Undergraduate Catalog 2016-2017

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

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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)

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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. The combination of MTH 1020 + MTH 1030 + MTH 1040 is equivalent to MTH 1010.

Prerequisites:
MTH 1020 (Minimum Grade of C, May be taken concurrently) AND
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 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 1250 Foundations of Engineering Mathematics ICredit Hours: 4

Function based approach to fundamental engineering mathematics, including: algebraic methods, graphing, data analysis, approximation, mathematical modeling, and general problem solving. Function types include but are not limited to: polynomial, exponential, rational functions, and their inverses.

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

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MTH 1350 Foundations of Engineering Mathematics IICredit Hours: 4

Continuation of MTH 1250. Trigonometry from planar/spatial, circular function, and graphing/modeling perspectives, vectors and parametric equations, sequences and series, limits from numerical, graphical, and functional perspectives, derivatives, and other topics in calculus.

Prerequisites:
MTH 1250 (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) OR
MTH 1350 (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 to MTH 9999 (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 2411 Analytic Geometry and Calculus III Part ACredit Hours: 2

Course topics include: vectors and analytic geometry in two and three dimensions, parametric curves, calculus of vector valued functions, and motion of a point in space, and functions of several variables and their derivatives.

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

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MTH 2412 Analytic Geometry and Calculus III Part BCredit Hours: 2

Course topics include: multiple integrals and vector calculus.

Prerequisites:
MTH 2411 (Minimum Grade of B, 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 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 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 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 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 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 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 4590 Mathematical ModelingCredit 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 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 4900 Topics in Advanced MathematicsCredit Hours: 1 TO 3

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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