# Course Catalog

### Courses Offered

Tech’s mathematics department offers courses in eight subfields of mathematics. The middle digit of each mathematics course number specifies the sub‐field in which that course belongs. The middle digits and the subfields they represent are:

1—operations research and numerical methods

2—discrete mathematics

3—applied analysis

4—geometry

5—modern algebra

6—topology

7—real analysis (theory)

8—probability, statistics, stochastic processes

Thus, 415 is a course in operations research, etc. The middle digit 0 is used for the basic mathematics courses. The only exception to this system is MATH 581, the standard college number for directed studies.

**MATH 101, College Algebra**

3 credits

2 class hours, 3 lab hours

The fundamental algebraic operations—factoring, fractions, linear equations and inequalities, quadratic equations, ratio, proportion, variation, functions and their graphs, systems of equations. [NMCCNS MATH 1113: General Education Area II]

**MATH 103, 103D, Pre‐Calculus**

3 credits

2 class hours, 3 lab hours

*Prerequisites: ACT Math score of at least 21 or SAT Math score of at least 500 or
SAT Redesign Math score of at least 530 or a score of 24 or higher on the algebra
portion of the math placement test, or MATH 101 passed with grade C‐ or better*

Functions and relations, equations and inequalities, determinants and matrices, simultaneous equations, algebra of polynomials, complex numbers. [NMCCNS MATH 1613: General Education Area II]

**MATH 104, 104D, Trigonometry**

3 credits

2 class hours, 3 lab hours

*Prerequisite: MATH 103 passed with a grade of C– or better, or ACT Math score of at
least 26 or SAT Math score of at least 590 or SAT Redesign Math score of at least
610 or a score of 20 or higher on the advanced algebra portion of the math placement
test.*

Trigonometric functions, identities, related angles, radian measure, graphs, inverse functions, trigonometric equations, logarithms, solution of plane triangles. [NMCCNS MATH 1114: General Education Area II]

**MATH 131, Calculus and Analytic Geometry I**

4 credits

3 class hours, 3 lab hours

*Prerequisites: MATH 103 and 104 or the equivalent passed with grade C‐ or better;
or ACT Math score of at least 30 or SAT Math score of at least 670 or SAT Redesign
Math score of at least 700; or a score of at least 20 on the calculus readiness math
placement test; or MATH 104 and either ACT Math score of at least 26 or SAT Math score
of at least 590 or SAT Redesign Math score of at least 610.*

First course in calculus and analytic geometry. Includes introductory concepts in analytic geometry, limits, continuity, differentiation, applications of the derivative, the mean value theorem, the definite and indefinite integral, and applications of integration. [NMCCNS MATH 1614: General Education Area II]

**MATH 132, Calculus and Analytic Geometry II**

4 credits

4 class hours

*Prerequisite: MATH 131 passed with grade C‐ or better*

Continuation of MATH 131. Transcendental functions, techniques of integration, polar coordinates, infinite series, and applications. [NMCCNS MATH 1623: General Education Area II]

**MATH 221, Formal Logic and Discrete Mathematics**

3 credit

3 class hours

*Prerequisite: MATH 132 passed with a grade C‐ or better*

Analytical reasoning and critical thinking skills. Induction and recursion. Mathematical proofs. Propositional calculus and predicate calculus. Discrete and combinatorial mathematics: sets, functions, relations, trees, and graphs, permutations and combinations.

**MATH 231, Calculus and Analytic Geometry III**

4 credits

4 class hours

*Prerequisite: MATH 132 passed with grade C‐ or better*

Vectors in the plane and 3‐space, vector calculus in two dimensions, partial differentiation, multiple integration, topics in vector calculus, and complex numbers and functions.

**MATH 254, Introduction to Applied Linear Algebra**

3 credits

3 class hours, 1.5 lab hours

*Prerequisite: MATH 131 passed with grade C‐ or better*

Linear systems, matrix algebra, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, inner products and orthogonality, least squares problems.

