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Undergraduate Studies Catalog (1999-2001)


Department of Mathematics

290 Faculty Office Building
(716) 395-2194

Chairperson: Charles J. Sommer; Professors: Mou-ta Chen, Joseph B. Harkin, John G. Michaels, Sanford S. Miller, Kazumi Nakano; Associate Professors: Norman J. Bloch, Richard T. Mahoney; Lecturer: Marcella H. Esler.

An in-depth understanding of mathematics is of great importance to many careers in our tech nologically complex society. Moreover, the study of mathematics promotes analytical and critical thinking skills, and therefore is a valuable part of any program of study. The major and minor programs in mathematics are designed to provide the knowledge and skills necessary to pursue graduate study or to support career goals in a range of professions. Recent graduates who have majored in mathematics have found rewarding careers in business, teaching, computing, government, law, engineering, and medicine. A major or minor in mathematics is a natural adjunct to the study of physics, chemistry, biology, earth science, business, economics, computer science, or the social sciences.

The department offers a major in mathematics, a minor in mathematics, and a minor in mathematics/statistics. In addition, it supports a double major in mathematics and computer science and a five-year, two-degree mathematics/engineering program. To complete a major in mathe matics, students take nine required courses that provide a thorough foundation in several central areas of mathematics, a computer science course that emphasizes the design of algorithms, and a minimum of three advanced courses chosen to give special depth in at least one area. The two minor programs require students to take six mathematics courses that coherently complement their particular major.

Because of the sequential nature of the study of mathematics, students should meet with the department's advisement coordinator as soon as possible to declare a major or minor, be assigned a departmental advisor, and plan an academic program.

Major in Mathematics (40 credits)
Students must complete a minimum of 36 credits in mathematics and four credits in computer science, as follows:
1. Required MTH courses (27 credits) Credits
MTH 201, 202, 203 Calculus I, II, III 9
MTH 281 Discrete Mathematics I 3
MTH 346, 446 Probability and Statistics I, II 6
MTH 424 Linear Algebra 3
MTH 425 Modern Algebra 3
MTH 457 Real Analysis 3

2. Elective courses (9 credits) 9
Nine credits in mathematics, by advisement, from courses numbered MTH 399 or higher.
CSC 483 may be substituted for one of these MTH courses.

3. Computer science course: CSC 203 Fundamentals of Computer Science I. 4

Total: 40

Notes:
(a) Students intending to obtain secondary education certification in mathematics must com plete MTH 432 or 438.

(b) At least three 400-level MTH courses must be taken at SUNY Brockport, including at least one of the following: MTH 425, 446, or 457.

Students who have successfully completed a calculus course in high school may qualify for college credit for MTH 201 and 202. Qualifying students must contact the department before they register for their first calculus course at SUNY Brockport.

More details concerning the mathematics major, including sample programs of study and infor mation on advisement for majors, student awar ds, computing facilities, library holdings, the Mathematics Club, and the Student Chapter of the Mathematical Association of America, can be found in the Mathematics Majors Handbook. Copies are available in the department office.

Minor in Mathematics

Students must complete a minimum of 18 credits in mathematics, as follows:

1. Required courses: MTH 201 and 202, Calculus I and II.

2. Elective courses: 12 credits in mathematics, chosen from MTH 203 or courses numbered MTH 243 or higher. Students should choose these electives after consultation with an advisor from their major department as well as with a mathematics faculty member.

3. At least nine credits toward the minor must be earned at SUNY Brockport.

Minor in Mathematics/Statistics (18 credits) Students must complete either sequence A or B below.

