# Undergraduate course descriptions

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**100 INTERMEDIATE ALGEBRA. 3 credits Prerequisite:** Placement.

A review of high school algebra: real numbers, exponents, radicals, factoring, linear

and quadratic equations, graphing, and problem solving. Does not meet General Studies

mathematics requirement.

**135 EXCURSIONS IN MATHEMATICS. 3 credits**

Prerequisites:placement test, 100 or 2030:153.

Prerequisites:

Contemporary applications of mathematics for the non-science major to develop skills

in logical thinking and reading technical material. Topics include voting, apportionment,

scheduling, patterns, networks.

**140 FUNDAMENTALS OF MATHEMATICS FOR PRIMARY EDUC. 3 credits**

Prerequisites:Either completion of 3450:100 with a C- or better, or completion of 3470:250 with

Prerequisites:

a grade of C- or better, or placement test. Corequisite: 5100:200. A problem-solving and

inquiry-based approach to number systems; bases; operations, properties, relationships, algorithms

of Real Numbers; patterns and algebra.

**145 COLLEGE ALGEBRA. 4 credits Prerequisite:** Mathematics Placement Test or completion of 100 with a grade of C- or better.

Real numbers, equations and inequalities, linear and quadratic functions. Exponential and

logarithmic functions. Systems of equations, matrices, determinants. Permutations and combinations.

**149 PRECALCULUS MATHEMATICS. 4 credits**

Prerequisite:Completion of 145 with a grade of C- or better or placement.

Prerequisite:

Functions, polynomial functions, complex numbers, exponential and logarithmic functions,

systems of equations, trigonometric functions, mathematical inductions, sequences,

and binomial theorem.

**208 INTRODUCTION TO DISCRETE MATHEMATICS. 4 credits**

Prerequisites:Completion of 145 or 149 with a grade of C- or better or placement.

Prerequisites:

A foundation course in discrete mathematics with applications. Topics include sets, number

systems, Boolean Algebra, logic, relations, functions, recursion, matrices, induction, graphs, and trees.

**209 DISCRETE MATHEMATICS FOR EDUCATORS. 4 credits**

Prerequisites:Completion of 140 with a grade of C- or better. Corequisite: 231. Introduction to discrete

Prerequisites:

mathematics topics for middle school instruction: sets, counting, probability, recurrence

relations, graph theory, logic and elementary proof techniques.

**210 CALCULUS WITH BUSINESS APPLICATIONS. 3 credits**

Prerequisites:Mathematics Placement Test or completion of 145 with a grade of C- or

Prerequisites:

better.

Review of functions, derivatives of functions, extrema and concavity, optimization, logarithmic

and exponential functions, extrema for multivariate functions. Graphing calculator

required. For business majors only.

**215 CONCEPTS OF CALCULUS. 4 credits**

Prerequisite:Completion of 145 or 149 with a grade of C- or better or placement.

Prerequisite:

Functions; limits and continuity; differentiation and applications of differentiation; logarithmic

and exponential functions; integration and applications of integration; partial differentiation.

**221 ANALYTIC GEOMETRY-CALCULUS I (OMT 005). 4 credits**

Prerequisite:Completion of 149 with the grade(s) of C- or better.

Prerequisite:

Analytic geometry, limits, continuity, derivatives, tangent and normal lines, extrema of functions,

Rolle's theorem, mean value theorem, related rates, antiderivatives, definite integrals, areas,

volumes, arc length.

**222 ANALYTIC GEOMETRY-CALCULUS II (OMT 006). 4 credits**

Prerequisite:Completion of 221 with a grade of C- or better.

Prerequisite:

Derivatives of exponential, logarithmic trigonometric, inverse trigonometric, hyperbolic and

inverse hyperbolic functions; methods of integration, sequences, series; moments, centroids,

indeterminate forms, polar coordinates.

**223 ANALYTIC GEOMETRY-CALCULUS III (OMT 007). 4 credits**

Prerequisite:Completion of 222 with a grade of C- or better.

Prerequisite:

Vector algebra, cylindrical, spherical coordinates, vector-valued functions, curvature; functions

of several variables, limit, continuity, partial derivatives, differentials, directional derivatives,

maxima and minima, multiple integrals, Divergence Theorem.

