2021-2022 Catalog [ARCHIVED CATALOG]
Courses
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Marketing |
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MKTG 9400 - Independent Study in Marketing - Undergraduate 1 Credits (Minimum) 3 Credits (Maximum)
With the consent of the instructor who directs the study and the dean. Prer., Junior standing.
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MKTG 9500 - Independent Study in Marketing - Graduate 1 Credits (Minimum) 3 Credits (Maximum)
Independent study in Marketing at the graduate level given with the consent of the instructor who directsthe study and the dean. Prer., Consent of instructor and dean.
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Mathematics |
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MATH 90 - Algebra I: Fundamentals of Algebra 4 Credits (Minimum) 4 Credits (Maximum)
Graph and solve first-degree equations and inequalities; convert word problems into first-degree problems; add, multiply, and divide polynomials; use scientific notation; factor and solve word problems involving quadratic expressions; use algebra and coordinate geometry to solve problems involving one or more lines; manipulate algebraic fractions. Administered through the Department of Mathematics. Does not count toward BA or BS degree. Prer., Placement exam.
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MATH 99 - Algebra II: Intermediate Algebra 4 Credits (Minimum) 4 Credits (Maximum)
Equations and inequalities; graphs and functions; systems of equations and inequalities; polynomials and polynomial functions; rational expressions and equations; roots, radicals, and complex numbers; quadratic functions. Administered through the Department of Mathematics. Does not count toward BA or BS degree. Prer., MATH 90 with a grade of “C” or better, or test into MATH 99.
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MATH 1040 - College Algebra 4 Credits (Minimum) 4 Credits (Maximum)
An intensive study of algebraic functions, equations, and inequalities required for calculus. Emphasis on underlying algebraic structure and development of algebraic skills. The study includes: polynomial, rational, radical, absolute value, exponential, and logarithmic functions. Approved for Compass Curriculum and LAS requirement: Quantitative Reasoning. Prer., Math 99 with a grade of ΓÇ¥CΓÇ¥ or better, or pass the Math Placement Test for MATH 1040. GT-MA1.
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MATH 1050 - Elementary Functions of Calculus 4 Credits (Minimum) 4 Credits (Maximum)
An intensive study of the elementary functions required for calculus. These functions will include polynomial, rational, exponential, logarithmic, and trigonometric functions. Emphasis is on their algebraic structure and graphs. Analysis of conic sections and analytic geometry will be included. GT-MA1. Prer., MATH 1040 with a grade of “C” or better, or test into MATH 1050. **See Mathematics Department prerequisite policy. ***
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MATH 1060 - Trigonometry 3 Credits (Minimum) 3 Credits (Maximum)
An intensive study of trigonometric functions required for calculus. Discussion of angles, right triangle trigonometry, the unit circle, graphs of trigonometric functions, trigonometric identities, and solving trigonometric equations. Prer., MATH 1040 with a grade of “C” or better or pass the Math Placement Test for MATH 1060.
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MATH 1110 - Topics in Linear Algebra 3 Credits (Minimum) 3 Credits (Maximum)
For business and economics students. Systems of linear equations, matrix algebra, linear programming, probability, statistics. Prer., MATH 1040 or score 17 or more on algebra diagnostic exam. **see Mathematics Department prerequisite policy**
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MATH 1120 - Calculus for Business and Economics 3 Credits (Minimum) 3 Credits (Maximum)
Calculus for business and economics students. Prer., MATH 1040 with a grade of “C” or better, or test into MATH 1120. **See Mathematics Department prerequisite policy**
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MATH 1200 - Reasoning About Data 3 Credits (Minimum) 3 Credits (Maximum)
Helps students develop quantitative and qualitative reasoning skills by applying inductive and deductive reasoning, mathematics, and statistics to real world data.
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MATH 1310 - Calculus I with Refresher Precalculus Part A. 3 Credits (Minimum) 3 Credits (Maximum)
See MATH 1350 for calculus topics covered. Algebraic and elementary function topics are covered throughout, as needed. MATH 1310 and 1320 together are equivalent to MATH 1350. The sequence MATH 1310 - 1320 is designed for students whose manipulative skills in the techniques of high school algebra and precalculus may be inadequate for MATH 1350. Credit not granted for both this course and MATH 1350. This course is one of the means to satisfy the the LAS and Compass Curriculum Qualitative and Quantitative Reasoning requirements. Prer., MATH 1050 or MATH 1060 with a grade of “C” or better, or pass the Math Placement TEST for MATH 1350.
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MATH 1320 - Calculus I with Refresher Precalculus Part B 3 Credits (Minimum) 3 Credits (Maximum)
Continuation of MATH 1310. See MATH 1350 for calculus topics covered. Algebraic and trigonometric topics are studied throughout, as needed. Credit not granted for both this course and MATH 1350. Prer., MATH 1310 with a grade of “C” or better.