**MATH 283, Introduction to Applied Statistics**

3 credits

3 class hours, 1.5 lab hours

*Corequisite: MATH 132*

Exploratory data analysis. Introduction to probability and random variables. Concepts of population and sample. Estimation and hypothesis testing. Simple linear regression and one‐way analysis of variance. Techniques in data analysis using statistical computer packages.

**MATH 332, Vector Analysis**

3 credits

3 class hours

*Prerequisite: MATH 231 passed with grade C‐ or better*

Scalar and vector fields, gradient, divergence, curl, del operator, general orthogonal curvilinear coordinates, line integrals, surface and volume integrals, divergence theorem, Green’s theorem, Stokes’s theorem, applications.

**MATH 335, Ordinary Differential Equations**

3 credits

3 class hours

*Prerequisite: MATH 132 passed with grade C‐ or better*

Solution methods for first order ordinary differential equations of various types, including separable, linear, Bernoulli and exact. Solution methods for second (and higher) order linear differential equations with constant coefficients. Series solutions. Laplace transforms. Applications.

**MATH 335L, Ordinary Differential Equations Computer Lab**

1 credits

1 class hour

*Corequisite: MATH 335 or equivalent.*

Optional lab to accompany MATH 335. Basic introduction to the “Maple” syntax required to solve ordinary differential equations with computers. Emphasis on modeling, using graphing capabilities to illustrate how responses (solutions) are influenced by changes in the initial data and physical parameters.

**MATH 336, Introduction to Partial Differential Equations**

3 credits

3 class hours

*Prerequisites: MATH 231, 335, and one of MATH 254 or MATH 337, each passed with grade
C‐ or better*

Orthogonal functions, Sturm‐Liouville theory, Fourier series and integrals, heuristic derivation of examples of partial differential equations taken from heat conduction, vibration problems, electromagnetism, etc.; separation of variables, application to boundary value problems.

**MATH 337, Engineering Mathematics**

3 credits

3 class hours

*Prerequisites: MATH 231 Corequisite: MATH 335*

Selected topics from linear algebra are discussed, including vectors, matrices, determinants, Gaussian elimination, vector spaces and basis as well as Eigenvalues, eigenvectors and diagonalization of matrices. Of particular interest will be linear algebra techniques which are utilized of solving systems of (linear) algebraic equations and solving systems of coupled ordinary differential equations using Laplace transforms and linear algebra tools.

**MATH 352, Basic Concepts of Mathematics**

3 credits

3 class hours

*Prerequisite: MATH 132 passed with grade C‐ or better*

Mathematical proofs, set theory, mathematical induction and recursion, binary relations, functions, definition and development of some common number systems, cardinal numbers, abstract algebra.

**MATH 372, Basic Concepts of Analysis**

3 credits

3 class hours

*Prerequisite: MATH 352 or equivalent passed with grade C‐ or better*

Real numbers, sequences, limits, continuity, uniform continuity, differentiation, Reimann integral.

**MATH 382, Probability and Statistics**

3 credits

3 class hours

*Prerequisite: MATH 132 passed with grade C‐ or better*

Exploratory data analysis, random variables, estimation and hypothesis testing, linear regression and analysis of variance, basic concepts of discrete and continuous probability distributions, bivariate probability distribution functions, expected values, moment generating function and weak law of large numbers. Uses of the central limit theorem and its applications. This course provides an introduction to probability theory and statistical inference. The theory of probability is the primary mathematical tool used in statistical inference and therefore this course will concentrate heavily on probability and statistics. The course has been designed for computer science and engineering students; however, it is broad enough for students from outside these disciplines.

**MATH 382L, Probability and Statistics Lab**

1 credits

1 class hour

*Corequisite: Math 382 or equivalent*

Entering data, descriptive statistics, graphing data, cross tabulation, hypothesis testing, and calculation of probabilities from different probability distributions. Each lab introduces a problem, provides some scientific background, suggests investigations for the data, and provides a summary of the theory used in the investigations.

