Undergraduate Catalog 2013-2014


UDM Academic Policies Course Descriptions List of All Programs Faculty
Mathematics Courses

MTH 1010 AlgebraCredit Hours: 3

Sets and real numbers; algebra of polynomials; algebra of rational expressions; exponents and radicals; linear equations and inequalities; systems of linear equations; quadratic equations.

Prerequisites:
UAS 0950 (Minimum Grade of C, May not be taken concurrently)

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MTH 1020 Algebra ACredit Hours: 1

Linear equations and applications; systems of linear equations; linear functions in the rectangular coordinate system. The combination of MTH 1020 + MTH 1030 + MTH 1040 is equivalent to MTH 1010.

Prerequisites:
UAS 0950 (Minimum Grade of C, May not be taken concurrently)
Corequisites: MTH 1030 MTH 1040 MTH 1030 MTH 1040

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MTH 1030 Algebra BCredit Hours: 1

Algebra of polynomials; algebra of rational expressions; solving polynomial and rational equations; ratio and proportion; literal equations. The combination of MTH 102 + MTH 103 + MTH 104 is equivalent to MTH 101.

Prerequisites:
MTH 1020 (Minimum Grade of C, May be taken concurrently)
Corequisites: MTH 1040

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MTH 1040 Algebra CCredit Hours: 1

Rational exponents; radical expressions; solving equations containing radical expressions; quadratic equations; applications of quadratic equations.

Prerequisites:
MTH 1030 (Minimum Grade of C, May be taken concurrently)

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MTH 1090 Engineering MathCredit Hours: 2

This course introduces high school students to the basic concepts behind right triangle and circle based trigonometry. Topics covered include angles, right triangle trigonometry formulas, law of sines and cosines, applications of triangle-based trigonometry, circle trigonometry formulas, the relationship between right triangle and circle trigonometry, the unit circle, circumference, reference angles.
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MTH 1100 Applications in StatisticsCredit Hours: 2

A special course for high school students providing an introduction to statistics along with applications. Through a combination of lectures and problem solving sessions, the student will be exposed to the topics of central measures - mode, mean, and standard deviation - as well as with topics in confidence levels.
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MTH 1110 Mathematical Analysis ICredit Hours: 3

Equations and inequalities; graphs and functions; polynomials and rational functions; exponential and logarithmic; systems of equations and inequalities; matrices and determinants; conic sections.

Prerequisites:
MTH 1010 (Minimum Grade of C, May not be taken concurrently) OR
MTH 1040 (Minimum Grade of C, May not be taken concurrently)

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MTH 1120 Mathematical Analysis IICredit Hours: 3

Pre-calculus topics; derivatives and integrals; applications; techniques of integration.

Prerequisites:
MTH 1110 (Minimum Grade of C, May not be taken concurrently)

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MTH 1400 Elementary FunctionsCredit Hours: 3

Study of functions, including polynomials; rational, algebraic, exponential, logarithmic and trigonometric functions. Computer laboratory included.

Prerequisites:
MTH 1010 (Minimum Grade of C, May not be taken concurrently) OR
MTH 1040 (Minimum Grade of C, May not be taken concurrently)

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MTH 1410 Analytic Geometry and Calculus ICredit Hours: 4

Functions; limits and continuity; derivatives and integrals of polynomial, rational and trigonometric functions. Computer laboratory included.

Prerequisites:
MTH 1400 (Minimum Grade of C, May not be taken concurrently)

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MTH 1420 Analytic Geometry and Calculus IICredit Hours: 4

Topics in analytic geometry, differentiation and integration of exponential, logarithmic and inverse trigonometric functions; sequences and series. Computer laboratory included.

Prerequisites:
MTH 1410 (Minimum Grade of C, May not be taken concurrently)

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MTH 2140 Basic StatisticsCredit Hours: 3

Statistical analysis for business and social science applications; descriptive statistics; probability; sampling; estimation; hypothesis testing; regression analysis.

Prerequisites:
MTH 1010 (Minimum Grade of C, May not be taken concurrently) OR
MTH 1020 (Minimum Grade of C, May not be taken concurrently) AND
MTH 1030 (Minimum Grade of C, May not be taken concurrently) AND
MTH 1040 (Minimum Grade of C, May not be taken concurrently) OR
MTH 1100 (Minimum Grade of C-, May not be taken concurrently)

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MTH 2410 Analytic Geometry and Calculus IIICredit Hours: 4

Plane curves; polar coordinates; vectors in two and three dimensions; analytic geometry in the three dimensions; vector valued functions; partial derivatives and multiple integrals.

Prerequisites:
MTH 1420 (Minimum Grade of C, May not be taken concurrently)

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MTH 2760 Discrete StructuresCredit Hours: 3

Sets; functions and proof techniques; logic and logic circuits; relations; combinatorics; some graph theory; application to Computer Science.

Prerequisites:
MTH 1410 (Minimum Grade of C, May not be taken concurrently)

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MTH 3020 Linear Algebra with ApplicationsCredit Hours: 3

Vector spaces, matrices, systems of linear equations, determinants, inner products, linear transformations, similar matrices, eigenvalues and eigenvectors of a matrix.