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MATH 1330 - Calculus for Life Sciences 4 Credits (Minimum) 4 Credits (Maximum)
A systematic introduction to calculus concepts useful in the life sciences, such as rates of change, limits, differentiation and integration, with emphasis on applications in the life sciences and the areas connected to modeling biological processes, such as differential equations and dynamical systems. Students may not take MATH 1330 and MATH 1350 and receive credit for both. Approved for Compass Curriculum requirement: Explore: Physical and Natural World. Prer., MATH 1050 or MATH 1060 with a grade of “C” or better, or pass the Math Placement Test for MATH 1330.
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MATH 1350 - Calculus I 4 Credits (Minimum) 4 Credits (Maximum)
Selected topics in analytical geometry and calculus. Rates of change of functions, limits, derivatives of algebraic and transcendental functions, applications of derivatives, and integration. Approved for Compass Curriculum requirement: Explore: Physical and Natural World. Prer., MATH 1050 or MATH 1060 with a grade of “C” or better, or pass the Math Placement TEST for MATH 1350.
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MATH 1360 - Calculus II 4 Credits (Minimum) 4 Credits (Maximum)
Continuation of MATH 1350. Transcendental functions, techniques and applications of integration, Taylor’s theorem, improper integrals, infinite series, analytic geometry, polar coordinates. Prer., MATH 1320 or MATH 1350 with a grade of “C” or better.
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MATH 2020 - Problem Solving Seminar 3 Credits (Minimum) 3 Credits (Maximum)
This course is intended for students who enjoy solving mathematical problems. It aims to invite students to appreciate the joy of analytical thinking, ingenuity, and problem solving in general. Problems and topics chosen make the course accessible to freshmen. Prer., MATH 1350 or instructor consent.
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MATH 2150 - Discrete Mathematics 3 Credits (Minimum) 3 Credits (Maximum)
Introduction to mathematical proofs. Topics include logic, set theory, number theory, induction, and recursion. Prer., MATH 1320 or MATH 1350 with a grade of “C” or better.
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MATH 2350 - Calculus III 4 Credits (Minimum) 4 Credits (Maximum)
Continuation of MATH 1360. Parametric curves, vector functions, partial differentiation, multiple integrals, Green’s Theorem and Stoke’s Theorem. Prer., MATH 1360 with a grade of “C” or better.
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MATH 2650 - Introduction to Computational Mathematics 1 Credits (Minimum) 1 Credits (Maximum)
An introduction to the use of computers in mathematics using the Matlab computer algebra system. Representation of equations and functions using arrays. Visualization of data and functions. Matlab programs, including general program organization, subprograms, files, and built-in mathematical functions. Prer., MATH 2350.
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MATH 2810 - Introduction to Basic Statistics 3 Credits (Minimum) 3 Credits (Maximum)
Study of the elementary statistical measures. Introduction to probability, statistical distributions, statistical inference and hypothesis testing. Prer., MATH 1040 or equivalent.
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MATH 3010 - Mathematics for Elementary Teachers I 3 Credits (Minimum) 3 Credits (Maximum)
Covers the whole number, integer, and rational number systems that are of prime importance to the elementary teacher. For students planning on elementary teacher certification. Approved for Compass Curriculum requirement: Explore-Physical and Natural World. This course, when taken with MATH 3020, is one of the means to satisfy the LAS and Compass Curriculum Quantitative and Qualitative Reasoning requirement.
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MATH 3020 - Mathematics for Elementary Teachers II 3 Credits (Minimum) 3 Credits (Maximum)
Intuitive and logical development of the fundamental ideas of geometry such as parallelism, congruence, and measurement. Includes study of plane analytical geometry. For students planning on elementary teacher certification. Approved for Compass Curriculum requirement: Explore-Physical and Natural World. This course, when taken with MATH 3010, is one of the means to satisfy the LAS and Compass Curriculum Quantitative and Qualitative Reasoning requirement.
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MATH 3100 - Statistics for the Sciences 3 Credits (Minimum) 3 Credits (Maximum)
Descriptive probability, hypothesis testing, nonparametric methods. Discrete and continuous random variables, mean and variance, confidence limits, correlation and regression. Satisfies the LAS and Compass Curriculum Quantitative and Qualitative Reasoning requirement as a statistics course when taken by a student who has either 1) successfully completed MATH 1040 (or a mathematics course that has college algebra as a prerequisite), OR 2) scored 87% or higher on the College Algebra placement test and scored 50% or higher on the Business Calculus placement test. Prer., MATH 1350.