**MATH 383, Introduction to Biostatistics**

3 credits

3 class hours

*Prerequisite: Math 132 passed with a grade of C– or better*

This course covers the fundamental statistical concepts related to the practice of public health: descriptive statistics, design of biological research studies, probability, sampling, statistical distributions, confidence intervals, hypothesis testing, comparison of means and proportions, chi‐squared tests, one‐way & two‐way ANOVA, simple and multiple linear regression, Fisher’s Exact test and Mantel Hansel test for comparing several 2x2 tables. The course also uses the R statistical software and includes many applications of statistics to health sciences and medical studies, emphasizing concepts and interpretation of results. Optional topics: principal components and factor analysis.

**MATH 384, Applied Regression and Design of Experiments**

3 credits

3 class hours

*Prerequisite: MATH 283 or 382 passed with grade C‐ or better*

Design of experiments, analysis of variance and covariance, linear and nonlinear curve fitting. Applications taken from metallurgy, mining and petroleum engineering, hydrology, and other disciplines.

**MATH 386, Nonparametric Statistics**

3 credits

3 class hours

*Prerequisite: MATH 283 or 382 passed with grade C‐ or better*

Tests based on ranks for one‐sample and two‐sample problems, nonparametric estimates, multiple comparisons, nonparametric methods in regression. Applications in science and engineering.

**MATH 391, Special Studies**

Credit hours to be arranged

**MATH 401, Putnam Competition**

1 credit

1 class hour

*Graded S/U*

Students in this course will prepare for and then participate in the annual William Lowell Putnam Competition in mathematics. In preparation for the competition, students will learn problem‐solving strategies and practice on problems from previous competitions. May be taken multiple times for credit.

**MATH 410, Numerical Methods for Scientists and Engineers I**

3 credits

3 class hours

*Prerequisite: CSE 107, CSE 113, ES 111, or EE 251 Corequisite: MATH 335*

Floating point arithmetic, solution of linear and nonlinear systems of equations, interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations.

**MATH 411, Numerical Linear Algebra**

3 credits

3 class hours

*Prerequisites: MATH 254; CSE 113 or ES 111*

Direct and iterative methods for solving linear systems, conditioning and stability, methods for computing eigenvalues and eigenvectors, linear least squares problems, applications, performance, software.

**MATH 414, Introduction to High Performance Computing**

3 credits

3 class hours

*Prerequisite: MATH 410 passed with grade C‐ or better*

Solving scientific problems in high‐performance computing systems. Topics include: numerical methods, using software libraries and packages such as MATLAB, Mathematica, NAG, LAPACK, etc., matching algorithms to machines, measuring performance and scientific visualization. A number of computing architectures—such as high ‐performance workstations, the Cray Y‐MP, and the Connection Machine—will be used to solve a small set of prototype problems.

**MATH 415, Introduction to Operations Research: Deterministic Methods**

3 credits

3 class hours

*Prerequisite: MATH 254 passed with grade C‐ or better*

A survey of operations research techniques including linear programming, nonlinear models, and graph theoretical models.

**MATH 430, Mathematical Modeling**

3 credits

3 class hours

*Prerequisites: MATH 335 and one of MATH 254 or MATH 337, each passed with grade C‐
or better*

Introduction to the process of developing, analyzing, and refining mathematical models. Deterministic and probabilistic models considered for both discrete and continuous problems. Applications to a variety of fields.

**MATH 435, Complex Analysis**

3 credits

3 class hours

*Prerequisite: MATH 336 passed with grade C‐ or better*

Algebra of complex numbers, analytic functions and Cauchy‐Riemann equations, complex integration and Cauchy’s theorem, integral formulae, power series, residues and contour integration, analytic continuation, Riemann surfaces.