Prerequisites:
MTH 1420 (Minimum Grade of C, May not be taken concurrently)

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MTH 3050 Mathematics of FinanceCredit Hours: 3

Measurement of interest; nominal and effective interest; force of interest; present value factor; annuities; amortization schedules and sinking funds; reinvestment rates; bonds and other securities.

Prerequisites:
MTH 1120 (Minimum Grade of D, May not be taken concurrently) OR
MTH 1420 (Minimum Grade of D, May not be taken concurrently)

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MTH 3060 Mathematical ThinkingCredit Hours: 3

Students will learn how to form plausible conjectures. Students will be introduced to various techniques of proofs such as direct proof, proof by contrapositive, proof by induction, etc. Applications of these techniques on set theory, analysis, conmbinatories group theory, and functions and relations will be discussed.

Prerequisites:
MTH 1420 (Minimum Grade of C, May not be taken concurrently) AND
MTH 2760 (Minimum Grade of C, May not be taken concurrently)

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MTH 3270 Introduction to Probability and StatisticsCredit Hours: 2

Introductory probability theory; elements of sampling and descriptive statistics; sampling distributions; computer laboratory using a statistical software package.

Prerequisites:
MTH 2410 (Minimum Grade of C, May not be taken concurrently)

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MTH 3720 Differential Equations with Linear AlgebraCredit Hours: 4

Linear dependence; linear differential equations and applications; systems of linear differential equations; series solutions.

Prerequisites:
MTH 1420 (Minimum Grade of C, May not be taken concurrently)

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MTH 4050 Abstract Algebra ICredit Hours: 3

Sets and mappings, an axiomatic approach to the number system, groups, rings, ideals, fields, isomorphism theorems, induction, permutations.

Prerequisites:
MTH 2760 (Minimum Grade of C, May not be taken concurrently) AND
MTH 4020 (Minimum Grade of C, May not be taken concurrently) OR
MTH 3020 (Minimum Grade of C, May not be taken concurrently)

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MTH 4060 Abstract Algebra IICredit Hours: 3

Euclidean domains, polynomial rings, field extension, finite fields, finite groups, p-groups, the Sylow theorems, introduction to Galois theory.

Prerequisites:
MTH 4050 (Minimum Grade of C, May not be taken concurrently)

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MTH 4150 Theory of NumbersCredit Hours: 3

Divisibility, congruences, quadratic reciprocity, number theoretic functions, Diophantine equations, prime number theorems, recent developments in number theory.

Prerequisites:
MTH 1420 (Minimum Grade of C, May not be taken concurrently)

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MTH 4230 ProbabilityCredit Hours: 3

Probability theory based on the Kolmogorov axioms, combinatorics, independence, random variables, expectation, probability distributions, Chebyshev's inequality, central limit theorem.

Prerequisites:
MTH 2410 (Minimum Grade of C, May not be taken concurrently)

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MTH 4270 Applied Probability and StatisticsCredit Hours: 3

Introductory probability theory; elements of sampling and descriptive statistics; sampling distributions; estimations and hypothesis testing; regression and correlation analysis; computer laboratory using a statistical software package.

Prerequisites:
MTH 1420 (Minimum Grade of C, May not be taken concurrently)

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MTH 4280 Analysis of VarianceCredit Hours: 3

Completely randomized design; randomized complete block design; complete factorial designs; split-plot designs; analysis of covariance; multivariate regression; covariance and correlation; introduction to distribution-free methods.

Prerequisites:
MTH 4270 (Minimum Grade of C, May not be taken concurrently)

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MTH 4350 Real Analysis ICredit Hours: 3

Techniques of mathematical proofs chosen from real numbers, sets, functions, point set theory, theory of limits, continuity, differentiation, Riemann integral, and infinite series.

Prerequisites:
MTH 2760 (Minimum Grade of C, May not be taken concurrently) AND
MTH 3060 (Minimum Grade of C, May not be taken concurrently)

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MTH 4360 Real Analysis IICredit Hours: 3

Infinite series, sequences of functions, differentiation of functions of several variables, maxima and minima, function spaces, norms, operator theory.

Prerequisites:
MTH 4350 (Minimum Grade of C, May not be taken concurrently)

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MTH 4370 Complex VariablesCredit Hours: 3

Analytic functions; complex integration; application of Cauchy's theorem; conformal mapping; applications.

Prerequisites:
MTH 2410 (Minimum Grade of C, May not be taken concurrently)

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MTH 4450 Numerical AnalysisCredit Hours: 3

Iterative methods, equations in one variable, polynomial approximation, numerical integration and differentiation, polynomial approximation of functions, numerical methods in matrix algebra, least squares method, numerical methods in differential equations including initial value problems, computer projects. Recommended additional prerequisites: MTH 3020 Linear Algebra with Applications, or MTH 3720 Differential Equations with Linear Algebra.

