Mathematics

(Note: Students will be assigned to a beginning course on the basis of their high school records and/or the results of the departmental placement exam in mathematics.)

**MTH 080. 3 cr.
Basic Mathematics
**Number concepts; basic operations with counting numbers, whole numbers, integers, and fractions; factoring; real numbers; ratio, proportion, and percent; decimal representations; exponents; scientific notation; geometric interpretation of numbers. This course does not generate earned hours toward graduation requirements.

**MTH 095. 3 cr.
Elementary Algebra
**Fundamental operations with signed numbers, linear equations and inequalities; graphing, linear systems; exponents and polynomials; factoring. This course does not generate earned hours toward graduation requirements.

**MTH 101. 3 cr.
Algebra
**Prerequisite: MTH 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.

**MTH 109. 3 cr.
Engineering Math
**A course for high school students that covers functions, graphs of functions, descriptive statistics including mean, mode, median, standard deviation, and right triangle trigonometry.

**MTH 110. 2 cr.
Applications in Statistics
**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.

**MTH 111. 3 cr.
Mathematical Analysis I
**Prerequisite: MTH 101 or equivalent.

Functions and graphs; linear systems; linear programming; sets and counting; exponential and logarithmic functions; mathematics of finance; probability.

**MTH 112. 3 cr.
Mathematical Analysis II
**Prerequisite: MTH 111 or equivalent.

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

**MTH 140. 3 cr.
Elementary Functions
**Prerequisite: MTH 101 or equivalent.

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

**MTH 141. 4 cr.
Analytic Geometry and Calculus I
**Prerequisite: MTH 140 or equivalent.

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

**MTH 142. 4 cr.
Analytic Geometry and Calculus II
**Prerequisite: MTH 141 or equivalent.

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

**MTH 214. 3 cr.
Statistics
**Prerequisite: MTH 111 or MTH 140, or permission of instructor.

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

**MTH 241. 4 cr.
Analytic Geometry and Calculus III
**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.

**MTH 276. 3 cr.
Discrete Structures
**Prerequisite: MTH 141.

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

**MTH 305. 3 cr.
Mathematics of Compound Interest
**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.

**MTH 327. 2 cr.
Introduction to Probability and Statistics
**Prerequisite: MTH 241.

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

**MTH 372. 4 cr.
Differential Equations with Linear Algebra
**Prerequisite: MTH 142.

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

**MTH 402. 3 cr.
Linear Algebra with Applications
**Prerequisite: MTH 142 or permission of instructor.

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

**MTH 405. 3 cr.
Introduction to Modern Algebra I
**Prerequisite: MTH 276, 402 or 410, or permission of instructor.

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

**MTH 406. 3 cr.
Introduction to Modern Algebra II
**Prerequisite: MTH 405.

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

**MTH 410. 3 cr.
Foundations of Mathematics
**Prerequisite: MTH 402 or permission of instructor.

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

**MTH 415. 3 cr.
Theory of Numbers
**Prerequisite: MTH 142 or permission of instructor.

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

**MTH 423. 3 cr.
Probability
**Prerequisite: MTH 241.

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

**MTH 427. 3 cr.
Applied Probability and Statistics
**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.

**MTH 428. 3 cr.
Analysis of Variance
**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.

**MTH 435. 3 cr.
Modern Analysis I
**Prerequisite: MTH 276 or 410, or permission of instructor.

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

**MTH 436. 3 cr.
Modern Analysis II
**Prerequisite: MTH 435.

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

**MTH 437. 3 cr.
Complex Variables
**Prerequisite: MTH 241.

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

**MTH 451. 3 cr.
Techniques of Advanced Calculus
**Prerequisites: MTH 241 and 372.

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

**MTH 452. 3 cr.
Nonlinear Differential Equations
**Prerequisites: MTH 451 or permission of instructor.

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

**MTH 453. 3 cr.
Linear Partial Differential Equations
**Prerequisite: MTH 451 or permission of instructor.

First and second order equations; initial and boundary value problems; integral transforms; Green’s function; perturbation; variational and asymtotic methods.