**231 MODELING WITH ALGEBRAIC AND TRANSCENDENTAL FUNCTIONS. 4 credits**

Prerequisites: Completion of 140 with a grade of C- or better; and 100 with a grade of C- or

Prerequisites

better or placement test. Modeling and regression with algebraic, exponential, logarithmic,

and trigonometric functions; systems of equations and matrices. These topics will be

enhanced by the use of CAS.

**240 MATHEMATICAL FOUNDATIONS FOR EARLY CHILDHOOD EDUCATORS. 3 credits**

Prerequisite:Completion of 140 with a grade of C- or better.

Prerequisite:

A problem-solving and inquiry based approach to fundamentals of Euclidean Geometry and

elementary data analysis.

**289 SELECTED TOPICS IN MATHEMATICS. 1-3 credits**

Prerequisite:permission.

Prerequisite:

Selected topics of interest in mathematics.

**307 FUNDAMENTALS OF ADVANCED MATHEMATICS. 3 credits**

Prerequisite:Completion of 222 with a grade of C- or better.

Prerequisite:

Logic, solving problems, and doing proofs in mathematics. Sets, extended set operations, and

indexed family sets, induction. Binary relations. Functions, cardinality. Introductory concepts

of algebra and analysis.

**312 LINEAR ALGEBRA (OMT 008). 3 credits**

Prerequisite:Completion of 223 with a grade of C- or better or permission of instructor.

Prerequisite:

Study of vector spaces, linear transformations, matrices, determinants, inner products,

the eigenvalue problem, quadratic forms and canonical forms.

**331 MODELING WITH CALCULUS. 4 credits**

Prerequisites: Completion of 231 with a grade of C- or better. Introduction to limits, continuity,

Prerequisites

differentiation with applications, integration with applications, sequences and series.

These topics will be enhanced by the use of CAS.

**335 INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS (OMT 009). 3 credits**

Prerequisite:Completion of 223 with a grade of C- or better or permission of instructor.

Prerequisite:

Basic techniques for solving ODEs and systems of ODEs. Analysis of models involving

differential equations of first order and simple equations of second order.

**341 GEOMETRY AND MEASUREMENT. 3 creditsPrerequisite: **Completion of 209 with a grade of C- or better, or 307 with a grade of C- or

better and be admitted to the College of Education. Basic Constructions, Polygons,

Similarity, Pythagorean Theorem, Circles, Congruence, Perimeters and Areas of Plane

Figures, Surface and Volumes of Solids, Rigid Motions and Symmetry, Coordinate Geometry.

**401 HISTORY OF MATHEMATICS. 3 credits Prerequisite:** Completion of 307 with a grade of C- or better.

Origin and development of mathematical ideas.

**410 ADVANCED LINEAR ALGEBRA. 3 credits**

Prerequisite:Completion of 312 with a grade of C- or better.

Prerequisite:

Study of vector spaces, linear transformation, canonical and quadratic forms,

inner product spaces.

**411 ABSTRACT ALGEBRA I. 3 credits**

Prerequisite:Completion of 307 with a grade of C- or better or permission of instructor.

Prerequisite:

Study of groups, rings, fields, integral domains.

**412 ABSTRACT ALGEBRA II. 3 credits**

Prerequisite:Completion of 411 with a grade of C- or better or permission of instructor.

Prerequisite:

Study of groups, rings, fields, integral domains, vector spaces, field extensions, Galois theory.

**413 THEORY OF NUMBERS. 3 credits**

Prerequisite:Completion of 222 with a grade of C- or better or permission.

Prerequisite:

Euclidean algorithm, unique factorization theorem, congruences, primitive roots, indices, quadratic

residues, number theoretic functions, Gaussian integers and continued fractions.

**415 COMBINATORICS AND GRAPH THEORY. 3 credits**

Prerequisite:Completion of 222 with a grade of C- or better or permission.

Prerequisite:

Introduction to basic ideas and techniques of mathematical counting;

properties of structure of systems.

**420 MATHEMATICAL TECHNOLOGY AND COMMUNICATION. 3 credits**

Prerequisites:Completion of 222 and 312 with grades of C- or better, or permission.

Prerequisites:

Graphical, numerical and algebraic computation with applications using a variety of mathematical

hardware and software: symbolic manipulators, dynamic geometry software, programs, scripts

and web browsers.

