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Department of Mathematics

200 Faculty Office Building
(585) 395-2036

Chairperson: Mihail Barbosu; Professors: John G. Michaels, Sanford S. Miller; Associate Professors: Charles J. Sommer; Assistant Professors: Dawn M. Jones, Izuru Mori, Gabriel T. Prajitura, Howard J. Skogman, Rebecca Smith, Pierangela Veneziani, Ruhan Zhao.

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An in-depth understanding of mathematics is of great importance to many careers in our technologically 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, computational 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. To complete a major in mathematics, 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 Abstract 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:

  1. Students intending to obtain secondary education certification in mathematics must complete MTH 432.
  2. 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.
  3. Students receiving elementary certification may substitute MTH 314 for one of the Mathematics electives.

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 information on advisement for majors, student awards, 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 (18 credits)
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.

At least nine credits toward the minor must be completed 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 II
MTH 346 Probability and Statistics I MTH 441 Statistical Methods I
MTH 446 Probability and Statistics II MTH 442 Statistical Methods II

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

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 110 Introduction to Mathematics (A). (Placement for students with weak backgrounds in mathematics. Closed to students who have passed MTH 111 or 121 or higher or any statistics course.) Places major emphasis on algebraic skills, basic operations on signed numbers (decimal and fractional forms): percents; techniques for solving linear and quadratic equations and systems of equations using two variables; algebraic operations on polynomials, roots and radicals. 3 Cr. Every Semester

MTH 111 Quantitative Skills (A). (Placement preparatory to MTH 112. Closed to students who have passed MTH 121 or higher (except MTH 243).) Covers basic mathematical concepts involving linear and non-linear relationships and graphic representations; basic concepts of probability and statistics. Requires students to perform at a satisfactory level during the course and pass the final exam, which is a comprehensive exam, in order to obtain a passing grade. 3 Cr. Every Semester

MTH 112 College Mathematics (A). (Placement for most students with good high school mathematics background. Meets Brockport General Education Mathematics course requirement.) Develops college-level skills in algebra, geometry, data analysis, and quantitative reasoning. Practice with linear and non-linear equations, geometric problem-solving, probability, algorithms, tabular and graphic techniques, modeling real world problems. Must pass final comprehensive examination to pass course. 3 Cr. Every Semester

MTH 121 College Algebra (A). Prerequisite: Two years of high school mathematics. (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 algebraic fractions, solution of first- and second-degree equations, graphs of functions and equations, logarithms and exponential functions. 3 Cr. Every Semester

MTH 122 Pre-Calculus (A). Prerequisite: Three years of high school mathematics or MTH 121. (Closed to students who have credit for MTH 201.) Designed to prepare students for the study of calculus. Covers algebraic, exponential, logarithmic, and trigonometric functions. 3 Cr. Every Semester

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

MTH 201 Calculus I (A). Prerequisite: Three and-one-half-years of college preparatory mathematics or MTH 122. Covers limits and continuity; derivatives and integrals of algebraic, trigonometric, exponential, 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 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 Laboratory (A). Corequisite: MTH 201. Students work in small groups on problems 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 Laboratory (A). Corequisite: MTH 202. Allows students to work in small groups on problems 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, Social and Life Sciences I (A). 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). Closed to students 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. Covers the use and limitations of various statistical concepts, including frequency distributions, measures of central tendency and of variation, use of normal curve and t-tables, sampling, estimation, tests of significance for means, and correlation. 3 Cr. Every Semester

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

MTH 255 Differential Equations (A). Prerequisite: MTH 202. Covers first order differential equations and applications, second order and higher order linear differential equations, series solutions about ordinary points and the Laplace Transform. 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. Includes these topics: 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 either MTH 111 or MTH 112 or three years of college-preparatory mathematics. Open only students seeking elementary teaching certification. Includes: sets, relations, number systems, elementary number theory, algebra, and mathematical systems. 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. Covers various aspects of geometry, including area, volume, coordinate and transformational geometry, probability and statistics. Emphasizes problem solving and the instructional use of calculators and computers. 3 Cr. Every Semester

MTH 324 Linear Algebra (A). Prerequisites: MTH 202 and either MTH 245 or MTH 281. Covers matrices, determinants, vector spaces and subspaces, dimension, linear transformations, and Euclidean vector spaces. 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 the estimation of means, totals and proportions, calculation of variance of estimates and sample size determinations when using simple random sampling, stratified sampling, cluster sampling and systematic sampling methods. 3 Cr.

MTH 346 Probability and Statistics I (A). Prerequisites: MTH 202 and either MTH 245 or MTH 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 P (A). Prerequisite: MTH 446. Emphasizes the development of strong problem-solving skills in preparation for the Course P exam of the Society of Actuaries. Develops rigorously the concepts of calculus, mathematical probability and statistics. 3 Cr.

MTH 399 Independent Study in Mathematics (A). To be defined in consultation with the instructor 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). Prerequisite: MTH 202 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 MTH 281. Covers mathematical induction, divisibility, primes, arithmetic functions, congruences, Diophantine problems, Gaussian primes, and the distribution of primes. 3 Cr. Fall

MTH 425 Abstract Algebra (A). Prerequisites: MTH 203 and MTH 324. Provides a study of algebraic systems, with special attention to groups and rings and their classification properties. Emphasizes theory 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 324. Provides a study of 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. Requires extensive writing. 3 Cr. Every Semester

MTH 439 Topics in Geometry (A). 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). Prerequisites: MTH 243 or MTH 346. Covers estimation, hypothesis testing, simple regression, categorical data, and non-parametric 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 MTH 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 Gauss' and Stokes' theorems. 3 Cr.

MTH 456 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 457 Real Analysis (A). Prerequisites: MTH 203 and MTH 324. 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 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 Deterministic Mathematical Models (A). Prerequisites: MTH 245 or MTH 281. Teaches applied mathematics techniques to be used in engineering, business, finance, and other management fields. Topics covered include linear programming, sensitivity analysis, the simplex method, shortest path method, integer linear programming and network models. 3 Cr. Fall

MTH 462 Stochastic Mathematical Models (A). Prerequisite: MTH 346. Teaches applied mathematics techniques to be used in engineering, business, finance, and other management fields. Topics covered include project scheduling, decision theory, simulation, risk analysis, multicriteria decision problems, inventory and queuing models, forecasting, dynamic programming, and Markov analysis. 3 Cr. Spring

MTH 463 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 471 Numerical Analysis I (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 differentiation and integration. Mathematical software, such as MAPLE, will be used. 3 Cr.

MTH 481 Discrete Mathematics II (A). Prerequisites: MTH 201 and MTH 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). 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. 1-6 Cr.

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

The information in this publication was current as of June 2005 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.