Fall Semester 2000 through Summer Semester 2002
Go to current catalog
Fall Semester 2000 through Summer Semester 2002
Go to current catalog
Professors: Sherwood D. Silliman (Chairperson), Ching Lung Chang, Shih-Hung Chang, Pratibha Ghatage, Thomas W. Hungerford, Keith M. Kendig, Rasul A. Khan, Sundaresan Kondagunta, Roger H. Marty, John F. Oprea, Brian M. Scott, Allan J. Silberger, Bhushan L. Wadhwa, John J. Walsh; Professor Emeritus: Chester W. Topp; Associate Professors: Paula C. Gnepp, Arthur Lieberman, Gregory M. Lupton, Luis Felipe Martins, Ieda W. Rodrigues, Sally SaiLai Shao, Chung-yi Suen; Associate Professors Emeriti: Richard H. Black, Leonard F. Bruening, Joseph M. Egar, David Herlacher, Shirley A. Lilge, Frank W. Lozier, Benjamin H. McLemore, Stewart M. Robinson; Assistant Professor: Barbara Haas Margolius.
Students with credit in MTH 173, 174, 176, 182, or in any mathematics course numbered above 220 may not register for a mathematics course numbered 168 or lower. A student who attempts to do so will be given a grade of W in the ineligible course. This rule takes precedence over the university regulations on repeated courses whenever both are applicable. Return to top
All students must take the Mathematics Placement Examination before they will be permitted to register for mathematics courses numbered 115, 118, 119, 127, 147, 151, 167, 168, and 181, except for students who have passed the appropriate prerequisite course. Mandatory placement for these courses is in effect. Students are not permitted to register for a higher level course than indicated by their placement exam score. Return to top
A student who has been unconditionally admitted to the university should have already mastered the material in these courses. Credit earned in MTH 087 or MTH 088 does not count toward graduation.
MTH 087 Basic Math and Algebra for Liberal Arts Majors (4-0-4). MTH 087 begins with a review of arithmetic topics such as fractions, decimals, percents, integers, and order of operation. It then proceeds to a review of algebra topics such as solving and graphing linear equations and inequalities, solving and graphing simultaneous equations and inequalities. MTH 087 concludes with an introduction to statistics and probability. Pass/fail system of grading, but students receive modified letter grades: S(A), S(B), S(C), U(D), U(F). The letter grades in parentheses are not computed in the students' GPA's. No credit toward graduation. Return to top
MTH 088 Basic Math and Algebra for Business and Science Majors (4-0-4). MTH 088 begins with a pre-algebra review. It then proceeds to basic algebra topics such as linear and quadratic equations and inequalities, rational and radical expressions, linear systems with emphasis on graphing and applications through problem solving as well as relations and functions. Pass/fail system of grading, but students receive modified letter grades: S(A), S(B), S(C), U(D), U(F). The letter grades in parentheses are not computed in the students' GPA's. No credit toward graduation. Return to top
MTH 115 Intermediate Algebra (4-0-4). Prerequisite: MTH 087 or MTH 088 or suitable placement-test score. Extension of basic algebra techniques, linear equations, and linear inequalities, an introduction to functions, roots, radicals, exponents, quadratic equations, solution of second degree equations and applications, and the analysis and solution of word problems. Return to top
Any course in this section, except MTH 127, is suitable for meeting the Mathematics and Logic requirement in the Approaches to the Disciplines section of the GenEd. Credit earned in these courses does not count toward the mathematics major.