**MATH 436, Applications of Complex Analysis**

3 credits

3 class hours

*Prerequisite: MATH 435 passed with grade C‐ or better*

Topics selected from linear ordinary differential equations in the complex plane, special functions, conformal mapping, Laplace transform, Fourier and Hilbert transforms.

**MATH 437, Systems of Ordinary Differential Equations**

3 credits

3 class hours

*Prerequisites: MATH 254 and 335, each passed with grade C‐ or better*

Theory and application of systems of ordinary differential equations, linear and nonlinear systems, two‐ dimensional autonomous systems, stability, periodic solutions and limit cycles, interspecies competition and predator/prey problems, pendulum equation, Duffing equation, Van der Pol equation, Lienard equation.

**MATH 438, Partial Differential Equations**

3 credits

3 class hours

*Prerequisite: MATH 336 passed with grade C‐ or better*

Classification of classical partial differential equations of mathematical physics, boundary conditions, uniqueness theorems, first and second order equations, characteristics, boundary value problems, Green’s functions, maximum principle.

**MATH 442, Introduction to Differential Geometry**

3 credits

3 class hours

*Prerequisite: MATH 254 passed with grade C‐ or better*

Introduction to the theory of manifolds, vector fields, tensors and differential forms.

**MATH 454, Linear Algebra**

3 credits

3 class hours

*Prerequisites: MATH 254 and 352, each passed with grade C‐ or better*

Vector spaces, linear transformations, linear systems, eigenvalues and eigenvectors, Jordan canonical forms, inner product spaces, least squares problems, normal, unitary, and Hermitian transformations.

**MATH 455, 456, Introduction to Abstract Algebra**

3 credits

3 class hours each semester

*Prerequisite: MATH 352 passed with grade C‐ or better*

A study of abstract algebraic structures, semi‐groups, groups, rings, ideals, integral domains, fields, vector spaces, field extensions.

**MATH 458, Introduction to Theory of Numbers**

3 credits

3 class hours

*Prerequisite: MATH 352 passed with grade C‐ or better*

Properties of integers, primes, congruences, related topics.

**MATH 461, Introduction to Topology**

3 credits

3 class hours

*Prerequisite: MATH 372 passed with grade C‐ or better*

Fundamental concepts of point‐set topology, abstract topological spaces, metric spaces, continuous mappings, separation axioms, compactness, connectedness.

**MATH 464, Knot Theory**

3 credits

3 class hours

*Prerequisite: MATH 335 and MATH 352 passed with grade C‐ or better*

General survey of knot theory concentrating on knot invariants, including numerical, polynomial and invariants of finite type, theory of braids, the Artin braid group, elementary template theory, applications to physics and biology.

**MATH 471, 472, Introduction to Analysis**

3 credits

3 class hours each semester

*Prerequisite: MATH 372 passed with grade C‐ or better*

Basic concepts of the real‐number system, elements of point‐set theory, infinite sequences, limits, continuity, differentiation of functions of one variable, Riemann‐Stieltjes integral, series, functions of several variables.

**MATH 483, Mathematical Statistics**

3 credits

3 class hours

*Prerequisite: MATH 382 passed with grade C‐ or better*

Introduction to decision theory. Multivariate distributions. Sampling distributions for the normal case. Convergence of random variables. Different methods of estimation. Principles of hypothesis testing.

**MATH 484, Reliability and Quality Control**

3 credits

3 class hours

*Prerequisite: MATH 382 passed with grade C‐ or better*

Order statistics, testing and estimation for common lifetime distributions in reliability, accelerated life tests, Bayesian methods in reliability. Statistical techniques of industrial quality control, sampling methods, control charts. Applications in industry.

**MATH 486, Introduction to Stochastic Processes**

3 credits

3 class hours

*Prerequisites: MATH 254 and 382, each passed with grade C‐ or better*

Conditioning. The Poisson process. Theory of Markov chains, continuous time Markov and semi‐ Markov processes. Topics from renewal theory and Markov renewal theory. Queuing Theory. Applications in science and engineering.

