MATH 099. Intermediate Algebra. A review of basic algebra and arithmetic, including algebra of polynomials, factorization of simple polynomials, arithmetic operations on fractions and rational expressions, laws of exponents, linear equations and inequalities in one variable, quadratic equations using factoring. Administered through LAS Extended Studies. Does not count toward BA or BS degree.
MATH 1040- College Algebra. An in-depth study of algebraic equations and inequalities. Comprehension of the underlying algebraic structure will be stressed as well as appropriate algebraic skills. The study will include polynomials, rational, exponential, and logarithmic functions as well as systems of equations/inequalities. Prerequisite: Online Math Placement Test for College Algebra of 50% or higher.
MATH 1050 Elementary Functions for Calculus (Precalculus). An intensive study of the elementary funtions 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. Prerequisite: MATH 1040- College Algebra or Onine Math Placement Test for Precalculus of 70% or higher.
MATH 1110. Topics in Linear Algebra. For business and economics students. Systems of linear equations, matrix algebra, linear programming, probability, statistics. Prer., MATH 1040 or Math Placement Test for College Algebra of 50% or higher.
MATH 1120 Calculus for Business & Economics. Calculus for the business and economics students. Prer., MATH 1040 or Math Placement Tests for College Algrebra at 87% or higher AND 50% or higher on the Calculus for Business and Economics Test
MATH 1310. Calculus I with Precalculus, Part A. See MATH 1350 for calculus topics covered. Algebraic and elementary function topics are covered throughout, as needed. MATH 1301 and MATH 1320 together are equivalent to MATH 1305. 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 1305. Prer., 4 years high school math (algebra, geometry, trigonometry or their equivalents). Credit not granted for this course and MATH 1350.
MATH 1320. Calculus I with Precalculus, Part B. Continuation of MATH 1310. See MATH 1350 for calculus topics covered. Algebraic and trigonometric topics are studied throughout, as needed. Prer., MATH 1310. Credit not granted for this course and MATH 1350.
MATH 1330. Calculus for Life Sciences. 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. Req., MATH 1050 or score 20 or more on the Algebra Placement Exam and score 10 or more on the Calculus Readiness Exam.
MATH 1350. Calculus I. Selected topics in analytical geometry and calculus. Rates of change of functions, limits, derivatives of algebraic and transcendental functions, applications of derivatives, and integration. Prer., MATH 1050 or Online Math Placement Tests for College Algebra at 87% or higher AND 50% or higher on the Calculus Test.
MATH 1360. Calculus II. Continuation of MATH 1350. Transcendental functions, techniques and applications of integration, Taylor's theorem, improper integrals, infinite series, analytic geometry, polar coordinates. Prer., MATH 1350.
MATH 2150 Discrete Mathematics. Introduction to most of the important topics of discrete mathematics, including set theory, logic, number theory, recursion, combinatorics, and graph theory. Much emphasis will be focused on the ideas and methods of mathematical proofs, including induction and contradiction. Prer., MATH 1350.
MATH 2350. Calculus III. Continuation of MATH 1360. Parametric curves, vector functions, partial differentiation, multiple integrals, Green's Theorem and Stoke's Theorem. Prer., MATH 1360.
MATH 2650. Intro to Computational Math. one (1) credit hour. 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
MATH 3010. Mathematics for Elementary Teachers I. 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.
MATH 3020. Mathematics for Elementary Teachers II. 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.
MATH 3100. Statistics for the Sciences. Descriptive probability, hypothesis testing, non- parametric methods. Discrete and continuous random variables, mean and variance, confidence limits, correlation and regression. Prer., MATH 1350.
MATH 3110. Theory of Numbers. A careful study, with emphasis on proofs, of the following topics associated with the set of integer: divisibility, congruences, arithmetic functions, sums of squares, quadratic residues and reciprocity, and elementary results on distributions of primes. Prer., MATH 1360 and MATH 2150.
MATH 3130. Introduction to Linear Algebra. 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.
MATH 3400. Introduction to Differential Equations. First order differential equations, linear differential equations, the Laplace transform method, power series solutions, numerical solutions, linear systems. Prer., MATH 2350.
MATH 3410. Estimation, Convergence and Approximation. Sequences, numerical series, and power series. Integrals and the analysis of functions defined by integrals. This course provides a thorough introduction to proofs in analysis, and is strongly recommended for students planning to take MATH 4310. Prer., MATH 2350.
MATH 3500. Graph Theory. 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.
MATH 3510. Topics in Combinatorial Analysis. A survey of important areas of combinatorics. Topics may include enumeration techniques, recurrence relations, combinatorial designs, graph theory, matching and optimization. Prer., MATH 2150.
MATH 3810. Introduction to Probability and Statistics. 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. Prer., MATH 2350.
MATH 4050/5050. Topics in Mathematics Secondary Classroom. 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.
MATH 4100/5100. Technology in Mathematics Teaching and Curriculum. 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.
MATH 4130/5130. Linear Algebra I. Vector spaces, Linear transformation and matrices, determinants, eigenvalues, similarity transformations, orthogonal and unitary transformations, normal matrices and quadratic forms. Prer., MATH 3130.
MATH 4140. Modern Algebra I. 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.
