COURSES IN MATHEMATICS
MATH 1101 Introduction to Mathematical Models - 3 hours
An introduction to mathematical modeling using graphical, numerical, symbolic,
and verbal techniques to describe and explore real-world data and phenomena.
Emphasis is on the use of elementary functions to investigate and analyze
applied problems and questions, supported by the use of appropriate technology,
and on effective communication of quantitative concepts and results.
MATH 1111 College Algebra - 3 hours
Topics include real and complex numbers, algebraic and absolute value,
equations and inequalities, functions, graphs, polynomial and rational functions,
systems of equations, matrices and determinants.
MATH 1113 Precalculus - 3 hours
An intensive course that focuses on applications of the functions, concepts,
and methods necessary for success in calculus. Topics include exponential
and logarithmic functions, trigonometric and inverse trigonometric functions,
right triangle trigonometry, trigonometric identities and equations, oblique
triangles, complex numbers, and parametric equations.
MATH 2040 Brief Calculus - 3 hours
Prerequisite: Grade of C or above in Math 1111. This course
is intended for non-science majors, with particular emphasis on applications
of calculus to business. It will develop familiarity with such concepts
as limits, the derivative, the definite integral, the indefinite integral
and their applications.
MATH 2400 Elementary Statistics - 3 hours
Prerequisite: Three hours of college mathematics. A student
will not be allowed credit for MATH 2400 after completing MATH 3300 with a
grade of “C” or above. A noncalculus introduction to descriptive and
inferential statistics. Topics include graphical and numerical methods
of describing data, hypothesis testing, linear regression and correlation,
the normal distribution and estimation.
MATH 2450 Calculus I - 4 hours
Prerequisite: Grade of C or above in MATH 1113
An introduction to differential calculus. Topics include limits,
differentiation of algebraic and trigonometric functions, applications of
derivatives, antidifferentiation, simple differential equations, the area
under a curve, the fundamental theorem of calculus, and differentiation
and integration of exponential and logarithmic functions.
MATH 2460 Calculus II - 4 hours
Prerequisite: Grade of C or above in MATH 2450
A continuation of Calculus I. Topics include application of definite
integrals; derivatives and integrals with inverse trigonometric functions;
indeterminate forms and l’Hopital’s rule; techniques of integration; polar
coordinates; infinite sequences and series.
MATH 2470 Calculus III - 4 hours
Prerequisite: Grade of C or above in MATH 2460
A continuation of Calculus II. Topics include functions of several
variables; partial differentiation; multiple integrals; vector algebra,
lines, planes, and curves in three dimensions; and vector calculus.
MATH 2800 Introduction to Mathematical Proof - 3 hours
Prerequisite: Grade of C or above in MATH 2450
Topics include propositions and their truth values, tautologies, quantifiers,
methods of proof, sets, relations, equivalence relations and partitions,
functions, and mathematical induction.
MATH 3000 Differential Equations - 3 hours
Prerequisite: Grade of C or above in MATH 2460 An introductory
course in ordinary differential equations with emphasis upon linear differential
equations of the first and second orders. Topics include solution
of second order differential equations by the methods of undetermined coefficients,
variation of parameters, and Laplace transforms.
MATH 3010 Partial Differential Equations - 3 hours
Prerequisite: Grade of C or above in MATH 2470 and 3000.
Topics include power series method for solving ordinary differential equations,
Fourier series and integrals, orthogonal functions and partial differential
equations with boundary conditions.
MATH 3020 Nonlinear Dynamics and Chaos - 3 hours
Prerequisite: Grade of C or above in MATH 2460
Topics include one-dimensional flows and bifurcation, phase portraits,
linearization and classification of equilibrium points, limit cycles,
chaos, one-dimensional maps, and fractals.
MATH 3100 Number Systems - 3 hours
Credit not applicable toward a mathematics major or minor. Prerequisite:
MATH 2400 and a junior or senior standing. Corequisite for early childhood
and middle school majors: PHYS 3000. Topics include problem
solving strategies, sets and counting, logic, numeration systems, number
systems, number theory, ratio and proportion, and an introduction to plane
figures.
