Course Descriptions

Students with questions involving the prerequisites for a course should see the instructor of the course. In most cases, admission to a course by permission of the instructor is possible.

Mathematics / 143

M 010 Algebra [3] Numbers; sets; functions; the real number system; equations; inequalities; systems of linear relations; exponents. Designed for the student who needs a review of secondary school mathematics. [Noncredit]

M 100, 200, 300, 400, 500 Cooperative Education Program [variable] These courses are intended for students in the cooperative education program. The program is designed to provide the students with a series of "real world" problems that must be analyzed and modeled to provide solutions that are usable in their work environment. These courses carry 1 to 3 credits with the actual number of credits awarded on the basis of work involvement. Cooperative Education courses may be repeated for a total of up to 15 credits. All courses must be taken on a Pass/No Pass basis. Prerequisite: Sophomore standing, 2.5 GPA.

M 102 Trigonometry [1] Definitions and graphs of the trigonometric functions; solutions of triangles; analytic trigonometry including circular and inverse trigonometric functions. Note: This course does not satisfy the mathematics portion of the general education requirements in Arts and Sciences. Prerequisite: Two years of algebra.

M 110 Pre-calculus Mathematics [3] A study of linear and quadratic equations and inequalities; the Cartesian coordinate system for the plane, and the graphing of functions with special emphasis on polynomial, exponential and logarithmic functions. Solutions of word problems are stressed throughout. The goal of this course is to prepare students for M 112 Prerequisite: Two years of algebra.

M 112 A Short Course in Calculus [3] A one semester introduction to the basic concepts and applications of differential and integral calculus. For students who wish to satisfy the Arts and Sciences mathematics requirements, the Barney School of Business and Public Administration calculus requirement, or the mathematics requirement in the health sciences. No credit given to students who have previously received credit for M 144 or its equivalent. Prerequisite: M 110 or its equivalent.

M 114 Everyday Statistics [3] Designed to introduce basic concepts of probability; random sampling; data organization; measures of central tendency and variability; binomial and normal probability distributions; statistical inference; elements of hypothesis testing; one and two sample tests for means and proportions; chi-square tests for tabular data, an introduction to linear regression and correlation. Prerequisite: Two years of algebra.

M 116 Contemporary Mathematics [3] Designed to introduce the student to a variety of mathematical fields and some of their contemporary applications. Topics selected from logic, set theory, mathematical systems, recursive sequences, probability, statistics, game theory, linear programming, graph theory, computer programming, voting methods, and topology. Prerequisite: Two years of algebra.

M 118 Introduction to Modern Mathematics [4] Sets, operations on sets, historical background for numeration, system of natural numbers, number bases, systems of integers, rational numbers, real numbers, metric geometry, modular systems, groups, fields, rings, integral domains, relations, and functions. A two hour laboratory period per week is included. Note: This course does not satisfy the mathematics portion of the general education requirements in Arts and Sciences. Prerequisite: Two years of algebra or M 010.

M 140 Pre-calculus with Trigonometry [4] A study of linear and quadratic equations and inequalities, the Cartesian coordinate system for the plane; and the algebra and graphing of functions with special emphasis on polynomial, exponential and logarithmic functions. Definitions and graphs of the trigonometric functions; solutions of triangles; analytic trigonometry including circular and inverse trigonometric functions. Solutions of word problems are stressed throughout. A programmable graphing calculator is required. The goal is to prepare students for M 144. Prerequisite: Two years of algebra.

M 144 Calculus I [4] Functions, limits, continuity, differentiation of algebraic and trigonometric functions, applications of derivatives, definite integrals, approximate integration, and applications of the definite integral. Only 1 additional credit given to students who have received credit for M 112. Prerequisites: M140 or equivalent.

M 145 Calculus II [4] Logarithmic and exponential functions; techniques of integration; indeterminate forms; improper integrals; infinite sequences and series, and complex numbers. Prerequisites: M 144.

M 220 Linear Algebra and Matrix Theory [3] Linear equations and matrix algebra; determinants; vector spaces; linear independence and bases; inner product spaces; linear transformations and their matrix representations; eigenvalues and

eigenvectors; diagonalizable matrices. Selected topics from: quadratic forms, linear programming, or numerical linear algebra. Prerequisite: M 145.

M 221 Discrete Mathematics I [4] Topics include propositional calculus, combinatorics, graph isomorphisms, paths, planarity, colorability, trees and graph algorithms, occupancy problems, generating functions, and recurrence equations. Prerequisite: M 145.

M 222W Discrete Mathematics 11 [4] A formal introduction to the basic concepts of modern abstract mathematics. Topics include symbolic logic, predicate calculus, methods of proof, elements of set theory, functions, relations, cardinality, and graph theory. Prerequisite: M 221. (Writing intensive course)

M 240 Calculus of Several Variables [4] Vectors in three dimensions; curves and parametric equations in three dimensions; geometry of surfaces; differential calculus of functions of more than one variable with applications; multiple integrals and their applications; the differential and integral calculus of vector fields. Prerequisite: M 145.

M 242 Differential Equations [3] Solutions of first order linear, separable, exact equations, and applications; higher order linear constant coefficient equations and applications, Euler equations; nonhomogeneous equations: Method of Undetermined Coefficients and Variation of Parameters; Laplace transforms and initial value problems; matrices, eigenvalues, and linear systems of differential equations. Prerequisite: M 145.

M 246 Applied Mathematics for Civil Engineers [3] Introduction to probability and statistics, matrix algebra, solution of linear equations by numerical methods, solution of partial differential equations by separation of variables and numerical methods. (A student may not receive credit for both this course and M 344.)

M 260 Data Analysis [4] An introduction to exploratory and confirmatory data analysis. Classical, portable and robust statistical methods. Emphasis on model building, analysis, interpretation, and refinement using statistical software (Minitab, SAS, BMDP, SPSSx) Prerequisite: M 145.

