Undergraduate Catalog 2007-2008
UDM Academic PoliciesCourse DescriptionsList of All ProgramsFaculty


MTH 101 Algebra
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
UAS 095 or equiv
Prerequisite: UAS 095 or equivalent.


Sets and real numbers; algebra of polynomials; algebra of rational expressions; exponents and radicals; linear equations and inequalities; systems of linear equations; quadratic equations.
00000

MTH 102 Algebra A
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
UAS 095
UAS 095 or equivalent


Linear equations and applications; systems of linear equations; linear functions in the rectangular coordinate system. The combination of MTH 102 + MTH 103 + MTH 104 is equivalent to MTH 101.
10000

MTH 103 Algebra B
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 102
Grade of C or higher in MTH 102


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.
10000

MTH 104 Algebra C
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 103
Grade of C or higher in MTH 103


Rational exponents; radical expressions; solving equations containing radical expressions; quadratic equations; applications of quadratic equations.
10000

MTH 109 Engineering Math
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:




A course for high school students that covers functions, graphs of functions, descriptive statistics including mean, mode, median, standard deviation, and right triangle trigonometry.
30000

MTH 110 Applications in Statistics
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:




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.
20000

MTH 111 Mathematical Analysis I
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 101 or equiv
Prerequisite: MTH 101 or equivalent.


Equations and inequalities; graphs and functions; polynomials and rational functions; exponential and logarithmic; systems of equations and inequalities; matrices and determinants; conic sections.
30000

MTH 112 Mathematical Analysis II
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 111
Prerequisite: MTH 111 or equivalent.


Pre-calculus topics; derivatives and integrals; applications; techniques of integration.
30000

MTH 140 Elementary Functions
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 101 or equiv
Prerequisite: MTH 101 or equivalent.


Study of functions, including polynomials; rational, algebraic, exponential, logarithmic and trigonometric functions. Computer laboratory included.
30000

MTH 141 Analytic Geometry and Calculus I
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 140 or equiv
Prerequisite: MTH 140 or equivalent.


Functions; limits and continuity; derivatives and integrals of polynomial, rational and trigonometric functions. Computer laboratory included.
40000

MTH 142 Analytic Geometry and Calculus II
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 141
Prerequisite: MTH 141


Topics in analytic geometry, differentiation and integration of exponential, logarithmic and inverse trigonometric functions; sequences and series. Computer laboratory included.
40000

MTH 214 Basic Statistics
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 101
Prerequisite: MTH 101


Statistical analysis for business and social science applications; descriptive statistics; probability; sampling; estimation; hypothesis testing; regression analysis.
30000

MTH 241 Analytic Geometry and Calculus III
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 142
Prerequisite: MTH 142.


Plane curves; polar coordinates; vectors in two and three dimensions; analytic geometry in the three dimensions; vector valued functions; partial derivatives and multiple integrals.
40000

MTH 276 Discrete Structures
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 141
Prerequisite: MTH 141.


Sets; functions and proof techniques; logic and logic circuits; relations; combinatorics; some graph theory; application to Computer Science.
30000

MTH 305 Mathematics of Compound Interest
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 111 or
MTH 140
Prerequisite: MTH 111 or 140.


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.
30000

MTH 306 Mathematical Thinking
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 241
MTH 276



Plausible conjectures, techniques of proofs, direct proof, proof by contrapositive, proof by induction, application to set theory, analysis, combinatories, group theory, functions, relations.
33000

MTH 327 Introduction to Probability and Statistics
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 241
Prerequisite: MTH 241.


Introductory probability theory; elements of sampling and descriptive statistics; sampling distributions; computer laboratory using a statistical software package.
20000

MTH 372 Differential Equations with Linear Algebra
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 142
Prerequisite: MTH 142.


Linear dependence; linear differential equations and applications; systems of linear differential equations; series solutions.
40000

MTH 402 Linear Algebra with Applications
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 141
or permission of instructor.


Vector spaces, matrices, systems of linear equations, determinants, inner products, linear transformations, similar matrices, eigenvalues and eigenvectors of a matrix.
300

MTH 405 Introduction to Modern Algebra I
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 402



Sets and mappings, an axiomatic approach to the number system, groups, rings, ideals, fields, isomorphism theorems, induction, permutations.
300

MTH 406 Introduction to Modern Algebra II
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 405



Euclidean domains, polynomial rings, field extension, finite fields, finite groups, p-groups, the Sylow theorems, introduction to Galois theory.
300

MTH 410 Foundations of Mathematics
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 402
(Prerequisite: MTH 402 or permission of instructor.)


Logic, set theory, axiomatic structure of the number system, infinite sets, cardinal numbers, ordinal numbers, axiom of choice.
300

MTH 415 Theory of Numbers
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 142



Divisibility, congruences, quadratic reciprocity, number theoretic functions, Diophantine equations, prime number theorems, recent developments in number theory.
300

MTH 423 Probability
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 241



Probability theory based on the Kolmogorov axioms, combinatorics, independence, random variables, expectation, probability distributions, Chebyshev's inequality, central limit theorem.
300

MTH 427 Applied Probability and Statistics
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 241
Prerequisite: MTH 241.


