Zorn's
Lemma and some of its logical equivalents. 3 Cr.

**MTH 619 Topics for Teachers I 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.