**MTH 455. 3 cr.
Operations Research
**Prerequisites: MTH 402.

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

**MTH 457. 3 cr.
Regression Modelling
**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.

**MTH 458. 3 cr.
Applied Analysis
**Prerequisite: MTH 372.

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

**MTH 459. 3 cr.
Model Building
**Prerequisite: MTH 142.

A study of mathematical modeling techniques using arms race models, ecological models, social choice and voting models, Markov processes, and simulations as case studies.

**MTH 460. 3 cr.
Graph Theory
**Prerequisite: MTH 142.

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

**MTH 461. 3 cr.
Transformational Geometry
**Prerequisite: MTH 142.

Transformation of the Euclidean, Affine and Projective planes; classification of these transformations by groups and their invariant properties.

**MTH 462. 3 cr.
The Projective Plane
**Prerequisite: MTH 142.

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

**MTH 466. 3 cr.
Introduction to Topology
**Prerequisite: 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.

**MTH 469.
Seminar in Mathematics
**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.

**MTH 477. 3 cr.
Concepts of Modern Elementary School Mathematics I
**Prerequisite: MTH 101 or equivalent.

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.

**MTH 478. 3 cr.
Concepts of Modern Elementary School Mathematics II
**Prerequisite: MTH 477.

Credit applies only in undergraduate or graduate programs in mathematics education. Foundations of algebra, metric and non-metric geometry, probability and statistics.

**MTH 480. 3 cr.
Analysis for Teachers
**Prerequisite: MTH 101 or equivalent.

Credit applies only in undergraduate or graduate programs in mathematics education. Real number system, polynomials, rational expressions, powers and radicals, relations, functions, with emphasis on linear, quadratic, exponential, logarithmic, and trigonometric functions. Computer laboratory included.

**MTH 481. 3 cr.
Modern Algebra for Teachers
**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).

**MTH 482. 3 cr.
Linear Algebra for Teachers
**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.

**MTH 483. 3 cr.
Fundamental Concepts of Geometry
**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.

**MTH 484. 3 cr.
History of Mathematics
**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.

**MTH 485. 3 cr.
Statistics for Teachers
**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.

**MTH 486. 3 cr.
Higher Arithmetic for Teachers
**Prerequisite: MTH 101 or equivalent.

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

**MTH 487. 3 cr.
Finite Mathematics
**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.

**MTH 490. 1-3 cr.
Topics in Advanced Mathematics
**Prerequisite: Permission of chair.

Course may be repeated for additional credit. Topics will be determined according to the needs of the student.

**MTH 491. 1 cr.
Mathematics Seminar I
**Prerequisite: Permission of instructor.

Topics will be announced prior to the first class meeting.

**MTH 492. 1 cr.
Mathematics Seminar II
**Prerequisite: Permission of instructor.

Topics will be announced prior to the first class meeting.

**MTH 493. 1 cr.
Mathematics Seminar III
**Prerequisite: Permission of instructor.

Topics will be announced prior to the first class meeting.

**MTH 499. Variable credit
Independent Study IV
**Prerequisite: Permission of chair.

Content of course will be designed to meet the needs of the student.

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Mechanical Engineering

**ME 361. 2-1-3
Mechanical Measurements Laboratory
**Prerequisites: E 312, MTH 427.

An extensive set of laboratory experiences to illustrate mechanical measurements and data analysis. Experiments are designed to demonstrate the application of force, temperature, pressure and other transducers. Data acquisition and presentation of data are emphasized.

**ME 380. 3-3-0
Thermodynamics II
**Prerequisite: E 315.

The application of the First and Second Laws of Thermodynamics to power and reversed cycles, psychometric processes, and combustion phenomena. Thermodynamic relations for simple compressible substances are developed. The design of power plants, refrigeration and climate control systems are considered.