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.
30000

MTH 428 Analysis of Variance
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 427
Prerequisite: MTH 427.


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.
30000

MTH 435 Modern Analysis I
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 402



Techniques of mathematical proofs chosen from real numbers, sets, functions, point set theory, theory of limits, continuity, differentiation, Riemann integral, and infinite series.
300

MTH 436 Modern Analysis II
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 435



Infinite series, sequences of functions, differentiation of functions of several variables, maxima and minima, function spaces, norms, operator theory.
300

MTH 437 Complex Variables
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 241
Prerequisite: MTH 241.


Analytic functions; complex integration; application of Cauchy?s theorem; conformal mapping; applications.
30000

MTH 451 Techniques of Advanced Calculus
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 214
Mth 372



Real vector spaces, Laplace transforms, Fourier series, boundary value theorems, series solution about singular points, Bessel functions, Legendre polynomials.
300

MTH 452 Nonlinear Differential Equations
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 451



Boundary value problems, asymtotic solutions, autonomous systems, systems of equations, applications.
300

MTH 453 Linear Partial Differential Equations
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 451



First- and second-order equations, initial and boundary value problems, integral transforms, Green's function, perturbations, variational and asymtotic methods.
300

MTH 455 Operations Research
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 402



Linear programming, project scheduling, dynamic programming, integer programming, queuing theory.
300

MTH 457 Regression Modelling
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 142
Prerequisite: MTH 142.


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.
30000

MTH 458 Applied Analysis
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 372
Prerequisite: MTH 372.


Optimization concepts, maxima and minima for functions of one and several variables, calculus of variations using direct and indirect methods.
30000

MTH 459 Principles of Model Building
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours


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.
300

MTH 460 Graph Theory
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 142 or
permission of instructor
Prerequisite: MTH 142 or permission of instructor.


Trees, connectivity, coverings, planarity, colorability, networks and digraphs
30000

MTH 461 Transformational Geometry
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 142



Transformations of the Euclidean, affine and projective planes. Classification of these transformations by groups and their invariant properties.
300

MTH 462 The Projective Plane
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 142



An axiomatic development of the projective plane, models of the projective plane, analytic plane geometry.
300

MTH 466 Introduction to Topology
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 435



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.
300

MTH 469 Seminar in Mathematics
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:




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.
30000

MTH 477 Concepts of Modern Elementary School Mathematics I
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours


(Credit applies only in undergraduate or graduate programs in mathematics education.) Sets, logic, mathematical systems, systems of numeration, natural numbers, whole numbers, integers, rational numbers, real numbers.
300

MTH 478 Concepts of Modern Elementary School Mathematics II
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours


(Credit applies only in undergraduate or graduate programs in mathematics education.) Foundations of algebra, metric and nonmetric geometry, probability and statistics.
300

MTH 480 Analysis for Teachers
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours


(Credit applies only in undergraduate or graduate programs in mathematics education.) Topics chosen from algebra and trigonometry, including roots of polynomial equations, root approximation techniques, the factor theorem, the remainder theorem, Descartes' rule of signs, trigonometric functions, law of sines, law of cosines, complex numbers.
300

MTH 481 Modern Algebra for Teachers
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 480
Prerequisite: MTH 480.


Credit only applies in mathematics education. Structure of a mathematical system, groups, fields, ordered fields including important models (namely the real number system).
30000

MTH 482 Linear Algebra for Teachers
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 480
Prerequisite: MTH 480.


Credit only applies in mathematics education. Matrices, vectors, mathematical systems, determinants, inverse of a matrix system of linear equations, matrix solutions, linear inequalities, linear programming
30000

MTH 483 Fundamental Concepts of Geometry
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:

Prerequisites: Permission of instructor.


Credit only applies in mathematics education. Intuitive geometry; axiomatic geometry including treatment of lines, planes, congruence, measures, parallelism and similarity; non-Euclidean geometries.
30000

MTH 484 History of Mathematics
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 101
Prerequisite: MTH 101 or equivalent.


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.
30000

MTH 485 Statistics for Teachers
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 101
Prerequisite: MTH 101 or equivalent.


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.
30000

MTH 486 Higher Arithmetic for Teachers
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 101
Prerequisite: MTH 101 or equivalent.


Credit only applies in mathematics education. Divisibility, prime numbers, congruences, quadratic reciprocity law.
30000

MTH 487 Finite Mathematics
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
MTH 111 or
MTH 482
Prerequisite: MTH 111 or MTH 482.


Credit only applies in mathematics education. Topics selected from combinatorial analysis, probability, stochastic processes and Markov chains, theory of games.
30000

MTH 490 Topics in Advanced Mathematics
Credit HoursRecitation/Lecture HoursStudio HoursClinical HoursLab Hours

Prerequisites:
(Prerequisite: Permission of the chairperson.)


Course may be repeated for additional credit. Content of the course varies according to the needs or desires of the students.
100

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