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MATH 3110 - Theory of Numbers 3 Credits (Minimum) 3 Credits (Maximum)
A careful study, with emphasis on proofs, of the following topics associated with the set of integers: divisibility, congruences and modular arithmetic, arithmetic functions, sums of squares, and elementary results on distributions of primes. The history of various developments in the subject, along with biographies of important contributors, will be included. Prer., MATH 1360 and MATH 2150.
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MATH 3130 - Introduction to Linear Algebra 3 Credits (Minimum) 3 Credits (Maximum)
Systems of linear equations, matrices, vector spaces, linear independence, basis, dimension, determinants, linear transformations and matrices, eigenvalues and eigenvectors. Prer., MATH 2350 with a grade of “C” or better.
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MATH 3210 - Introduction to Geometry 3 Credits (Minimum) 3 Credits (Maximum)
An introduction to the major theorems of Euclidean and non-Euclidean geometries. The role of axiom systems and the history of alternative geometries will be discussed. Students will learn to write, teach, and evaluate rigorous proofs in geometry. Prer., MATH 2350, MATH 2150.
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MATH 3400 - Introduction to Differential Equations 3 Credits (Minimum) 3 Credits (Maximum)
First order differential equations, linear differential equations. Additional methods selected from the Laplace transform method, power series solutions, numerical solutions, linear systems. Prer., MATH 2350.
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MATH 3410 - Introduction to Analysis 3 Credits (Minimum) 3 Credits (Maximum)
An introduction to proofs in analysis. Topics include completeness of the real numbers, sequences and limits, infinite series, and continuous functions. Prer., MATH 2150 and MATH 2350.
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MATH 3480 - Functions and Modeling 3 Credits (Minimum) 3 Credits (Maximum)
Data collection and exploration of a variety of situations that can be modeled using linear, exponential, polynomial, and trigonometric functions. Use of technology in teaching, connections between various areas of mathematics, non-routine problem solving, problem-based learning, and applications for mathematics. Meets with UTLS 2040. Prer., MATH 2350.
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MATH 3500 - Graph Theory 3 Credits (Minimum) 3 Credits (Maximum)
Standard material on the theory of both directed and undirected graphs, including the concepts of isomorphism, connectivity, trees, traversability, planar graphs, coloring problems, relations and matrices. Prer., MATH 2150.
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MATH 3510 - Topics in Combinatorial Analysis 3 Credits (Minimum) 3 Credits (Maximum)
A survey of important areas of combinatorics. Topics may include enumeration techniques, recurrence relations, combinatorial designs, graph theory, machining and optimization. Prer., MATH 2150.
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MATH 3650 - Advanced Computational Math 2 Credits (Minimum) 2 Credits (Maximum)
Advanced computational techniques with applications in mathematics, science and engineering. Topics include numerical linear algebra, dynamical systems and stability, calculus in the complex plane and elements of Fourier analysis, the DFT and FFT method, Monte Carlo Simulations, other applications in science and engineering. Prer., MATH 2650, MATH 3130, MATH 3400.
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MATH 3670 - Introduction to Scientific Computation 3 Credits (Minimum) 3 Credits (Maximum)
This is the 3-credit-hour alternative to MATH 2650 (1 credit) and MATH 3650 (2 credits). Introduction to computational math (see course description for MATH 2650) and advanced computational techniques (see course description for MATH 3650). Prer., MATH 3130, MATH 3400.
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MATH 3810 - Introduction to Probability and Statistics 3 Credits (Minimum) 3 Credits (Maximum)
The axioms of probability and conditional probability will be studied as well as the development, applications and simulation of discrete and continuous probability distributions. Also, expectation, variance, correlation, sum and joint distributions of random variables will be studied. The Law of Large Numbers and the Central Limit Theorem will be developed. Applications to statistics will include regression, confidence intervals, and hypothesis testing. Satisfies the LAS and Compass Curriculum Quantitative and Qualitative Reasoning requirement as a statistics course when taken by a student who has either 1) successfully completed MATH 1040 (or a mathematics course that has college algebra as a prerequisite), OR 2) scored 87% or higher on the College Algebra placement test and scored 50% or higher on the Business Calculus placement test. Prer., MATH 2350.
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MATH 4040 - Senior Math Seminar 1 Credits (Minimum) 1 Credits (Maximum)
This is a capstone experience for the students in the mathematics program. Students will give oral presentations on mathematical topics, and will actively participate in peer presentations. Approved for LAS Oral Communication area requirement. Approved for Compass Curriculum requirement: Summit. Prer., Senior standing.
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MATH 4050 - Topics in Mathematics Secondary Classroom 1 Credits (Minimum) 3 Credits (Maximum)
The topics covered will vary from one offering to the next. Topics will be chosen to meet the needs of secondary mathematics teachers for additional training to teach to the Colorado Model Content Standards. Prer., One semester of calculus, or instructor approval. Meets with MATH 5050.