A B
MTH 201 Calculus I MTH 201 Calculus I
MTH 202 Calculus II MTH 202 Calculus II
MTH 203 Calculus III MTH 245 Finite Mathematics or
MTH 245 Finite Mathematics or MTH 281 Discrete Mathematics I
MTH 281 Discrete Mathematics I MTH 346 Probability and Statistics I
MTH 346 Probability and Statistics I MTH 441 Statistical Methods I
MTH 446 Probability and Statistics II MTH 442 Statistical Methods II

Secondary Certification in Mathematics
Students who wish to teach mathematics at the secondary level can pursue a program at SUNY Brockport that leads to provisional certification. The program requires completion of a major in mathematics, including a geometry course, and a prescribed group of professional courses offered chiefly by the Department of Education and Human Development. Students seeking certification should contact the Department of Education and Human Development as soon as possible.

Mathematics Courses

MTH 121 College Algebra (A). Prerequisite: Two years of high school mathematics, or QNT 110. (Closed to students who have completed more than three years of high school mathematics or MTH 122 or a calculus course). Covers algebra at the intermediate level, including operations on polynomials and alge braic fractions, solution of first- and second-degree equations, graphs of functions and equations, logarithms and exponential functions. 3 Cr. Every Semester.

MTH 122 Precalculus (A). Prerequisite: Three years of high school mathematics, or MTH 121. (Closed to students who have credit for MTH 201.) Covers alge braic, exponential, logarithmic, and trigonometric functions. 3 Cr. Every Semester.

MTH 132 Precalculus Lab (A). Corequisite: MTH 122. Allows students to work in small groups on exercises related to topics being covered in Precalculus. Includes the use of calculators, computer soft ware, or the writing of computer programs. 1 Cr.

MTH 201 Calculus I (A,N). Prerequisite: Three and-one-half years of college-preparatory mathematics, or MTH 122. Covers limits and continuity; derivatives and integrals of algebraic, trigonometric, expo nential, and logarithmic functions; and applications of the derivative. 3 Cr. Every Semester.

MTH 202 Calculus II (A). Prerequisite: MTH 201 or one year of calculus in high school. Covers techniques and applications of integration, approximation methods, Taylor polynomials, improper integrals and L'Hospital's rule, and an introduction to infinite series. 3 Cr. Every Semester.

MTH 203 Calculus III (A). Prerequisite: MTH 202. Covers infinite series, polar coordinates, vectors and 3-space, functions of several variables, applications of partial derivatives, and multiple integrals. 3 Cr. Every Semester.

MTH 211 Calculus I Lab (A). Corequisite: MTH 201. Allows students to work in small groups on exercises related to topics being covered in Calculus I. Includes the use of calculators, computer software, or the writing of computer programs. 1 Cr.

MTH 212 Calculus II Lab (A). Corequisite: MTH 202. Allows students to work in small groups on exercises related to topics being covered in Calculus II. Includes the use of calculators, computer software, or the writing of computer programs. 1 Cr.

MTH 221 Calculus for Business (A,N). Prerequisite: MTH 121. (Closed to students who have completed MTH 201 with a grade of "C" or better .) Provides an introduction to calculus, with an emphasis on its applications to business and the behavioral sciences. Covers derivatives of functions of one and several variables, applied maximization and minimization problems, exponential growth and decay models, the natural logarithm function, and an introduction to integration. 3 Cr. Every Semester.

MTH 243 Elementary Statistics (A). Covers the use and limitations of various statistical concepts, including frequency distributions, measures of cen tral tendency and of variation, use of normal curve and t-tables, sampling, estimation, tests of significance for means, and correlation. S tudents who have received academic credit for ECN 204, PSH 202, PLS 300, SOC 200, or transfer credit for an elementary statistics course at another institution may not receive credit for this course. 3 Cr. Every Semester.

MTH 245 Finite Mathematics (A,N). Prerequisite: Three years of college-preparatory mathematics, or MTH 121. Covers linear equations, matrix algebra, linear programming, and probability theory. Uses these concepts to build mathematical models to solve problems arising in various disciplines. Closed to students who have successfully completed MTH 281. 3 Cr. Every Semester.