MATH 4150/5150. Modern Algebra II. Continuation of MATH 414 through Galois theory. Prer., MATH 4140.
MATH 4210/5210. Higher Geometry. Axiomatic systems. The foundations of Euclidean and Lobachevskian geometries. Prer., MATH 3110 or MATH 3130.
MATH 4230/5230. Fractal Geometry. 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.
MATH 4250/5250. Introduction to Chaotic Dynamical Systems. 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.
MATH 4310. Modern Analysis I. Calculus of one variable, the real number system, continuity, differentiation, integration. Prer., MATH 2150 and MATH 2350, MATH 3410 is strongly recommended.
MATH 4320/5320. Modern Analysis II. Sequence and series, convergence, uniform convergence; Taylor's theorem; calculus of several variables including continuity, differentiation, and integration. Prer., MATH 4310.
MATH 4420/5420. Optimization. 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.
MATH 4430/5430 Ordinary Differential Equations. Linear systems of differential equations, existence and uniqueness theorems, stability, periodic solutions, eigenvalue problems, and analysis of equations important for applications. Prer., MATH 3130 and MATH 3400.
MATH 4450/5450. Complex Variables. Theory of functions of one complex variable including integrals, power series, residues, conformal mapping, and special functions. Prer., MATH 2350.
MATH 4470/5470. Methods of Applied Mathematics. Boundary value problems for the wave, heat, and Laplace equations, separation of variables method, eigenvalue problems, Fourier series, orthogonal systems. Prer., MATH 2350, MATH 3130 and MATH 3400.
MATH 4480/5480. Mathematical Modeling. The use of diverse mathematical techniques to analyze and solve problems from science and engineering, particularly 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 3130, MATH 3400, and MATH 3100 or MATH 3801 or ECE 3610.
MATH 4650/5650. Numerical Analysis. 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, and MATH 3400.
MATH 4670/5670. Scientific Computation. Description and analysis of algorithms used for numerical solutions of partial differential equations of importance in science and engineering. The main emphasis is on theoretical analysis, but some practical computations are included. Prer., MATH 2350, MATH 3130, MATH 3400, and CS 1150 or equivalent.
MATH 4810/5810. Mathematical Statistics I. 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.
MATH 4820/5820. Mathematical Statistics II. 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.
MATH 4830/5830. Linear Statistical Models. 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.
MATH 4850/5850. Stochastic Modeling. 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 5110. Technology in Math Education Seminar. 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.
MATH 5170/6170. Rings and Modules I. 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. Prer., MATH 4140.
MATH 6180. Rings and Modules II. Further topics in ring and module theory, including: division rings, perfect and semiperfect rings. Prer., MATH 5170/6170.
MATH 5270. Algebraic Coding Theory. The basic ideas of the theory of error-correcting codes are presented. We will study some important examples and give applications. These codes are important for the digital transmission of data. Prer., MATH 4140.
MATH 5330/6330. Real Analysis I. Lebesgue measure, measurable and nonmeasurable sets, sigma algebras. Lebesgue integral, comparison with Riemann intergration, 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 and MATH 5350/6350.
MATH 5350/6350. Applied Functional Analysis. 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 4310/5320.
MATH 5430/6430. Ordinary Differential Equations. Existence and uniquess theorem, linear systems, Floquet theory, stability analysis of equilibrium solutions of two dimensional systems, series solutions at regular singular points, Sturm-Liouville problems. Prer., MATH 3130, 3400, 4310.
MATH 5440/6440. Approximation Methods in Applied Mathematics. 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 5610/6610.
MATH 5520. Perturbation Theory in Astrodynamics. Perturbation methods including Lagrange and Hamiltonian mechanics and the generalized method of averaging. Gravitational and atmosphere modeling. Prer., MAE 4410/5410 or PHYS 5510.
MATH 5610/6610. Complex Analysis I. Complex numbers, Cauchy-Riemann equations, harmonic functions, Elementary functions and conformal mapping. Contour integrals, Cauchy integral representation. Uniform convergence and power series. Residues. Prer., MATH 4310.
MATH 5620/6620. Complex Analysis II. Argument principle, Rouche's Theorem. Homotopy, and contour 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.
MATH 5840. Computer Vision. 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 CS 5840.
MATH 5900. Graduate Seminar. Various topics in mathematics at the graduate level. Prer., Consent of instructor.
MATH 5910/6910. Theory of Probability I. Theoretical approach to probability. 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, recurrence, Martingales. Prer., MATH 4310.
MATH 5920/6920. Theory of Probability II. Probability theory for sequences of dependent random variables, with the major focus on martingale theory and its applications. Prer., MATH 5910/6910.
MATH 6310. Mathematics and Economics for K-12 Teachers. 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.
MATH 7000. Master's Thesis.
MATH 8000. PhD Dissertation. Enrollment is limited to those students who are in the PhD program in Applied Science, Mathematics, and have primary thesis advisor in the Department of Mathematics. Prer., Consent of instructor.
MATH 9400. Independent Study Math Undergraduate. (Student Must Contact Math Department for Permission Number)
MATH 9500. Independent Study Math, Graduate. (Student Must Contact Math Department for Permission Number)
MATH 9990. Candidate for Degree.