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MATH 4100 - Technology in Mathematics Teaching and Curriculum 3 Credits (Minimum) 3 Credits (Maximum)
Methodology for using technology as a teaching/learning tool for high school and college math courses. Use of graphing calculators, computer algebra systems, computer geometry systems and the internet will be emphasized. Students are required to develop and present a portfolio of in-depth projects. Prer., MATH 1360. Meets with MATH 5100.
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MATH 4130 - Linear Algebra I 3 Credits (Minimum) 3 Credits (Maximum)
Proof-based treatment of vector spaces, linear transformations and matrices, determinants, eigenvalues, similarity transformations, orthogonal and unitary transformations, normal matrices and quadratic forms. Prer., MATH 3130 and one of MATH 2150, 3110, 3410, 4140, or 4310. Meets with MATH 5130.
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MATH 4140 - Modern Algebra I 3 Credits (Minimum) 3 Credits (Maximum)
A careful study of the elementary theory of groups, rings, and fields. Mappings such as homomorphisms and isomorphisms are considered. The student will be expected to prove theorems. Prer., MATH 2150 and MATH 3130. One of MATH 3110, MATH 3500, or MATH 3510 (preferably MATH 3110) is strongly recommended.
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MATH 4150 - Modern Algebra II 3 Credits (Minimum) 3 Credits (Maximum)
Continuation of MATH 4140. The relationship between groups and fields is explored via a thorough investigation of Galois theory. Prer., MATH 4140. Meets with MATH 5150.
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MATH 4210 - Differential Geometry 3 Credits (Minimum) 3 Credits (Maximum)
Presents topics in geometry suitable for advanced undergraduates, such as differential geometry of curves and surfaces, geometry of manifolds, or more in-depth exploration of non-Euclidean geometries. Prer., MATH 3130, MATH 3410. Meets with MATH 5210.
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MATH 4230 - Fractal Geometry 3 Credits (Minimum) 3 Credits (Maximum)
Introduction to iterated function systems and mathematical aspects of fractal sets. Includes metric spaces and the space fractals live in, transformations, contraction mapping and Collage Theorem, chaotic dynamics, shadowing theorem, fractal dimension, fractal interpolation, and measures on fractals. Prer., MATH 2350 and MATH 3130. Meets with MATH 5230.
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MATH 4250 - Introduction to Chaotic Dynamical Systems 3 Credits (Minimum) 3 Credits (Maximum)
Introduction to dynamical systems or processes in motion, that are defined in discrete time by iteration of simple functions, or in continuous time by differential equations. Emphasis on understanding chaotic behavior that occurs when a simple non-linear function is iterated. Topics include orbits, graphical analysis, fixed and periodic points, bifurcations, symbolic dynamics, chaos, fractals, and Julia sets. Prer., MATH 2350. Meets with MATH 5250.
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MATH 4310 - Modern Analysis I 3 Credits (Minimum) 3 Credits (Maximum)
Rigorous treatment of calculus. Topics include differentiation, integration, Taylor’s Theorem, uniform convergence of sequences of functions, and power series. Prer., MATH 3410.
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MATH 4320 - Modern Analysis II 3 Credits (Minimum) 3 Credits (Maximum)
Careful theoretical study of topology of Euclidean space, metric spaces, sequences and series of functions, calculus of several variables. Prer., MATH 4310. Meets with MATH 5320.
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MATH 4420 - Optimization 3 Credits (Minimum) 3 Credits (Maximum)
Topics selected from linear and nonlinear programming, the simplex algorithm and other approaches to linear optimization, minimax theorems, convex functions, introduction to calculus of variations. Prer., MATH 3130 and MATH 3400. Meets with MATH 5420.
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MATH 4430 - Ordinary Differential Equations 3 Credits (Minimum) 3 Credits (Maximum)
Existence and uniqueness theorem, linear equations, linear systems with periodic coefficients (Floquet theory), stability analysis of planar systems, series solutions at regular singular points, Sturm-Liouville problems. Prer., MATH 3130 and MATH 3400. Meets with MATH 5430.
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MATH 4450 - Complex Variables 3 Credits (Minimum) 3 Credits (Maximum)
Theory of functions of one complex variable including integrals, power series, residues, conformal mapping and special functions. Prer., MATH 2350. Meets with MATH 5450.
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MATH 4470 - Methods of Applied Mathematics 3 Credits (Minimum) 3 Credits (Maximum)
Boundary value problems for the wave, heat, and Laplace equations, separation of variables methods, eigenvalue problems, Fourier series, orthogonal systems. Prer., MATH 2350, MATH 3130 and MATH 3400. Meets with MATH 5470.