**MATH 488, Introduction to Operations Research: Probabilistic Methods**

3 credits

3 class hours

*Prerequisite: MATH 382, passed with grade C‐ or better*

Monte Carlo Simulation Theory. Application of simulation to problems in science, engineering, and business. Queuing systems simulation. Inventory theory.

**MATH 491, Directed Study**

Credit hours to be arranged

**MATH 500, Directed Research**

Credit hours to be arranged

**MATH 501, 502, Professional Development Seminar**

3 credits

3 class hours each semester

A seminar in which students will develop skills in problem solving, communication,
and research. Students will be expected to actively participate in the seminar by
a ending presentations, solving assigned problems, and preparing written and oral
presentations. *Graded S/U.*

**MATH 503, Graduate Seminar**

0‐1 credits

1 class hour

*Prerequisite: Graduate standing.*

Attend and participate in departmental seminars. Graded on an S/U basis.

**MATH 505, Neural Nets**

3 credits

3 class hours

*Prerequisites: CS 344; MATH 254 and 382; or consent of instructor*

Neuron modeling. The perceptron and multilayer perceptrons. Learning algorithms. The Kohonen model, the Grossberg model, the Hopfield model. Associative memory. Applications. Recent developments in the field. (Same as CSE 565)

**MATH 509 Graduate Internship**

Credit hours to be arranged

*Prerequisite: Graduate standing*

**MATH 510 Computational Fluid Dynamics**

3 credits

3 class hours

*Prerequisite: MATH 254, 336, 410 or equivalent*

Equations of fluid dynamics, flow models, discretization techniques, analysis of numerical schemes, numerical methods for solving linear and nonlinear systems of equations, numerical methods for inviscid and viscous flows.

**MATH 511, Numerical Methods for Partial Differential Equations**

3 credits

3 class hours

*Prerequisite: MATH 410 or consent of instructor*

Finite difference or finite element methods for parabolic and elliptic partial differential equations; approximation, stability, and convergence; applications.

**MATH 512, Numerical Methods for Wave Propagation**

3 credits

3 class hours

*Prerequisite: MATH 410 or consent of instructor*

Finite volume methods for hyperbolic partial differential equations; Riemann problems; Godunov’s and Roe’s methods; high resolution methods; applications.

**MATH 513, Advanced Topics in Numerical Analysis**

3 credits

3 class hours

*Prerequisite: MATH 410 or consent of instructor*

Topics chosen from areas in numerical analysis, numerical partial differential equations, multigrid and domain decomposition methods, numerical linear algebra. May be taken multiple times for credit.

**MATH 515, Topics in Deterministic Operations Research**

3 credits

3 class hours

*Prerequisite: MATH 415 or consent of instructor*

Study of a special topic in deterministic operations research. May be taken multiple times for credit.

**MATH 516, Topics in Stochastic Operations Research**

3 credits

3 class hours

*Prerequisites: MATH 486 or consent of instructor*

Study of a special topic in stochastic operations research. May be taken multiple times for credit.

**MATH 517, Combinatorial Optimization**

3 credits

3 class hours

*Prerequisite: MATH 415 or consent of instructor*

Maximum flow, shortest path, and minimum cost flow problems on networks. Matching. Matroids. Cu ing plane and branch and bound methods for integer programming. Computational complexity of combinatorial optimization problems.

**MATH 518, Methods of Nonlinear Programming**

3 credits

3 class hours

*Prerequisite: MATH 410 or 415 or consent of instructor*

Theory of constrained and unconstrained optimization. Methods for nonlinear programming, including quasi‐ Newton methods, conjugate direction methods, Levenberg‐Marquardt methods, sequential quadratic programming, and sequential unconstrained minimization techniques.