M 310 History of Mathematics [3] A historical study of the principal mathematicians of the past 2500 years and their contributions to the development and growth of the various fields of mathematics. Prerequisite: M 145.

M 320 Theory of Numbers [3] Investigation of the arithmetic properties of the integers. Unique factorization, congruences, quadratic reciprocity, and other topics will be treated Prerequisite: M222

M 340 Introductory Analysis [3] A rigorous treatment of differentiation and Riemann integration. Topology of the real line; real valued sequences and their limits; continuity of real valued functions; the Mean Value Theorem; a rigorous definition of the definite (Riemann) integral, and proofs of its elementary properties; the Fundamental Theorem of Calculus. Other topics may include sequences of functions, series or function spaces. Prerequisites: M 220, 221, 240.

M 344 Advanced Engineering Mathematics [3] Series solutions of ordinary differential equations and Bessel functions; SturmLiouville systems and Fourier series. Partial differential equations in Cartesian and cylindrical coordinates. Prerequisite: M 242.

M 350 Numerical Analysis [3] Floating point arithmetic; algorithms and error analysis; roots of nonlinear equations; systems of linear equations; direct methods, factorization schemes, and iterative techniques; interpolation: difference schemes, splines; numerical differentiation and integration; solutions of ordinary differential equations; the matrix eigenvalue problem. Prerequisites: M 145, M 220, CS 114 or CS 117.

M 354 Studies in Mathematical Modeling [3] The process of developing and simulating mathematical models of real world phenomena will be studied. The types of models considered will vary from year to year. They may include discrete and continuous dynamical models, stochastic models, neural networks, and optimization models. Applications may he to the natural sciences, management science, engineering, or industry. With departmental permission, the course may be repeated for credit. Prerequisites: M240 and permision of instructor.

M 360 Probability Theory [3] Basic combinatorial probability; conditional probability; random variables; expectations; special discrete and continuous random variables and their properties; transformation of variables; Central Limit Theorem. Prerequisite:M240

M 362 Elements of Statistics [3] Sampling distibutions; theory of point and interval estimation; hypothesis testing, significance level, power, NeymanPearson Lemma, likelihood ratio tests, chi-square test on categorical data; theory and application of linear models; regression and ANOVA; non parametric techniques based on ranks. Prerequisite: M 360.

M 370 Foundations of Geometry [3] An axiomatic development of Euclidean geometry; attempts to prove the parallel postulate; the discovery of non-Euclidean geometries and their properties. Prerequisite: M 222W

 M420 Introduction to Modern Algebra [3] A study of the fundamental algebraic structure of groups, rings, and fields, including substructure, quotient structure, and morphism concepts. Prerequisites: M 220, 221.

M 440 Partial Differential Equations [3] Derivation and classification of classical partial differential equations; separation of variables; integral transform techniques; methods of complex variables; introduction to the theory of eigenvalues, eigenfunctions and Green's functions; applications to problems in heat conduction, fluid flow, quantum mechanics, and wave propagation. Prerequisites: M 220, M 242.

M 442 Introduction to Complex Analysis [3] Field of complex numbers, algebraic and geometric representations; analytic functions, the CauchyRiemann equations, harmonic functions; integration in the complex plane; power series; Laurent series and singularities of functions; theory of residues and evaluation of integrals. Prerequisite:

M 470 Introduction to Topology [3] An introduction to pointset topology. Topics considered are topological spaces, homeomorphisms, connectedness, compactness, separation axioms, and metric spaces. Prerequisites:

M 480, 481 Independent Study in Mathematics [1-3, 1-3] Provides an opportunity for the student to study mathematical topics under the direction of a faculty member. Prerequisite: Approval of the department. The signature of the department chairman is required to register for these courses.

M 190,191,290,291,390,391,490,491 Special Topics in Mathematics [14] Investigates mathematical topics not covered in the regular curriculum. Prerequisite: M 221 or permission of department.

Graduate Courses

M 515 Methods of Applied Mathematics I [3] Matrix algebra, simultaneous linear equations and numerical methods for their solution, inverses, and determinants. Linear ordinary differential equations, Laplace transform methods, and Green's functions. Eigenvalues and eigenvector.s; canonical fowls; matrix norms, algebraic variational methods; functions of matrices. Matrix methods for linear systems of ordinary differential equations, including the statetransition matrix. Quadratic forms and positive definite matrices; singular value decomposition. A brief survey of series solutions to ordinary differential equations and special functions. Introduction to nonlinear analysis (if time permits). Prerequisites: Undergraduate calculus, differential equations.

M 516 Methods of Applied Mathematics II [3] Numerical methods for ordinary differential equations: RungeKutta, linear multistep, and multivalue methods. Cartesian tensor notation and the summation convention. Vector integral theorems and the equations, boundary, and initial conditions of engineering analysis. Partial differential equations, characteristics, and classification. Introduction to the calculus of variations. Finite difference methods for regular and irregular grids. Introduction to the method of weighted residuals and one and two dimensional finite elements, choice of basis functions; Lagrange and Hermite polynomials. Prerequisite: M 515.

M 517 Applied Engineering Statistics [3] Data collection, display, and interpretation. Discrete probability. General distributions, expectation values. Special discrete and continuous distributions. Sampling distributions and the Central Limit Theorem. Point and interval estimation, including confidence, prediction, and tolerance intervals. Parametric and non-parametric methods of hypothesis testing. Analysis of variance and the design of experiments, including blocking, factorial designs, etc. Simple and multivariate regression analysis, correlation, residual plots, diagnostics and outlier detection. Introduction to statistical process control (if time permits). Prerequisite: Undergraduate calculus.