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MATH 4480 - Mathematical Modeling 3 Credits (Minimum) 3 Credits (Maximum)
The use of diverse mathematical techniques to analyze and solve problems from science and engineering, particular problems likely to arise in nonacademic settings such as industry or government. Converting a problem to a mathematical model. Commonly encountered classes of mathematical models, including optimization problems, dynamical systems, probability models and computer simulations. Communication of results of mathematical analysis. Prer., MATH 2650 or adequate experience with computer programming, MATH 3130, MATH 3400; and MATH 3100 or MATH 3810 or ECE 3610. Meets with MATH 5480.
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MATH 4510 - Topology 3 Credits (Minimum) 3 Credits (Maximum)
An introduction to Point-set topology and elements of geometric or algebraic topology. Prer., MATH 4310. Meets with MATH 5510.
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MATH 4650 - Numerical Analysis 3 Credits (Minimum) 3 Credits (Maximum)
Error analysis, root finding, numerical integration and differentiation, numerical methods for ordinary differential equations, numerical linear algebra and eigenvalue problems. Prer., MATH 3130, MATH 3400, and CS 1120 or CS 1150 or MATH 3670. Meets with MATH 5650.
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MATH 4670 - Scientific Computation I 3 Credits (Minimum) 3 Credits (Maximum)
Numerical solutions of initial-value problems, two-point boundary-value problems for ordinary differential equations, and applications. Numerical methods for solving linear partial differential equations, including finite difference and finite element method. Laplace, heat, and wave equation. Prer., MATH 3670 or MATH 4650/5650, and MATH 4470/5470. Meets with MATH 5670.
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MATH 4810 - Mathematical Statistics I 3 Credits (Minimum) 3 Credits (Maximum)
Exponential, Beta, Gamma, Student, Fisher and Chi-square distributions are covered in this course, along with joint and conditional distributions, moment generating techniques, transformations of random variables and vectors. Prer., MATH 2350 and MATH 3130. Meets with MATH 5810.
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MATH 4820 - Mathematical Statistics II 3 Credits (Minimum) 3 Credits (Maximum)
Point and confidence interval estimation, principles of maximum likelihood, sufficiency and completeness; tests of simple and composite hypotheses. Linear models and multiple regression analysis. Other topics will be included. Prer., MATH 3810 or MATH 3100. Meets with MATH 5820.
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MATH 4830 - Linear Statistical Models 3 Credits (Minimum) 3 Credits (Maximum)
Methods and results of linear algebra are developed to formulate and study a fundamental and widely applied area of statistics. Topics include generalized inverses, multivariate normal distribution and the general linear model. Applications focus on model building, design models and computing methods. The “Statistical Analysis System” (software) is introduced as a tool for doing computation. Prer., MATH 3810 or ECE 3610, or MATH 3100 and MATH 3130. Meets with MATH 5830.
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MATH 4850 - Stochastic Modeling 3 Credits (Minimum) 3 Credits (Maximum)
Mathematical development of continuous and discrete time Markov chains, queuing theory, reliability theory, and Brownian motion with applications to engineering and computer science. Prer., MATH 2650 or adequate experience with computer programming, and MATH 3810 or ECE 3610. Meets with MATH 5850.
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MATH 4900 - Advanced Topics Seminar 1 Credits (Minimum) 3 Credits (Maximum)
Various advanced topics in mathematics. Prer., Vary depending on course content. Consent of instructor required. Meets with MATH 5900.
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MATH 5050 - Topics in Mathematics for the Secondary Classroom 0.5 Credits (Minimum) 3 Credits (Maximum)
The topics covered will vary from one offering to the next. Topics will be chosen to meet the needs of secondary mathematics teachers for additional training to teach to the Colorado Model Content Standards. Prer., One semester of calculus, or instructor approval. Meets with MATH 4050.
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MATH 5100 - Technology in Mathematics Teaching and Curriculum 3 Credits (Minimum) 3 Credits (Maximum)
Methodology for using technology as a teaching/learning tool for high school and college math courses. Use of graphing calculators, computer algebra systems, computer geometry systems and the internet will be emphasized. Students are required to develop and present a portfolio of in-depth projects. Prer., MATH 1360. Meets with MATH 4100.
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MATH 5110 - Technology in Math Education Seminar 1 Credits (Minimum) 3 Credits (Maximum)
A follow-up to MATH 4100/5100. Students will present demonstrations, projects and/or laboratories they have developed for use in their math courses. Extended in-depth coverage of computer algebra or geometry systems and/or graphing calculators and internet. Basic familiarity with computer algebra or geometry systems and/or graphing calculators is required. Prer., MATH 5100 or consent of instructor.