MTH 281 Discrete Mathematics I (A). Prerequisite: Three-and-one-half years of college-preparatory mathematics, or MTH 122. Provides an introduction to discrete mathematics. Topics include: propositional and predicate logic, sets, functions, matrix algebra, algorithms, valid arguments, direct and indirect proofs, mathematical induction, permutations and combinations, and discrete probability. 3 Cr. Every Semester.

MTH 313 Mathematics for Elementary Teachers I (A). Prerequisite: MTH 121 or QNT 111 or three years of college-preparatory mathematics. Open only to students seeking elementar y teaching certification. Includes: sets, relations, number systems, elementary number theor y, mathematical systems, and probability. Uses a problem-solving approach where appropriate. 3 Cr. Every Semester.

MTH 314 Mathematics for Elementary Teachers II (A). Prerequisite: MTH 313 or any MTH course numbered 201 or higher. Open only to students seeking elementary teaching certification. Covers various aspects of geometry, including area, volume, coordinate and transformational geometry. Emphasizes problem-solving and the instructional use of calculators and computers. 3 Cr. Every Semester.

MTH 343 Sampling Methods (A). Prerequisite: MTH 243 or an equivalent elementary statistics course. Introduces the concepts and techniques in statistical sampling having applications to sample surveys used in a variety of disciplines. Covers: simple random sampling, estimation of means, totals and proportions, variance of estimates, sample size determination, stratification, and systematic and cluster sampling. Requires students to design and conduct a sample survey on issues of interest to the campus community. 3 Cr.

MTH 346 Probability and Statistics I (A). Prerequisites: MTH 202 and either 245 or 281. Covers random variables and vectors, moments and moment generating functions, discrete and continuous probability distributions, and sampling distributions. 3 Cr. Every Semester.

MTH 353 Actuarial Problem Solving: Exam 100 (A). Prerequisites: MTH 203 and 424. Emphasizes the development of strong problem-solving skills in preparation for Exam 100 of the Society of Actuaries. Develops rigorously the underlying concepts of calculus and linear algebra. Includes: limits, continuity, sequences and series, differentiation and inte gration of functions of one and several variables, vector spaces, bases, linear transformations, and eigenvalues and eigenvectors. 3 Cr.

MTH 399 Independent Study in Mathematics (A). To be defined in consultation with the instruc tor- sponsor and in accordance with the procedures of the Office of Academic Advisement prior to registration. 1-3 Cr.

MTH 405 Mathematical Problem Solving (A). Prerequisites: MTH 202, junior or senior status and instructor's permission. Develops problem-solving ability in mathematics. Includes how to get started, methods of proof, devising a strategy, and "looking back." Places strong emphasis on critical reasoning and clarity of written expression. 3 Cr.

MTH 412 History of Mathematics (A). Prerequisite: MTH 203. 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. Spring.

MTH 421 Number Theory (A). Prerequisites: MTH 202 and 281. Covers mathematical induc tion, divisibility, primes, arithmetic functions, congruences, Diophantine problems, Gaussian primes, and the distribution of primes. 3 Cr.

MTH 424 Linear Algebra (A). Prerequisites: MTH 202 and either 245 or 281. Covers matrices and determinants and their uses, vector spaces and sub spaces, dimension, linear transformations, and Euclidean vector spaces. 3 Cr. Every Semester.

MTH 425 M odern Algebra (A). Prerequisite: MTH 424. Provides a study of algebraic systems, with special attention to groups and rings and their classification properties. Emphasizes theor y and proofs, but clarifies the ideas by means of specific examples involving modular arithmetic, real and complex numbers, permutations, matrices, and the factorization of polynomials over fields. Requires extensive writing. 3 Cr. Every Semester.

MTH 429 Topics in Algebra (A). Prerequisite: Instructor's permission. Addresses specific topics in abstract algebra not covered in other courses. A list of topics to be covered will be announced before course is offered. 3 Cr.

MTH 432 College Geometry (A). Prerequisite: MTH 424. Provides a study of geometry from the synthetic, analytic, transformational, and vector viewpoints. Includes these topics: axiomatic systems, finite geometries, absolute geometry, Euclid ean geometry, non-Euclidean geometries, geometric transformations, and projective geometry. 3 Cr. Fall.