MATH 3110 Informal Geometry - 3 hours
Credit not applicable toward a mathematics major or minor. Prerequisite:
MATH 3100. Topics include plane figures, polygons and tessellations,
space figures, symmetric figures, systems of measurement, area and perimeter,
volume and surface area, congruence and similarity mappings, and topological
mappings.
MATH 3116 Modeling in Algebra for Teachers - 3 hours
Credit not applicable toward a mathematics major or minor.
Prerequisite: MATH 3100. This course designed for elementary and middle
grades pre-service teachers focuses on variables, expressions, equations,
inequalities, systems of equations, matrices, and linear, non-linear, and
inverse functions. Emphasis is on problem solving, active learning,
appropriate communication, substantive connections, technology utilization,
and multiple representations of algebraic structures.
MATH 3120 Geometry - 3 hours
Prerequisite: Grade of C or above in MATH 2800. A background
in plane geometry is helpful. Topics include classifications of geometries
(Euclidean, Non-Euclidean, and other) and geometry related concepts outside
the perspective of other mathematics courses.
MATH 3140 Data Analysis and Probability for Teachers - 3 hours
This course is designed for K-8 pre-service teachers and focuses on making
decisions and predictions in the context of solving real-world problems through
the process of collecting, representing, processing, summarizing, analyzing,
and transforming data.
MATH 3150 Problem Solving and Connections - 3
hours
Credit not applicable toward a mathematics major or minor. Prerequisite:
MATH 3100. This course designed for elementary pre-service teachers focuses
on recognizing and using mathematics in the context of real world problems.
Connections to the sciences, social sciences, and fine arts incorporate
topics from probability, discrete mathematics, algebraic and non-algebraic
functions, and data analysis.
MATH 3350 Probability and Statistics I - 3 hours
Prerequisite: Grade of C or above in MATH 2450. An introductory
calculus-based course in probability and statistics. Topics include
descriptive statistics and linear regression, basic probability and probability
distributions, point estimation, confidence intervals and hypothesis testing.
MATH 3450 Probability and Statistics II - 3 hours
Prerequisite: Grade of C or above in MATH 3350. A continuation
of the study of probability and statistics, emphasizing the theory of statistical
inference. Topics include two-sample estimation and tests of hypothesis,
analysis of variance and randomized block designs, regression analysis,
correlation, transformations and multiple regression, and quality control
methods.
MATH 3500 Introduction to Discrete Mathematics - 3 hours
Prerequisite: Grade of C or above in MATH 2450. An introductory
course in discrete mathematics emphasizing the formulation and solution
of problems which are discrete in nature. Topics include logic, sets,
relations, combinatorial methods, recurrence relations, graphs and networks,
directed graphs, and Boolean algebras.
MATH 3520 Graph Theory - 3 hours
Prerequisite: Grade C or above in MATH 2460. An introductory
course in Graph Theory. Topics include fundamental concepts and definitions,
trees, distance, matchings, factors, connectivity, paths, and graph colorings.
Applications of these topics will be investigated and will include the development
of appropriate algorithms.
MATH 3540 Introduction to Cryptography - 3 hours
Prerequisite: Grade C or above in 2460. An introduction to
the mathematics of cryptology and cryptanalysis. Topics include difficulty
of an algorithm in terms of polynomial time; number theory topics of divisibility,
greatest common divisor, the Euclidean Algorithm, prime numbers, congruence,
Fermat's little theorem, factoring, and discrete logarithms; encryption
schemes and the associated matrices or linear maps; perfect security; the
DES algorithm; public-key encryption; and digital signatures. The
ability to read a proof is expected.
MATH 3550 Numerical Analysis - 3 hours
Prerequisite: Grade of C or above in MATH 2460. A course in
numerical solutions to problems in mathematics: roots of non-linear
equations, zeros of polynomials, interpolation, systems of linear algebraic
equations, quadrature, ordinary differential equations with analysis of methods
and errors, and programming of methods on a computer.