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MATH 5130 - Linear Algebra I 3 Credits (Minimum) 3 Credits (Maximum)
Proof-based treatment of vector spaces, linear transformations and matrices, determinants, eigenvalues, similarity transformations, orthogonal and unitary transformations, normal matrices and quadratic forms. Prer., MATH 3130 and one of MATH 2150, 3110, 3410, 4140, or 4310. Meets with MATH 4130.
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MATH 5150 - Modern Algebra II 3 Credits (Minimum) 3 Credits (Maximum)
Continuation of MATH 4140. The relationship between groups and fields is explored via a thorough investigation of Galois theory. Prer., MATH 4140. Meets with MATH 4150.
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MATH 5170 - Rings and Modules I 3 Credits (Minimum) 3 Credits (Maximum)
Fundamentals of ring and module theory, including simple and semisimple rings and modules, projective and injective modules, chain conditions on ideals, Jacobson radical, von Neumann regular rings, group rings. Meets with MATH 6170. Prer., MATH 4140.
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MATH 5210 - Differential Geometry 3 Credits (Minimum) 3 Credits (Maximum)
Presents topics in geometry suitable for advanced undergraduates, such as differential geometry of curves and surfaces, geometry of manifolds, or more in-depth exploration of non-Euclidean geometries. Prer., MATH 3130, MATH 3410. Meets with MATH 4210.
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MATH 5230 - Fractal Geometry 3 Credits (Minimum) 3 Credits (Maximum)
Introduction to iterated function systems and mathematical aspects of fractal sets. Includes metric spaces and the space fractals live in, transformations, contraction mapping and collage theorem, chaotic dynamics, shadowing theorem, fractal dimension, fractal interpolation, and measures on fractals. Prer., MATH 2350 and MATH 3130. Meets with MATH 4230.
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MATH 5250 - Introduction to Chaotic Dynamical Systems 3 Credits (Minimum) 3 Credits (Maximum)
Introduction to dynamical systems or processes in motion, defined in discrete time by iteration of simple functions, or in continuous time by differential equations. Emphasis on chaotic behavior of an iterated simple nonlinear function. Orbits, graphical analysis, fixed and periodic points, bifurcations, symbolic dynamics, chaos, fractals, and Julia sets. Prer., MATH 2350. Meets with MATH 4250.
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MATH 5270 - Algebraic Coding Theory 3 Credits (Minimum) 3 Credits (Maximum)
The basic ideas, examples, and applications of the theory of error-correcting codes are presented, including linear codes and cyclic codes. These codes are important for the digital transmission of data. Finite fields, polynomial rings, and ideals play central roles. Prer., MATH 4140.
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MATH 5320 - Modern Analysis II 3 Credits (Minimum) 3 Credits (Maximum)
Careful theoretical study of topology of Euclidean space, metric spaces, sequences and series of functions, calculus of several variables. Prer., MATH 4310. Meets with MATH 4320.
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MATH 5330 - Real Analysis I 3 Credits (Minimum) 3 Credits (Maximum)
Lebesgue measure, measurable and nonmeasurable sets, sigma algebras. Lebesgue integral, comparison with Riemann integration, Monotone and Dominated Convergence Theorems, Fatou’s Lemma. Differentiation, functions of bounded variation, absolute continuity integration in product spaces, Fubini’s Theorem. Prer., MATH 4320/5320. Meets with MATH 6330. Graduate students only.
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MATH 5350 - Applied Functional Analysis 3 Credits (Minimum) 3 Credits (Maximum)
Basic concepts, methods, and applications of functional analysis. Complete metric spaces, contraction mapping, and applications. Banach spaces and linear operators. Inner product and Hilbert spaces, orthonormal bases and expansions, approximation, and applications. Spectral theory of compact operators, including self adjoint and normal operators. Prer., MATH 4320 or MATH 5320. Meets with MATH 6350. Graduate students only.
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MATH 5420 - Optimization 3 Credits (Minimum) 3 Credits (Maximum)
Topics selected from linear and nonlinear programming, the simplex algorithm and other approaches to linear optimization, minimax theorems, convex functions, introduction to calculus of variations. Meets with MATH 4420.
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MATH 5430 - Ordinary Differential Equations 3 Credits (Minimum) 3 Credits (Maximum)
Existence and uniqueness theorem, linear systems, linear systems with periodic coefficients (Floquet theory), stability analysis of planar systems, series solutions at regular singular points, Sturm-Liouville problems. Prer., MATH 3130, MATH 3400. Meets with MATH 4430.
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MATH 5440 - Approximation Methods in Applied Mathematics 3 Credits (Minimum) 3 Credits (Maximum)
Approximate solutions of differential equations by asymptotic expansions, asymptotic expansion of integrals, regular and singular perturbation methods, boundary layer analysis, WKB methods, and multiple-scale techniques. Prer., MATH 5430/6430 and MATH 5610/6610. Graduate students only. Meets with MATH 6440.
