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Undergraduate Bulletin of Information 2001-2002COLLEGE OF ARTS AND SCIENCESExponential functions and logarithms, theconcepts of limit and continuity, differential andintegral calculus of one variable, and functionsof two variables with applications.MATH 3063. CALCULUS III. Three credithours. Three hours of lecture per week.Prerequisite: MATH 3032 or MATH 3184.Differential and integral calculus of severalvariables, and an introduction to differentialequations with applications.MATH 3171. PRECALCULUS I. Three credithours. Three hours of lecture per week.Prerequisite: placement by examination.Properties and operations of real numbers;equations and inequalities; Cartesian coordinatesand graphs; algebraic, exponential, andlogarithmic functions and their graphs;trigonometry of right triangles.MATH 3172. PRECALCULUS II. Three credithours. Three hours of lecture per week. Prerequisite:MATH 3171 or MATH 3173.Analytic trigonometry; complex numbers; thefundamental theorem of algebra; conic sections;systems of equations; matrices operations;sequences; and mathematical induction.MATH 3181. DISCRETE MATHEMATICS I.Three credit hours. Three hours of lecture perweek. Prerequisite: MATH 3031.Sets, relations, and notation; algorithms; logic;graphs; trees.MATH 3182. DISCRETE MATHEMATICS II.Three credit hours. Three hours of lecture perweek. Prerequisite: MATH 3181.Combinatorics, difference equations, relations,Boolean algebra, computational models.MATH 4000. ELEMENTS OF TOPOLOGY.Three credit hours. Three hours of lecture perweek. Co-requisite: MATH 4008Introduction to topology including topologicalspaces, continuous functions andhomeomorphisms, metric spaces, compactspaces, connected spaces, separation axioms, andelements of homotopy.MATH 4003-4004. MATHEMATICSPRACTICE FOR COOP STUDENTS I-II.Three credit hours per semester. Prerequisite:Consent of the Director of the Department.Practical experience in mathematics incooperation with private industry or government,to be jointly supervised by the academicdepartment, the COOP Program Coordinator,and an official from the COOP organization. Areport will be required of the student and theofficial at the end of the semester.MATH 4007. HIGHER GEOMETRY. Threecredit hours. Three hours of lecture per week.Prerequisite: MATH 3063 or MATH 3185.Coordinate systems in Euclidean 3-space, basicconfigurations, vectors and geometry of n-space,transformations, introduction to projectivegeometry, axioms of non-Euclidean geometries.MATH 4008. INTRODUCTION TOALGEBRAIC STRUCTURES. Three credithours. Three hours of lecture per week.Prerequisite: MATH 3020.Introduction to algebraic systems; sets,semigroups, groups, rings, fields.MATH 4009. ORDINARY DIFFERENTIALEQUATIONS. Three credit hours. Three hoursof lecture per week. Prerequisite: MATH 3063or MATH 3185.Ordinary differential equations with applications:basic existence theorem, linear systems, theLaplace transform, series solutions, introductionto Fourier series and orthogonal functions.MATH 4010. INTRODUCTION TOCOMPLEX VARIABLES WITHAPPLICATIONS. Three credit hours. Threehours of lecture per week. Prerequisite: MATH3063 or MATH 3185.Course designed for students who desire aworking knowledge of complex variables.Topics to be covered include analytic functions,singularities, residues, complex integration,power series, conformal mapping.MATH 4020. PARTIAL DIFFERENTIALEQUATIONS AND FOURIER SERIES. Three180
COLLEGE OF ARTS AND SCIENCES Undergraduate Bulletin of Information 2001-2002credit hours. Three hours of lecture per week.Prerequisite: MATH 4009.Separation of variables in the solution of partialdifferential equations, orthogonal expansions,Fourier series in certain function spaces, and anintroduction to boundary value problems.MATH 4021. FUNDAMENTALS OFMATHEMATICAL LOGIC. Three credit hours.Three hours of lecture per week. Prerequisite:MATH 3020 or Consent of the Director of theDepartment.An introductory course to the fundamentalproblems of logic, such as variables, thesentencial calculus, the theory of identity, thetheory of classes, the theory of relations, and thedeductive method.MATH 4023. MATHEMATICS EDUCATIONI. Three credit hours. Three hours of lecture perweek. Prerequisite: MATH 3020.Strategies for teaching mathematics at theelementary and secondary levels; analysis ofinnovative programs of instruction inmathematics; the use of computers in theteaching of mathematics.MATH 4031. INTRODUCTION TO LINEARALGEBRA. Three credit hours. Three hours oflecture per week. Prerequisite: MATH 3032 orMATH 3184.Euclidean vector spaces, matrices and linearequations, spectral decomposition of normaloperators.MATH 4050. UNDERGRADUATESEMINAR. One credit hour. One hour oflecture per week. Prerequisite: Consent of theDepartment Director.Introduction to the methods of mathematicalresearch; application of abstract methods toconcrete situations. Recommended for allstudents who intend to pursue graduate studies inMathematics.MATH 4051. ADVANCED CALCULUS I.Three credit hours. Three hours of lecture perweek. Prerequisite: MATH 3063 or MATH3185.A rigorous treatment of the basic ideas andtechniques of mathematical analysis, includingsuch topics as point set algebra, the real numbersystem, functions, sequences, limits, continuity,theorems and continuous functions, uniformcontinuity, differentiation, Riemann integration,the Riemann-Stieltjes integral, power series,uniform convergency.MATH 4052. ADVANCED CALCULUS II.Three credit hours. Three hours of lecture perweek. Prerequisite: MATH 4051.Continuation of a rigorous treatment of the basicideas and techniques of mathematical analysis,including such topics as functions of severalvariables, implicit functions, Jacobians andtransformations of multiple integrals, line andsurface integrals, improper integrals, linearfunction spaces, Fourier series and orthogonalfunctions.MATH 4061. NUMERICAL ANALYSIS I.Three credit hours. Three hours of lecture perweek. Prerequisites: (MATH 3063 or MATH3185) and (MATH 3010 or GEEG 3016 orCOMP 3010).Roots of equations, interpolation andapproximation procedures, numerical integration,numerical solution of initial value problems forordinary differential equations of first andsecond order, direct and iterative methods forsolving systems of linear equations.MATH 4062. NUMERICAL ANALYSIS II.Three credit hours. Three hours of lecture perweek. Prerequisites: MATH 4031 and MATH4061.The numerical solution of Fredholm integralequations: extension of the difference calculus tofunctions of several variables; brief study ofanalytical methods for the solution of the partialdifferential equations of mathematical physics;the numerical solution of boundary valueproblems; introduction to the numerical solutionof eigen value problems.MATH 4071. INTRODUCTION TOMATHEMATICS OF MODERN SCIENCE I.Three credit hours. Three hours of lecture perweek. Prerequisite: MATH 4009.Brief explanation of certain mathematical topicsessential for science and engineering: infinite181
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