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Brockport / Catalogs / 2013-14 / Courses / Undergraduate / Math

Undergraduate Math 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 College Algebra (A). Prerequisite: Two years of good high school mathematics, with a sufficiently high score on the Regents Math AR Exam. 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, logarithms and exponential functions. 3 Cr. Every Semester. 3 Cr. Every Semester.

MTH 112 College Mathematics (A,M). Prerequisite: MTH111 (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 122 Pre-Calculus (A,M). Prerequisite: Any of the following: MTH 111, MTH 112, or MTH 121, or a sufficiently high score on the Regents Math B exam or on the SAT. (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. 3 Cr.

MTH 181 Introduction to Sets (A). The theory of sets provides both a language and a foundation for mathematics. Students will learn how to use this language, as well as how to read and carry out proofs. Students will learn about The Axiom of Choice, the natural number system, kinds of infinity, The Continuum Hypothesis, and much more. This course is intended to be a meaningful complement to courses that come early in the math major. 3 Cr. Fall.

MTH 201 Calculus I (A,M). Prerequisite: MTH 122 or a sufficiently high score on the Regents Math B exam. Covers limits and continuity; derivatives and integrals of algebraic, trigonometric, exponential, and logarithmic functions; and applications of the derivative. 4 Cr. 4 Cr. Every Semester.

MTH 202 Calculus II (A,M). Covers techniques and applications of integration, approximation methods, Taylor polynomials, improper integrals, polar coordinates, and an introduction to infinite series. 4 Cr. 4 Cr. Every Semester.

MTH 203 Calculus III (A,M). Covers vectors and 3-space, functions of several variables, applications of partial derivatives, multiple integrals, and vector calculus. 4 Cr. Every Semester.

MTH 221 Calculus for Business, Social and Life Sciences I (A,M). Prerequisite: MTH 111 or higher or placement by Math Department. 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. 3 Cr. Every Semester.

MTH 243 Elementary Statistics (A,M). 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 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: MTH 122 or a sufficiently high score on the Regents Math B exam. 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. 3 Cr. Every Semester.

MTH 313 Mathematics for Elementary Teachers I (A). Prerequisite: Any mathematics course that satisfies the College's General Education requirement in College 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. 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). Prerequisite: MTH 202 and MTH 281or instructor's permission. Covers matrices, determinants, vector spaces and subspaces, dimension, linear transformations and Euclidean vector spaces. 3 Cr. Every Semester. 3 Cr. Every Semester.

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 395 Research Seminar in Mathematics (A). Prerequisite MTH281: Provides an introduction to specific research methods and techniques. Will discuss typing of mathematical documents using LATEX. Each student will be assigned a research project. Emphasizes theory and proofs in different areas. Requires extensive writing. 1-3 Cr. Spring.

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 MTH281 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,Y). Prerequisite: MTH 202 and either MTH 245 or MTH 281. 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 420 Mathematics for Adolescent Teachers (A). Prerequisite: MTH 432. Analyzes the adolescence mathematics curriculum (grades 5-12) from an advanced prospective. Topics include algebra, geometry, data analysis, statistics, trigonometry, discrete mathematics, calculus. Students will examine their own understanding of these topics as well as examine the theoretical underpinning of each. 3 Cr. 3 Cr.

MTH 421 Number Theory (A). Prerequisites: MTH 202 and MTH 281. Topics include but are not limited to: mathematical induction, divisibility, primes, arithmetic functions, congruencies, modular arithmetic, Diophantine problems and the distribution of primes. 3 Cr. 3 Cr.

MTH 422 Introduction to Coding Theory (A). Provides an introduction to error-correcting codes emphasizing the theory behind code constructions as well as explicit computation with specific codes. Covers linear codes, encoding and decoding, bounds on codes, finite fields and codes designed using finite fields. 3 Cr.

MTH 425 Modern Algebra (A). Prerequisites: MTH 203 and MTH 324. Provides a study of algebraic systems, with special attention to groups 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, and matrices.Requires extensive writing. 3 Cr. Every Semester. 3 Cr. Every Semester.

MTH 426 Modern Algebra II (A). Prerequisite: MTH 425. Covers topics such as rings, ideals, fields and further group theory. Course requires extensive proof writing. 3 Cr. Spring. 3 Cr.