**ME 382. 3-3-0
Manufacturing Processes
**Prerequisite: E 312; Co-requisite: E 313, E 317.

The study of the unit processes of manufacturing: machining, forming, casting and joining. The course considers measurements, tolerances, quality control and materials as they relate to manufacturing. The design of a manufacturing process, gages and fixtures is considered.

**ME 383. 1-0-3
Manufacturing Processes Laboratory
**Co-requisite: ME 382.

A set of laboratory experiences to illustrate measurements, quality control and unit processes in manufacturing. Students will use machine tools, forming, casting and welding equipment.

**ME 390. 3-3-0
Design of Machine Elements I **

Prerequisites: E 313, E 317, E 326.

An application of engineering sciences to the design of mechanical components. The course considers theories of failure, selection and proportioning of machine elements, fatigue, stress concentration and buckling of columns. The design of machines containing power screws and fasteners is treated in depth.

**ME 392. 3-3-0
Design of Machine Elements II
**Prerequisite: ME 390.

The solution of problems involving systems of machine elements. The use of gears, springs, shafts and bearings is treated in depth. Static and dynamic considerations are made to system design. Design projects are used as a principal method of instruction.

**ME 402. 3-3-0
Design for Quality
**Prerequisite: ME 392; Co-requisites: MTH 427.

Techniques for the systematic and efficient design of high quality products and processes. The concept of a quality loss function, tolerance design, benchmarking and signal/noise ratios are introduced. The course considers orthogonal arrays, Taguchi methods and methods for process improvements.

**ME 430. 3-3-0
Metal Cutting Analysis
**Prerequisites: ME 382, E 313.

The in-depth study of material removal processes. The models of orthogonal and oblique cutting are considered. Topics include: tool life and wear, surface finish, cutting fluids, process economics, traditional and non-traditional machining.

**ME 432. 3-3-0
Metal Forming Analysis
**Prerequisites: ME 382, E 326.

The analysis of extrusion, drawing, rolling and forging processes. The role of formability of materials and processing conditions are treated with engineering science.

**ME 458. 3-3-0
Internal Combustion Engines I
**Prerequisites: ME 380.

The application of principles of chemistry and thermodynamics to the theory and design of gas power engines. The concepts of spark ignition, compression ignition, cycle analysis and combustion characteristics are treated in-depth.

**ME 459. 1-0-3
Internal Combustion Engines Laboratory
**Co-requisites: ME 458.

A set of laboratory experiences to illustrate the principles of gas power engines. Students will use various dynamometers and specialty engines.

**ME 472. 3-3-0
Noise and Vibration
**Prerequisites: E 313, MTH 372.

An overview of problems in acoustics and vibration control. The use of single and multiple degree of freedom lumped parameter systems are used to describe systems. Methods for controlling noise and vibration sources are discussed.

**ME 476. 3-3-0
Vehicle Dynamics
**Prerequisites: E 313, MTH 372.

The stability and control of vehicles in the accelerating and decelerating modes along straight and curved paths. Special attention is given to the behavior and limitations of the pneumatic tire as applied to motor vehicle requirements.

**ME 478. 3-3-0
Manufacturing Productivity
**Prerequisites: ME 382.

A critical analysis and examination of productivity measurements. The use of time and motion studies, ergonomics and simulation are used. The technological blocks to productivity and methods of enhancing productivity are considered.

**ME 480. 3-3-0
Energy Systems
**Prerequisites: E 314, E 315.

Applications of thermodynamics and fluid mechanics to energy conversion systems. Advanced modifications to basic vapor and gas power and refrigeration cycles are analyzed. Second Law (availability) analysis is applied to energy conversion processes. Other topics include: hydraulic machinery, nuclear power systems, solar energy, energy storage techniques, and wind power. Environmental issues surrounding the various types of energy systems are discussed.