MTH 438 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, and linear transformations. 3 Cr.

MTH 439 Topics in Geometry (A). Prerequisite: Instructor's permission. Addresses specific topics in geometry and topology not covered in other courses. A list of topics to be covered will be announced before course is offered. 3 Cr.

MTH 441 Statistical Methods I (A). Prerequisite: MTH 346 or 243 or an equivalent introductory statistics course. Covers estimation, hypothesis testing, simple regression, categorical data, and non- para metric methods. Uses computer statistical analysis packages such as MINITAB and SPSS. 3 Cr. Fall.

MTH 442 Statistical Methods II (A). Prerequisite: MTH 441 or instructor's permission. Covers one- and two-way analysis of variance, multiple regression, experimental design, and linear models. Uses computers for data analysis. 3 Cr. Spring.

MTH 446 Probability and Statistics II (A). Prerequisites: MTH 203 and 346. Covers the Central Limit Theorem, maximum likelihood estimation, unbiased and sufficient statistics, minimum variance, confidence intervals, Neyman-Pearson Lemma, power calculations, and likelihood ratio tests. 3 Cr. Every Semester.

MTH 449 Topics in Applied Mathematics (A). Prerequisite: Instructor's permission. Addresses specific topics in probability, statistics, applied analysis, and numerical methods not covered in other courses. A list of topics to be covered will be announced before course is offered. 3 Cr.

MTH 451 Advanced Calculus (A). Prerequisite: MTH 203. Covers vector differential calculus, line integrals including Green's theorem, independence of path, and surface integrals with G auss' and Stokes' theorems. 3 Cr.

MTH 452 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 455 Differential Equations (A). Prerequisite: MTH 202. Covers equations of first and second orders and their applications, linear equations, series solutions, approximate solutions, and the Laplace transform. 3 Cr. Fall.

MTH 457 Real Analysis (A). 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 the orem, 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 459 Topics in Analysis (A). Prerequisite: Instructor's permission. Addresses specific topics in real and complex analysis not covered in other courses. A list of topics to be covered will be announced before course is offered. 3 Cr.

MTH 461 Mathematical Models for Decision Making I (A). Prerequisite: MTH 245 or 281. Covers linear programming, transportation and assignment models, network models, and dynamic programming. 3 Cr. Fall.

MTH 462 Mathematical Models for Decision Making II (A). Prerequisite: MTH 346. Covers probability models, decision theory, inventory and queueing models, and Markov analysis. 3 Cr. Spring.

MTH 471 Numerical Analysis (A). Prerequisites: MTH 203 and CSC 203. Provides a survey of methods used to numerically approximate the solutions of a variety of mathematical problems. Covers the generation and propagation of round-off errors, convergence criteria, and efficiency of computation. Includes: roots of non-linear equations, systems of linear or non-linear equations, polynomial approximations, and an introduction to numerical differen tiation and integration. 3 Cr.

MTH 481 Discrete Mathematics II (A). Prerequisites: MTH 201 and 281. A second course in discrete mathematics. Includes: complexity of algorithms, recurrence relations, inclusion-exclusion principle, partial order and equivalence relations, graph theory, trees, Boolean algebra, grammars, formal languages, and finite-state machines. 3 Cr. Every Semester.

MTH 492 Mathematics Internship (A). Prerequisites: Junior or senior status, 3.0 or better GP A in mathematics courses, at least 18 credits towards major completed prior to starting internship, and instructor's permission. Allows for a supervised experience in applying mathematical skills and techniques in a practical work environment. Requires projects that may include applications in business, the social sciences, or physical sciences. A maximum of three credits can be applied toward the mathematics major. 3 or 6 Cr.

MTH 499 Independent Study in Mathematics (A). To be defined in consultation with the instruc tor- sponsor and in accordance with the procedures of the Office of Academic Advisement prior to registration. 1-3 Cr.


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