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 430 Topology (A). Prerequisite: MTH 281. Provides a study of topologies on various spaces. Emphasizes theory, abstraction, proof techniques and clarifies these by means of many specific examples. Bridges topics such as geometry, analysis and algebra. Topics include, but are not limited to set theory, continuous functions, connectedness, compactness, and separation. 3 Cr. Spring.

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. Fall.

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 440 Applied Statistics (A). Concepts of statistical models and sampling; descriptive and inferential methods; normal, t, chi-square, and F distributions; tests of hypothesis and estimation, analysis of variance, correlation, regression, analysis of categorical data; computer software applications. 3 Cr. Fall.

MTH 441 Statistical Methods (A). This course focuses on investigative statistics, emphasizing the process of data collection and data analysis. It will incorporate case studies from current events and interdisciplinary research, taking a problem-based approach to learn how to determine which statistical techniques are appropriate. Topics will typically include making connections between the two-sample t-test, Regression and ANOVA; Multiple Regression; Design and Analysis of Experiments; Logistic Regression and Survival Analysis. 3 Cr.

MTH 442 Statistical Computing (A). This course is an introduction to the methods of Simulation and Monte Carlo estimation. In Part-1 of the course we will study methods for generating random variables. In Part-2 we will simulate statistical models for a given system, formulate them in terms of appropriate random variables and then using Monte Carlo methods we will estimate various quantities of interest for the simulated systems. 3 Cr.

MTH 443 Regression Analysis (A). General linear model in matrix form, simple and multiple regression analysis, transformations, variable selection, multicollinearity, analysis of variance, robust regression, logistic regression, principal components and factor analysis, and statistical software applications. 3 Cr.

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. Spring.

MTH 447 Time Series (A). This course introduces the theory and practice of Time Series Analysis. Students will learn how to model and forecast a time series as well as read papers from the literature. 3 Cr.

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 452 Financial Mathematics (A). Prerequisite: MTH 202. Provides fundamental concepts of financial mathematics and prepares students for EXAM FM (Financial Mathematics) of the Society of Actuaries. Students will learn about inflation, rate of interest, stocks, bonds, and other financial instruments. 3 Cr.

MTH 453 Actuarial Mathematics (A). Prerequisites: MTH 346 or instructor's permission. Introduces students to Actuarial Science, emphasizes the development of strong problem solving skills in preparation for the Exam P (Probability) of the Society of Actuaries. 3 Cr. 3 Cr.

MTH 454 Partial Differential Equations (A). (A previous course in real analysis or topology would be helpful, but is not required.) Topics include the following: (i) Complete solution and analysis of four fundamental linear pde (transport, Laplace, heat and wave equations); (ii) Techniques for nonlinear pde (including characteristics and the calculus of variations); (iii) Additional techniques as time permits. Concepts will be reinforced and further explored using the Maple software package. 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.

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 458 Complex Analysis (A). Prerequisites: MTH203 and MTH324. Provides a study of functions of a complex variable. Focus on the theory of analytic functions. Includes: Cauchy-Rienmann equations, Cauchy’s Theorem, Cauchy’s integral formula, the Fundamental Theorem of Algebra, Laurent series, Residue Theorem, Contour intergration and applications to real integrals. 3 Cr.

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 460 Mathematical Modeling (A). Topics covered include Linear Programs, Duality Theory and Sensitivity Analysis, Simplex Method, Integer Programs, Branch and Bound, Markov chains (Ergodic and Absorbing), Critical Path Method, Birth and Death Processes, Intro to Queuing: M/M/1 queues; M/M/1 queues with finite capacity; M/M/s queues; finite source models; general distribution service models. Optimization and Algebra software will be used. 3 Cr.

MTH 461 Deterministic Mathematical Models (A,Y). Prerequisite: either MTH 245 or MTH 281 or instructors permission. 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.

MTH 462 Stochastic Mathematical Models (A,Y). 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.

MTH 463 Graph Theory (A). Prerequisite: MTH 324 or instructor's permission. . 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.

MTH 465 Combinatorics (A). Prerequisites: MTH 324. An introduction to combinatorics, including basic counting techniques involving permutations, combinations, compositions, and partitions; binomial coefficients; the twelve-fold way; recursions and generating functions. Other topics may include a more advanced study of permutations, sequences in combinatorics, magic squares, the probabilistic method, etc. 3 Cr.

MTH 471 Numerical Analysis I (A). Prerequisites: MTH 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: study of algorithms, recurrence relations, inclusion-exclusion principle, partial order and equivalence relations, graph theory and trees. 3 Cr. Every Semester. 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.