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MATH 5450 - Complex Variables 3 Credits (Minimum) 3 Credits (Maximum)
Theory of functions of one complex variable, including integrals, powering series, residues, conformal mapping and special functions. Prer., MATH 2350. Meets with MATH 4450.
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MATH 5470 - Methods of Applied Mathematics 3 Credits (Minimum) 3 Credits (Maximum)
Boundary value problems for the wave, heat, and Laplace equations, separation of variables methods, eigenvalue problems, Fourier series, orthogonal systems. Prer., MATH 2350, MATH 3130 and MATH 3400. Meets with MATH 4470.
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MATH 5480 - Mathematical Modeling 3 Credits (Minimum) 3 Credits (Maximum)
The use of diverse mathematical techniques to analyze and solve problems from science and engineering, particularly problems likely to arise in a nonacademic setting such as industry or government. Converting a problem to a mathematical model. Commonly encountered classes of mathematical models, including optimization problems, dynamical systems, probability models, and computer simulations. Communication of results of mathematical analysis. Prer., MATH 3130, MATH 3400, and MATH 3100 or MATH 3810 or ECE 3610. MATH 2650 or adequate experience in computer programming. Meets with MATH 4480.
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MATH 5510 - Topology 3 Credits (Minimum) 3 Credits (Maximum)
Point-set topology and elements of geometric or algebraic topology. Prer., MATH 4310. Meets with MATH 4510.
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MATH 5520 - Perturbation Theory in Astrodynamics 3 Credits (Minimum) 3 Credits (Maximum)
Perturbation methods including Lagrange and Hamiltonian mechanics and the generalized method of averaging. Gravitational and atmosphere modeling. Prer., MAE 4410/5410 or PHYS 5510.
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MATH 5610 - Complex Analysis I 3 Credits (Minimum) 3 Credits (Maximum)
Complex numbers, Cauchy-Reimann equations, harmonic functions. Elementary functions and conformal mapping. Contour integrals, Cauchy integral representation. Uniform convergence and power series. Residues. Prer., MATH 4310/5310. Graduate students only. Meets with MATH 6610.
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MATH 5620 - Complex Analysis II 3 Credits (Minimum) 3 Credits (Maximum)
Argument principle, Rouche’s Theorem. Homotopy and countour integrals. Compact sets of functions and uniform convergence. Conformal mappings and the Riemann Mapping Theorem. Infinite products, analytic continuation, special topics. Prer., MATH 5610/6610. Graduate students only. Meets with MATH 6620.
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MATH 5650 - Numerical Analysis 3 Credits (Minimum) 3 Credits (Maximum)
Error analysis, root finding, numerical integration and differentiation, numerical methods for ordinary differential equations, numerical linear algebra and eigenvalue problems. Prer., CS 1150, MATH 3130, MATH 3400. Meets with MATH 4650.
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MATH 5670 - Scientific Computation I 3 Credits (Minimum) 3 Credits (Maximum)
Numerical solutions of initial-value problems, two-point boundary-value problems for ordinary differential equations, and applications. Numerical methods for solving linear partial differential equations, including finite difference and finite element method. Laplace, heat, and wave equation. Prer., MATH 3670 or MATH 4650/5650, and MATH 4470/5470. Meets with MATH 4670.
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MATH 5680 - Scientific Computation II 3 Credits (Minimum) 3 Credits (Maximum)
Advanced numerical methods for solving linear and nonlinear partial differential equations, including spectral and pseudo-spectral methods. Iterative methods for solving large linear systems. Prer., MATH 4670 or MATH 5670. Graduate students only. Meets with MATH 6680.
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MATH 5810 - Mathematical Statistics I 3 Credits (Minimum) 3 Credits (Maximum)
Exponential, Beta, Gamma, Student, Fisher and Chi-square distributions are covered in this course, along with joint and conditional distributions, moment generating techniques, transformations of random variables and vectors. Prer., MATH 2350 and MATH 3130. Meets with MATH 4810.
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MATH 5820 - Mathematical Statistics II 3 Credits (Minimum) 3 Credits (Maximum)
Point and confidence interval estimation, principles of maximum likelihood, sufficiency and completeness; tests of simple and composite hypotheses. Linear models, and multiple regression analysis. Other topics will be included. Prer., MATH 3100 or MATH 3810. Meets with MATH 4820.