MTH 118 Mathematics for the Liberal Arts I (4-0-4). MTH 119 Mathematics for the Liberal Arts II (2-0-2). Prerequisite: MTH 115 or suitable placement test score. Two independent courses that may be taken in either order. Various topics from elementary mathematics, selected to help develop an appreciation for mathematics and its role in a liberal education. Mathematics and Logic courses. Return to top
MTH 127 Mathematics for Elementary and Middle School Teachers I (4-0-4). Prerequisite: MTH 087 or suitable placement-test score. Topics needed to teach elementary and middle school mathematics, including numeration systems and whole number arithmetic, integers and number theory, rational and real numbers, problem solving, and applications. Return to top
MTH 128 Mathematics for Elementary and Middle School Teachers II (4-0-4). Prerequisite: MTH 127. Additional topics for the elementary curriculum, including probability, statistics, geometry, measurement, and applications. Mathematics and Logic. Return to top
MTH 129 Mathematics for Elementary and Middle School Teachers III (2-0-2). Prerequisite: MTH 128. Technology in the classroom: An introduction to geometry with LOGO, other mathematical software for the classroom, computer algebra systems and mathematical activities on the Internet. Mathematics and Logic. Return to top
MTH 147 Statistical Concepts with Applications (4-0-4). Prerequisite: MTH 115 or suitable placement-test score. A first course in statistics that emphasizes statistical methodology as applied in the social and behavioral sciences, education, and business; topics include descriptive statistics, elementary probability, elementary sampling theory, estimation, hypothesis testing, regression and correlation. Mathematics and Logic. Return to top
MTH 151 through MTH 156 Mathematical Concepts. Each of these is a 1- or 2-credit course. Normally a student must register for MTH 151, 152, and 153, or for MTH 154, 155, and 156. One is taught at the beginning of the semester, one in the middle of the semester, and one at the end of the semester.
A graphing calculator is required for MTH 151 to 156. Consult the Mathematics Department for recommended models. Return to top
MTH 151 Mathematical Concepts 1a (1-0-1). Prerequisite: MTH 115 or suitable placement-test score. Equations of lines, word problems, linear, polynomial and rational inequalities, graphs of functions, linear and quadratic functions, and their applications. Mathematics and Logic. Return to top
MTH 152 Mathematical Concepts 1b (2-0-2). Prerequisite: MTH 151. Systems of three or more linear equations, Gauss-Jordan elimination, matrix methods, linear programming. Mathematics and Logic. Return to top
MTH 153 Mathematical Concepts 1c (1-0-1). Prerequisite: MTH 152. Polynomial, exponential, and logarithmic functions and graphs, math of finance. Mathematics and Logic.
MTH 154 Mathematical Concepts 2a (1-0-1). Prerequisite: MTH 153. Intuitive differential calculus, derivatives, applications of derivatives. Mathematics and Logic. Return to top
MTH 155 Mathematical Concepts 2b (2-0-2). Prerequisite: MTH 154. Intuitive integral calculus, antiderivatives, the definite integral, applications, partial derivatives. Mathematics and Logic. Return to top
MTH 156 Mathematical Concepts 2c (1-0-1). Prerequisite: MTH 155. Probability, permutations, combinations, Bayes' Theorem. Mathematics and Logic. Return to top
Precalculus and First Year Calculus Courses
The precalculus courses (MTH 167 and MTH 168) are designed for students who intend eventually to take calculus (MTH 181) and are not intended as general education courses. Depending on the placement-test score, a student starts with MTH 167 or with MTH 168. Credit earned in precalculus courses does not count toward the mathematics major.
A graphing calculator is required for MTH 167, 168, 181, and 182. Consult the Mathematics Department for recommended models.