**MATH 519, 519D, Inverse Problems**

3 credits

3 class hours

Theory and practice of the various techniques of inverting geophysical data to obtain models. Primary emphasis is on the understanding and use of linear inverse techniques. (Same as GEOP 529.)

**MATH 521, Advanced Combinatorics**

3 credits

3 class hours

*Prerequisite: MATH 221*

Graph theory and applications. Graphs, trees, connectivity, Euler tours and Hamiltonian cycles, matchings, planar graphs, directed graphs, networks, cycle space, and bond space.

**MATH 530, Modeling Case Studies**

3 credits

3 class hours

*Prerequisite: MATH 430 or equivalent*

Open‐ended modeling projects from actual applications.

**MATH 531, 531D, Topics in Ordinary Differential Equations**

3 credits

3 class hours each semester

*Prerequisite: MATH 437 or equivalent*

Study of a special topic in ordinary differential equations not usually treated. Normally one related to a field of research interest at Tech. May be taken multiple times for credit.

**MATH 532, 532D, Perturbation Methods**

3 credits

3 class hours

*Prerequisite: MATH 437 or equivalent*

A survey of expansion techniques. Regular and singular perturbations. Poincaré‐Linstedt method. Matched asymptotic expansions. Multiple scales.

**MATH 533, 534, Topics in Partial Differential Equations**

3 credits

3 class hours each semester

*Prerequisite: MATH 438 or equivalent*

Study of a special topic in partial differential equations not usually treated. Normally one related to a field of research interest at Tech. May be taken multiple times for credit.

**MATH 535, 536, Methods of Mathematical Physics**

3 credits

3 class hours each semester

*Prerequisite: MATH 436*

Advanced topics selected from asymptotic expansions of integrals and ordinary differential equations, integral equations, singular integral equations, Wiener‐Hopf technique, generalized functions.

**MATH 537, 537D, Bifurcation Theory**

3 credits, 3 class hours

*Prerequisite: MATH 437 or equivalent*

Discrete and continuous models. Nonlinear buckling, expansion of the bifurcated solution, stability analysis, Hopf bifurcation, degree theory, the Rabinowi theorem, and other topics.

**MATH 538, 538D, Wave Phenomena**

3 credits

3 class hours

*Prerequisite: MATH 438 or equivalent or consent of instructor*

Hyperbolic and dispersive waves. Characteristic methods, breaking and shock fitting, and weak solutions. Examples drawn from water waves, traffic flow problems, supersonic flight, and other areas.

**MATH 539, 539D, Fluid Dynamics**

3 credits

3 class hours

*Prerequisite: MATH 438 or equivalent*

The Navier‐Stokes equations, inviscid flow, irrotational fluids, viscosity, and turbulence. Other topics as time and interest permit.

**MATH 542, Topics in Differential Geometry**

3 credits

3 class hours

*Prerequisite: MATH 442 or consent of instructor*

Study of advanced topics in differential geometry such as: Brouwer degree, fundamental group, homology groups, De Rham cohomology, Be i numbers, fibre bundles, Morse theory, Lie groups, covering spaces, homotopy groups. May be taken multiple times for credit.

**MATH 561, 562, Topology**

3 credits

3 class hours each semester

*Prerequisites: MATH 471, 472; or MATH 461*

Point‐set topology, abstract topological spaces, generalized convergence, product and quotient spaces, metric spaces, uniform spaces; elementary concepts of algebraic topology.

**MATH 575, 576, Functions of a Real Variable**

3 credits

3 class hours each semester

*Prerequisites: MATH 471, 472; MATH 461 or MATH 561 recommended*

Topological concepts, category, measure theory, Lebesgue measure and integration, derivatives and the Radon‐ Nikodym theorem, product spaces and measures, function spaces, normed linear spaces.