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MATH 5830 - Linear Statistical Models 3 Credits (Minimum) 3 Credits (Maximum)
Methods and results of linear algebra are developed to formulate and study a fundamental and widely applied area of statistics. Topics include generalized inverses, multivariate normal distribution and the general linear model. Applications focus on model building, design models and computing methods. The “Statistical Analysis System” (software) is introduced as a tool for doing computations. Prer., MATH 3810 or ECE 3610, or MATH 3100 and MATH 3130. Meets with MATH 4830.
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MATH 5840 - Computer Vision 3 Credits (Minimum) 3 Credits (Maximum)
Representation and manipulation of digital images; Fourier analysis of images; enhancement techniques in spatial and frequency domain; segmentation procedures; digital geometry, region and boundary representation; texture processing; pattern recognition and application to robotics. Prer., Graduate standing in mathematics, engineering or computer science. Meets with C S 5840.
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MATH 5850 - Stochastic Modeling 3 Credits (Minimum) 3 Credits (Maximum)
Mathematical development of continuous and discrete time Markov chains, queuing theory, reliability theory and Brownian motion with applications to engineering and computer science. Prer., MATH 3810 or ECE 3610. MATH 2650 or adequate experience with computer programming. Meets with MATH 4850.
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MATH 5900 - Graduate Seminar 1 Credits (Minimum) 3 Credits (Maximum)
Various topics in mathematics at the graduate level. Prer., Consent of instructor. Meets with MATH 4900.
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MATH 5910 - Theory of Probability I 3 Credits (Minimum) 3 Credits (Maximum)
Measure theory is given form within a large body of probabilistic examples, ideas, and applications. Weak and strong laws of large numbers, central limit theory, and random walk in the context of independent random variables. Prer., MATH 4310. Graduate students only. Meets with MATH 6910.
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MATH 5920 - Theory of Probability II 3 Credits (Minimum) 3 Credits (Maximum)
Probability theory for sequences of dependent random variables, with the major focus on martingale theory and its applications. Prer., MATH 5910/6910. Graduate students only. Meets with MATH 6920.
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MATH 6170 - Rings and Modules I 3 Credits (Minimum) 3 Credits (Maximum)
Fundamentals of ring and module theory, including simple and semisimple rings and modules, projective and injective modules, chain conditions on ideals, Jacobson radical, von Neumann regular rings, group rings. Meets with MATH 5170. Prer., MATH 4140.
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MATH 6180 - Rings and Modules II 3 Credits (Minimum) 3 Credits (Maximum)
Further topics in ring and module theory, including division rings, perfect and semiperfect rings. Prer., MATH 5170 or MATH 6170.
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MATH 6210 - Mathematics Teachers’ Circle Academy 2 Credits (Minimum) 2 Credits (Maximum)
Designed to help secondary school mathematics teachers present and facilitate mathematical problem-solving activities with their students. Mathematical approaches to problem-oriented questions will be discussed, as well as teaching methodologies regarding optimal use of such classroom activities.
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MATH 6220 - Mathematics Teachers’ Circle Seminar 1 Credits (Minimum) 1 Credits (Maximum)
Designed to help secondary math teachers follow up on the educational and pedagogical benefits and issues of using a problem-solving approach to teaching mathematics in their classrooms. Prer., MATH 6210.
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MATH 6270 - Algebraic Coding Theory 3 Credits (Minimum) 3 Credits (Maximum)
The basic ideas, examples, and applications of the theory of error-correcting codes are presented, including linear codes and cyclic codes. These codes are important for the digital transmission of data. Finite fields, polynomial rings, and ideals play central roles. Meets with MATH 5270. Prer., MATH 4140.
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MATH 6310 - Mathematics and Economics for K-12 Teachers 0.5 Credits (Minimum) 3 Credits (Maximum)
Designed to provide K-12 teachers with various methods and concepts from mathematics and economics which can be incorporated into K-12 mathematics or economics curricula. Not an option for MATH majors or graduate students. Meets with ECON 6310.
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MATH 6330 - Real Analysis I 3 Credits (Minimum) 3 Credits (Maximum)
Lebesgue measure, measurable and nonmeasurable sets, sigma algebras. Lebesgue integral, comparison with Riemann integration, Monotone and Dominated Convergence Theorems, Fatou’s Lemma. Differentiation, functions of bounded variation, absolute continuity integration in product spaces, Fubini’s Theorem. Prer., MATH 4320/5320. Meets with MATH 5330. Graduate students only.
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MATH 6350 - Applied Functional Analysis 3 Credits (Minimum) 3 Credits (Maximum)
Basic concepts, methods, and applications of functional analysis. Complete metric spaces, contraction mapping, and applications. Banach spaces and linear operators. Inner product and Hilbert spaces, orthonormal bases and expansions, approximation, and applications. Spectral theory of compact operators, including self adjoint and normal operators. Prer., MATH 4320 or MATH 5320. Meets with MATH 5350. Graduate students only.
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