MTH 167 Precalculus Mathematics I (4-0-4). Prerequisite: MTH 088 or suitable placement-test score. Brief review of intermediate algebra techniques, rectangular coordinates, graphs of equations; and functions, lines, circles, detailed study of functions, graphing techniques. Mathematics and Logic. Return to top
MTH 168 Precalculus Mathematics II (4-0-4). Prerequisite: MTH 167 or suitable placement-test score. Functions, polynomial and rational functions, exponential, logarithmic, trigonometric, and inverse trigonometric functions. Mathematics and Logic. Return to top
MTH 181 Calculus I (4-0-4). Prerequisite: MTH 168 or suitable placement-test score. Differential calculus including functions, limits, derivatives, continuity, applications of derivatives. Integral calculus including antiderivatives, definite integrals. Mathematics and Logic. Return to top
MTH 182 Calculus II (4-0-4). Prerequisite: MTH 181. Applications of integration, transcendental functions, techniques of integration, l'Hospital's Rule, improper integrals, infinite series, power series, polar coordinates. Mathematics and Logic. Return to top
Intermediate Courses
MTH 211 Numerical Methods for Computer Sciences (4-0-4). Prerequisites: MTH 156 or MTH 182; and CIS 260 or equivalent. Introduction to computational algorithms, including the areas of equation solving, curve fitting, linear equation systems, and integration. Return to top
MTH 220 Introduction to Discrete Mathematics (4-0-4). Prerequisites: MTH 156 or MTH 182; and CIS 260 or equivalent. Sets, relations, and functions; the concept of algorithm; mathematical induction and recursive definition. Applications of these fundamentals are chosen at the instructor's discretion from graph theory, Boolean algebra, lattice theory, finite-state automata, elementary grammars, and the theory of recurrence relations. Return to top
MTH 281 Multivariable Calculus (4-0-4). Prerequisite: MTH 182. Multivariate and vector calculus, including three-dimensional analytic geometry, partial derivatives, multiple integrals, vector calculus, line integrals, Green's Theorem. Only two of the four credits may be counted toward graduation by students who have passed MTH 283. Return to top
MTH 283 Multivariable Calculus for Engineers (2-0-2). Prerequisite: MTH 182. Multivariate calculus including three-dimensional analytic geometry, partial derivatives, multiple integrals. Students who have passed MTH 281 may not register for MTH 283. A student who attempts to do so will be given a grade of W. Return to top
MTH 284 Matrices for Engineers (2-0-2). Prerequisite: MTH 182. Matrix algebra, including matrices and systems of linear equations, determinants, inverses, eigenvalues and eigenvectors. Students who have passed MTH 288 may not register for MTH 284. A student who attempts to do so will be given a grade of W. Return to top
MTH 286 Introduction to Differential Equations (4-0-4). Prerequisite: MTH 182. First-order differential equations, linear differential equations, first order systems, Laplace transform techniques, and applications. Return to top
MTH 288 Linear Algebra (4-0-4). Prerequisite: MTH 182. Systems of linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues, and eigenvectors. Only two of the four credits may be counted toward graduation by students who have passed MTH 284. Return to top
Advanced Courses
MTH 301 Introduction to Applied Mathematics (4-0-4). Prerequisite: At least one mathematics course numbered 280 or above. Applications of mathematics to real-world problems, including topics such as Monte-Carlo methods (pricing financial securities, light scattering, volumes of irregular shapes); population growth and other environmental issues; and encryption. Emphasis on formulating and evaluating solution strategies and carrying them out using standard software. Return to top
MTH 311 Numerical Analysis (4-0-4). Prerequisites: MTH 284 or MTH 288, MTH 286, and a computer programming language. Numerical methods for solving nonlinear equations, systems of linear equations, interpolation problems, integration problems, and differential equations. Return to top
MTH 317 Math Methods for Engineering & Physical Sciences (4-0-4). Prerequisites: MTH 281 and MTH 288 or MTH 283 and MTH 284. Elements of vector analysis, including vector algebra, vector functions and fields. Divergence and Stokes' Theorems. The basics of Fourier analysis; separation of variables techniques; applications to heat flow and wave propagation. Standard software will be integrated throughout to simplify the mechanics of computation. Return to top
MTH 321 Statistics for Engineers (4-0-4). Prerequisite: At least one mathematics course numbered 280 or above. This is an introductory statistics course for engineers. The purpose of this course is to provide the concepts of probability, statistics, and data analysis in engineering. Statistics computer software (such as MINITAB, SPSS, and SAS) will be used in the course to solve problems, explore a topic, or conduct a simulation. Return to top
MTH 323 Statistics with Probability (4-0-4). Prerequisite: MTH 281 or MTH 283. Probability, discrete and continuous distributions, multivariate distribution, descriptive statistics, statistical inference, estimation, hypothesis testing, regression and correlation, nonparametric method. Return to top