**MATH 577 Functional Analysis**

3 credits

3 class hours

*Prerequisite: MATH 471 or equivalent*

Normed vector spaces, Banach spaces, Banach fixed point theorem. Lebesgue integral, Lebesgue measure. Hilbert spaces and orthonormal systems, strong and weak convergence. Linear operators on Hilbert spaces, self‐adjoint operators, compact operators, spectral theory, Fourier transform. Applications to integral and differential equations, Fredholm theory. Distributions and partial differential equations, fundamental solutions, resolvent, Green’s functions, weak solutions.

**MATH 581, Directed Study**

Credit hours to be arranged

An advanced course offered on demand under the guidance of a senior staff member.

**MATH 582, Linear Statistical Models with Applications**

3 credits

3 class hours

*Prerequisite: MATH 483 or consent of instructor*

An in‐depth study of regression and analysis of variance models. Topics include multiple regressions and model building, analysis of residuals, analysis of variance as regression analysis, generalized linear models, generalized linear mixed models, nonlinear models, multi‐factor models with equal and unequal sample sizes, random and fixed effects models, randomized complete block designs, and analysis of covariance. The statistical packages SAS and Minitab will be used for data analysis.

**MATH 583, 584, Topics in Probability and Statistics**

3 credits

3 class hours each semester

*Prerequisites: MATH 384 or 483; MATH 486 or consent of instructor*

Advanced topics selected from linear regression analysis, the design of experiments, decision theory. Bayes and empirical Bayes procedures. Markov chains, Markov and semi‐Markov processes, renewal theory. May be taken multiple times for credit.

**MATH 585, Statistics for Technology Managers**

3 credits

3 class hours

*Prerequisite: Enrollment in the Engineering Management program*

Probability and random variables; simple and multiple linear regression using least squares and other methods; experimental design; other topics including nonlinear regression; applications to decision making.

**MATH 586, 586D, Spatial Variability and Geostatistics**

3 credits

3 class hours

*Prerequisite: MATH 382*

Introduction to spatial and temporal variability. Stationary and intrinsic random fields, variograms and estimation. Kriging, co‐kriging, and simulation of random fields. Conditioning and conditional simulation. Indicator kriging and simulation. Applications from hydrology, mining, petroleum engineering, and other fields of science and engineering.

**MATH 587, 587D, Analysis of Time Series and Spatial Data**

3 credits

3 class hours

Offered in alternate years

An introductory overview of methods for analyzing temporal and spatial series with an emphasis on scientific applications. Linear systems in continuous and discrete time, Fourier analysis, spectral estimation, convolution and deconvolution, filtering, the z and Laplace transforms, stationary and nonstationary time series, ARIMA modeling, forecasting, and generalizations to multidimensional and multichannel applications. (Same as GEOP 505)

**MATH 588, Advanced Data Analysis**

3 credits

3 class hours

*Prerequisite: MATH 483 or consent of instructor*

Topics include linear regression, inferential tools for regression, model checking and refinement, experimental design, repeated measures and other multivariate responses, comparisons of proportions or odds, logistic regressions and power analysis. Principal components and factor analysis are also introduced.

**MATH 589, Applied Multivariate Analysis**

3 credits

3 class hours

*Prerequisite: MATH 382; MATH 283 or 384 recommended*

Multivariate normal distribution and tests assessing multivariate normality. Estimation and hypotheses testing regarding the parameters of multivariate normal populations. Principal component analysis, factor analysis, canonical correlations analysis, classification and discriminant analysis, cluster analysis, multivariate linear models, and multivariate analysis of variance and covariance. Applications in science and engineering.

**MATH 590, Independent Study**

Credit hours to be arranged

Under the direction of a faculty member appointed by the department, the student shall prepare a paper making use of standard reference sources on some topic not covered by other course work.

**MATH 591, Thesis (master’s program)**

Credit hours to be arranged

**MATH 595 Dissertation (doctoral degree program)**

Credit hours to be arranged

*Prerequisite: Successful completion of PhD candidacy exam and Academic Advisor recommendation
for candidacy.*