**421,2 ADVANCED CALCULUS I AND II. 3 credits each**

Sequential. Prerequisite:Completion of 223 with a grade of C- or better; 307 is highly recommended.

Sequential. Prerequisite:

Real number system, sequences, series, set theory, continuity, differentiation, integration, partial

derivatives, multiple integration, maxima and minima, convergence and uniform convergence,

power series, improper integrals, transformations, line and surface integrals.

**425 COMPLEX VARIABLES. 3 credits**

Prerequisite:Completion of 223 with a grade of C- or better.

Prerequisite:

Complex variables; elementary functions,

differentiation and analytic functions; integration and Cauchy's theorem;

power series and Laurent series; residue theorem; applications such as conformal mappings,

inversion of integral transform.

**427 APPLIED NUMERICAL METHODS I. 3 credits**

Prerequisites:Completion of 222 and 3460:209 with grades of C- or better or permission.

Prerequisites:

Numerical methods in polynomial interpolation, root finding, numerical integration,

and numerical linear algebra.

**428 APPLIED NUMERICAL METHODS II. 3 credits**

Prerequisites:Completion of 335 and 427 with grades of C- or better or permission.

Prerequisites:

Numerical methods in the solution of ordinary and partial differential equations. Numerical

differentiation, Runge-Kutta methods, and iterative methods for ODEs, finite differences for PDEs.

**432 PARTIAL DIFFERENTIAL EQUATIONS. 4 credits**

Prerequisite:Completion of 335 with a grade of C- or better.

Prerequisite:

The classical initial value and boundary value problems of mathematical physics developed and solved

using Fourier series and integral transforms.

**435 SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS. 3 credits**

Prerequisites:Completion of 335 and either 312 or 428 with grades of C- or better or permission.

Prerequisites:

Analysis, solution of systems of equations, linear, nonlinear. Topics: stability theory, perturbation

methods, asymptotic methods, applications from physical, social sciences.

**436 MATHEMATICAL MODELS. 3 credits**

Prerequisite:Completion of 335 with a grade of C- or better, and a six-hour sequence in an approved

Prerequisite:

applied area, or permission.

Formulation and analysis of mathematical models in social and physical sciences.

Analysis of deterministic and stochastic models. Topics may include stochastic processes, linear

programming, graph theory, theory of measurement.

**438 ADVANCED ENGINEERING MATHEMATICS I. 3 credits**

Prerequisites:Completion of 335 and 312 with grades of C- or better or permission.

Prerequisites:

Matrices, eigenvalue problems, systems of ODEs, vector analysis, complex variables.

**439 ADVANCED ENGINEERING MATHEMATICS II. 3 credits**

Prerequisites:Completion of 335 and 312 with grades of C- or better or permission.

Prerequisites:

Special functions, Fourier series and transforms, PDEs.

**441 CONCEPTS IN GEOMETRY. 4 credits**

Prerequisite:Completion of 307 with a grade of C- or better or permission of instructor.

Prerequisite:

Axiomatic treatment of both Euclidean and non-Euclidean geometries. Other concepts included

are finite geometry, transformations, constructions and inversions.

**445 INTRODUCTION TO TOPOLOGY. 3 credits**

Prerequisite:Completion of 307 with a grade of C- or better or permission of instructor.

Prerequisite:

Introduction to topological spaces and topologies, mappings, cardinality, homeomorphisms,

connected spaces, metric spaces.

**489 TOPICS IN MATHEMATICS. 1-4 credits (May be repeated for a total of 12 credits)**

Prerequisite:permission of instructor.

Prerequisite:

Selected topics in mathematics and applied mathematics at an advanced level.

**491 WORKSHOP IN MATHEMATICS. 1-4 credits**

(May be repeated) Group studies of special topics in mathematics and applied mathematics. May

not be used to meet undergraduate or graduate major requirements. May be used for elective credit

only.

**497 INDIVIDUAL READING. 1-2 credits**

Prerequisites:senior standing and permission. Mathematics or applied mathematics majors only.

Prerequisites:

Directed studies designed as an introduction to research problems, under guidance of selected

faculty member.

**498 SENIOR HONORS PROJECT. 1-3 credits**

Prerequisite:489 (honors). Directed study for senior student in the Honors College who has

Prerequisite:

completed 489 (honors).

An introduction to research problems in mathematics and applied mathematics

under the guidance of selected faculty.