MTH 333 Geometry (4-0-4). Prerequisite: MTH 284 or MTH 288. This course deals with the fundamentals of three-dimensional geometry from both the Euclidean and coordinate points of view as well as applications to engineering and science. Topics in the course include congruence, parallelism, and transformational geometry as well as some applications to areas such as computer graphics, cartography, and robotics. Return to top
MTH 358 Abstract Algebra (4-0-4). Prerequisite: MTH 288. An introduction to modern abstract algebra, concentrating on the integers and number theory, rings, fields, polynomials, and applications of these concepts. Writing. Return to top
MTH 381 Analysis (4-0-4). Prerequisites: MTH 284 or MTH 288, and at least one mathematics course numbered 300 or above. Introduction to the real-number system, sequences, continuity properties in a metric space, applications to connectedness, sequences and series of functions, basics of differentiation, and Riemann integration. Writing. Return to top
MTH 386 Differential Equations (4-0-4). Prerequisites: MTH 281 and MTH 288 or MTH 283 and MTH 284, and MTH 286. Series solutions of second-order linear equations; qualitative behavior of linear and almost linear systems of first-order differential equations; boundary value problems; introduction to partial differential equations. Return to top
MTH 389 Functions of a Complex Variable (4-0-4). Prerequisite: MTH 281 or MTH 283. This course deals with the fundamentals of complex analysis, including basic properties of complex numbers, analytic functions, harmonic functions, integration, Taylor and Laurent series, residue calculus and conformal mapping. A main focus of the course is the application of conformal mapping techniques (such as Mobius transformations and symmetry) to solve electrostatics, fluid flow, and heat flow problems. Return to top
MTH 401 Mathematical Modeling (4-0-4). Prerequisites: MTH 284 or MTH 288, MTH 286, and at least one mathematics course numbered 300 or above (MTH 301 recommended). Deterministic and probabilistic models chosen from the areas of linear optimization, Markov chains, game theory, graphs and networks, axiom systems, growth processes, and queueing systems. Return to top
MTH 420 Combinatorial Mathematics (4-0-4). Prerequisite: At least one mathematics course numbered 300 or above. A survey of combinatorial methods, including binomial coefficients and other special numbers, recurrence relations, calculus of finite differences, and generating functions, emphasizing exact evaluation of combinatorial sums in closed form. Writing. Return to top
MTH 424 Applications of Probability (4-0-4). Prerequisites: MTH 284 or MTH 288 and MTH 321 or MTH 323. Survey of probability theory, modeling techniques for probabilistic systems, discrete and continuous time Markov chains, Poisson process, birth-and-death process; selected topics from among renewal theory, random walks, Brownian motion and analysis of Monte Carlo simulations. Applications include queueing theory, financial models, populations, inventory theory, and optimization of stochastic systems. Return to top
MTH 434 Differential Geometry (4-0-4). Prerequisites: MTH 281 or MTH 283, MTH 286, and at least one mathematics course numbered 300 or above. This course focuses on the calculus, linear algebra, and geometry of curves and surfaces, as well as applications to engineering and science. Material covered will include the curvature and torsion of curves, Gaussian and mean curvatures of surfaces, minimal surfaces, geodesics, holonomy, and the Gauss-Bonnet theorem. Optional material includes applications of the calculus of variations to geometry and of minimal surface theory to soap film formation. Return to top
MTH 487 Dynamical Systems (4-0-4). Prerequisites: MTH 284 or MTH 288, MTH 286, and at least one mathematics course numbered 300 or above (MTH 386 recommended). Systems of differential equations, local and global behavior of a vector field in the plane, discrete dynamical systems, structural stability, the Poincare-Bendixon theorem, bifurcations, chaos, and strange attractors. Return to top
MTH 493 Special Topics in Mathematics (4-0-4). Prerequisite: At least one mathematics course numbered 300 or above, or permission of instructor. Detailed study of a selected topic in advanced mathematics. Topic will vary, depending on instructor. May be taken for credit more than once, but no single topic may be repeated. Consult Mathematics Department for current information. Return to top
MTH 495 Senior Seminar (2-0-2). Prerequisites: At least two mathematics courses numbered 300 or above, or departmental approval. This is the department's main assessment tool. Students will read papers in technical journals, choose a research topic, and write a technical report. Three key assessment areas are mathematical modeling (translating real-world situations into mathematics), mathematical reasoning (manipulation, by hand or by computer, of data and expressions using valid mathematical techniques) and communication (ability to write cogent and well-formulated reports). Writing. Return to top
MTH 497 Readings in Mathematics (1 to 4 credits). Prerequisite: Departmental approval. Topics studied under supervision of an advisor. Return to top