Prerequisites:
CSSE 1710 (Minimum Grade of C, May not be taken concurrently)

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MTH 4510 Techniques of Advanced CalculusCredit Hours: 3

Real vector spaces, Laplace transforms, Fourier series, boundary value theorems, series solution about singular points, Bessel functions, Legendre polynomials.

Prerequisites:
MTH 2410 (Minimum Grade of C, May not be taken concurrently) AND
MTH 3720 (Minimum Grade of C, May not be taken concurrently)

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MTH 4520 Nonlinear Differential EquationsCredit Hours: 3

Boundary value problems, asymtotic solutions, autonomous systems, systems of equations, applications.

Prerequisites:
MTH 4510 (Minimum Grade of C, May not be taken concurrently)

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MTH 4530 Linear Partial Differential EquationsCredit Hours: 3

First- and second-order equations, initial and boundary value problems, integral transforms, Green's function, perturbations, variational and asymtotic methods.

Prerequisites:
MTH 4510 (Minimum Grade of C, May not be taken concurrently)

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MTH 4550 Operations ResearchCredit Hours: 3

Linear programming, project scheduling, dynamic programming, integer programming, queuing theory.

Prerequisites:
MTH 4020 (Minimum Grade of C, May not be taken concurrently)

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MTH 4570 Regression ModelingCredit Hours: 3

A study of mathematical modeling concepts utilizing qualitative and quantitative variables and applied regression analysis. The practical interaction of mathematics, basic statistics, and regression analysis is developed and applied to a real world setting.

Prerequisites:
MTH 1420 (Minimum Grade of C, May not be taken concurrently)

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MTH 4580 Applied AnalysisCredit Hours: 3

Optimization concepts, maxima and minima for functions of one and several variables, calculus of variations using direct and indirect methods.

Prerequisites:
MTH 3720 (Minimum Grade of C, May not be taken concurrently)

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MTH 4590 Model BuildingCredit Hours: 3

Introduction to the ideas of a mathematical model and model building, linear programming models, game-theoretic models, regression analysis models. Applications in business, ecology, psychology, sociology, and political science.

Prerequisites:
MTH 1420 (Minimum Grade of C, May not be taken concurrently)

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MTH 4600 Graph TheoryCredit Hours: 3

Trees, connectivity, coverings, planarity, colorability, networks and digraphs

Prerequisites:
MTH 1420 (Minimum Grade of C, May not be taken concurrently)

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MTH 4610 Transformational GeometryCredit Hours: 3

Transformations of the Euclidean, affine and projective planes. Classification of these transformations by groups and their invariant properties.

Prerequisites:
MTH 1420 (Minimum Grade of C, May not be taken concurrently)

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MTH 4620 The Projective PlaneCredit Hours: 3

An axiomatic development of the projective plane, models of the projective plane, analytic plane geometry.

Prerequisites:
MTH 1420 (Minimum Grade of C, May not be taken concurrently)

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MTH 4660 Introduction to TopologyCredit Hours: 3

Topics to be chosen from metric spaces, topological spaces, compactness, product spaces, the Tychonoff theorem, rubber sheet geometry, Euler's formula, the Four-Color Problem, the Jordan curve theorem, topological properties of figures.

Prerequisites:
MTH 1420 (Minimum Grade of C, May not be taken concurrently)

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MTH 4690 Mathematics SeminarCredit Hours: 3

Students will prepare and present paper(s) related to their primary area of interest. This course should be taken by mathematics majors in their final year of study.
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MTH 4840 History of MathematicsCredit Hours: 3

Credit only applies in mathematics education. A historical development of mathematics from primitive origins to the Twentieth Century concentrating on numeration systems, arithmetic methods. Euclidean and non-Euclidean geometries, number theory, theory of equations, and the origins of Calculus.

Prerequisites:
MTH 1010 (Minimum Grade of C, May not be taken concurrently) OR
MTH 1020 (Minimum Grade of C, May not be taken concurrently) AND
MTH 1030 (Minimum Grade of C, May not be taken concurrently) AND
MTH 1040 (Minimum Grade of C, May not be taken concurrently) OR
MTH 1100 (Minimum Grade of C-, May not be taken concurrently)

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MTH 4850 Probability and Statistics for TeachersCredit Hours: 3

Credit only applies in mathematics education. Organization and presentation of data, frequency distributions, measures of centrality and dispersion, percentiles and standard scores, sampling theory and distributions, tests of hypotheses and confidence intervals, correlation.

Prerequisites:
MTH 1010 (Minimum Grade of C, May not be taken concurrently) OR
MTH 1020 (Minimum Grade of C, May not be taken concurrently) AND
MTH 1030 (Minimum Grade of C, May not be taken concurrently) AND
MTH 1040 (Minimum Grade of C, May not be taken concurrently) OR
MTH 1100 (Minimum Grade of C-, May not be taken concurrently)

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MTH 4900 Topics in Advanced MathematicsCredit Hours: 1

Course may be repeated for additional credit. Content of the course varies according to the needs or desires of the students.
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