**ME 482. 3-3-0
Computer Aided Manufacturing
**Prerequisites: E 104, ME 382.

A series of topics in the application of computer technology to the manufacturing enterprise. Topics include: programmable logic, simulation, numerical control and the exchange of manufacturing data. Projects are the principal mode of instruction.

**ME 488. 3-3-0
Reliability in Design
**Prerequisites: ME 390, MTH 427.

A study of probabilistic models in engineering design. Topics include: reliability distribution functions, failure rate, system reliability, hazard analysis, FMEA and reliability testing. The use of the probabilistic approach to the design of mechanical components is treated in depth.

**ME 492. 3-3-0
Computer Aided Engineering
**Prerequisites: E 104, ME 390.

An introduction to the use of computer techniques to analyze mechanical components and systems. The course includes kinematic synthesis, optimal design, finite element methods and simulation.

**ME 493. 2-1-2
Prototype Design I
**Prerequisites: ME 390.

The first half of a two-term sequence dealing with the solution of an industrial design problem. Students work in teams to design, analyze, construct and test a working prototype of the solution to a specified problem. The use of standard design disciplines are emphasized (failure mode and effect analysis and design verification plans). The preparation and presentation of design proposals are central to the course.

**ME 495. 3-1-5
Prototype Design II
**Prerequisite: ME 493.

The second half of the two-term sequence that begins with ME 493. This course must be taken in the same academic year as ME 493. The fabrication and testing of a working prototype is emphasized. The methods for the presentation of results and alternative solutions are central to the sequence.

**ME 498. 3-3-0
Internal Combustion Engines II
**Prerequisites: ME 458.

The continuation of the theory and design of gas power engines. Particular attention is given to detailed design considerations. The effects of changes in engine parameters on fuel economy, performance and emissions are studied.

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Mexican American Partnership Program

**MAP 300. 12-18 cr.
Mexican American Partnership I
**A temporary course registration to cover course work taken in Mexico by UDM MAP students during their first academic term at Monterrey Tech. Upon receipt of the official transcripts from Monterrey Tech, MAP 300 will be replaced in the UDM student’s record by the classes for which credit is earned. Actual credit hours will be adjusted at the time of transcript evaluation.

**MAP 350. 12-18 cr.
Mexican American Partnership II
**A temporary course registration to cover course work taken in Mexico by UDM MAP students during their second academic term at Monterrey Tech. Upon receipt of the official transcripts from Monterrey Tech, MAP 350 will be replaced in the UDM student’s record by the classes for which credit is earned. Actual credit hours will be adjusted at the time of transcript evaluation.

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Music

**MUS 100. 1 cr.
UDM Chorale
**A mixed voice choral group open to interested male and female singers. Repertoire will include a mixture of classical, contemporary and popular choral music.

**MUS 202. 3 cr.
Survey of Our Music Heritage
**A broad panorama of the development of Western music from around 600 A.D. to the present. Explores music as diverse as Medieval Chant, orchestral, theatrical and popular. Each student will have the use of prerecorded music on cassette to supplement the classroom listening experience.

**MUS 306. 3 cr.
Music of the Theatre
**A survey of Broadway musicals, Hollywood filmscores and the ever-popular, seductive opera Carmen. Video and audio performances of the three genres will be an important aspect of the classroom experience.

**MUS 308. 3 cr.
American Music
**From Sousa to Satchmo! This course features audio and video performances of American music, from colonial times to the present, including folksongs, sacred music, minstrel show tunes, Broadway selections, concert hall music, jazz, and rock.

**MUS 165, 166; 265, 266; 365, 366; 465, 466 1 cr.
Private Voice
**Private 45-minute lessons once a week. (Beginning to advanced levels.)

**MUS 135, 136; 235, 236; 335, 336; 435, 436. 1 cr.
Private Piano
**Private 45-minute lessons once a week. (Beginning to advanced levels.)

**MUS 185, 186; 285, 286; 385, 386; 485, 486. 1 cr.
Private Instrument
**Private 45-minute lessons once a week. (Beginning to advanced levels.)