MATH 3600 Introduction to Abstract Algebra I (W)
- 3 hours
Prerequisite: Grade of C or above in MATH 2800. A formal introduction
to the algebra of groups, rings, and fields.
MATH 3610 Introduction to Abstract Algebra II
3 hours
Prerequisite: Grade of C or above in MATH 3600. A continuation
of MATH 3600. Topics include group theory, ring theory, field theory,
Galois theory, and finite fields.
MATH 3650 Introduction to Linear Algebra - 3 hours
Prerequisite: Grade of C or above in MATH 2460. An introduction
to the basic concepts of linear algebra. Topics include finite-dimensional
vector spaces, bases, linear transformations, and matrices.
MATH 4120 Elementary Differential Geometry - 3 hours
Prerequisite: Grade of C or above in MATH 2470. Topics include
curves, surfaces, coordinate charts, differentiable manifolds, the tangent
plane, the first fundamental form, the Gauss map, the second fundamental
form, curvature, geodesics, the Gauss-Bonnet theorem, projections with applications
to cartography.
MATH 4130 Introduction to Topology - 3 hours
Prerequisites: Grade of C or above in MATH 2800 & MATH 2470.
An introductory course in point set topology. Topics include topological
spaces, bases, subspaces, closed sets and limit points, the product topology,
connected spaces, compact spaces, countability axioms, separation
axioms, Urysohn’s lemma, the Tychonoff theorem, and complete metric
spaces.
MATH 4180 Functions of a Complex Variable - 3 hours
Prerequisite: Grade of C or above in MATH 2470. Topics include
conditions for analyticity, elementary functions, the fundamental theorem
of algebra, power series, residues, poles, and conformal mapping.
MATH 4200 Introduction to Real Analysis I - 3 hours
Prerequisite: Grade of C or above in MATH 2800. An introductory
course in functions of a real variable, limits, continuous functions, differentiation,
and Riemann integration.
MATH 4210 Introduction to Real Analysis II - 3 hours
Prerequisite: Grade of C or above in MATH 4200. This course
is a continuation of MATH 4200. Topics include numerical sequences and series,
sequences and series of functions, functions of several variables, and the
implicit function theorem.
MATH 4310 Theory of Numbers - 3 hours
Prerequisite: Grade of C or above in MATH 2800. A study of
elementary problems in number theory with topics from divisibility, congruences,
residues, special functions, Diophantine equations, and continued
fractions.
MATH 4550 Computer Applications in Operations Research - 3
hours
Prerequisite: Grade of C or above in MATH 3650 or BUSA 3110.
A study of various problems and models in the field of operations research.
Topics will include linear programming, the transportation problem, the
assignment problem, project scheduling, network models, and queuing
theory. Computer software will be available to assist students in
the computational aspects of their solutions.
MATH 4700 History of Mathematics - 3 hours
Prerequisite: Grade of C or above in MATH 2450. A survey
of the historical development of mathematics with emphasis on topics for
secondary teachers.
MATH 4900 Independent Study - 1, 2, or 3 hours
Prerequisite: Approval of the instructor and the department head.
Independent reading and study under the direction of a faculty member of
the department covering selected topics not normally discussed in major course
work. May be repeated for credit.
MATH 4910 Internship in Mathematics - 1, 2, or 3 hours
Prerequisite: Junior or Senior standing and approval of department
head. Hands-on experience in the area of mathematics in an industrial,
governmental, or education setting.
MATH 4950 Senior Project in Mathematics (W) (O) - 1
hour
Prerequisite: Senior status or approval of the department head.
This course is designed to function as a capstone course for mathematics
majors. Under the direction of a full-time mathematics faculty member,
the student will select a mathematical topic and conduct independent explorations.
Results will be communicated to the mathematics faculty by a research paper
and presentation.