Math Course Descriptions
• Information for the Online Math Placement Test (MPT)  can be  found HERE

• MATH 090 - Fundamentals of Algebra. 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.

• MATH 099 - Intermediate Algebra. 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 pass the Online Math Placement Test for MATH 99.

### 1000-2000 Level Courses

• 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: MATH 99 with a grade of "C" or better, or pass the Online Math Placement Test for College Algebra of 50% or higher.

• MATH 1050 - Elementary Functions for Calculus (Precalculus). 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. Prerequisite: Pass MATH 1040 - College Algebra with a grade of "C" or better, or the Online 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 score 17 or more on the Online Math Placement Test for College Algebra.

• MATH 1120 - Calculus for Business & Economics. Calculus for the business and economics students. Prer., MATH 1040 with a grade of "C" or better, or the Online Math Placement Test for College Algrebra at 87% or higher AND 50% or higher on the Calculus for Business and Economics Test

• MATH 1200 - Reasoning About Data. Helps students develop quantitative and qualitative reasoning skills by applying inductive and deductive reasoning, mathematics, and statistics to real world data. This course is one of the means to satisfy the Qualitative and Quantitative Reasoning requirement.

• 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 1350. Credit not granted for both this course and MATH 1350. Prer., MATH 1050 with a grade of "C" or better, or pass the Online Math Placement Test for 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. Credit not granted for both this course and MATH 1350. Prer., MATH 1310, the equivalents of MATH 1040 (College Algebra) and MATH 1050 (Elementary Functions for Calculus) or score 20 or more on the Calculus Readiness exam. Most students with 4 years of high school mathematics (Algebra I or higher) will qualify.

• 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. Prer., MATH 1050 with a grade of "C" or better, or pass the Math Placement Test for MATH 1350.

• 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 with a grade of "C" or better, or Online Math Placement Test for College Algebra at 87% or higher AND 50% or higher on the Calculus TestOnline

• 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 1320 or MATH 1350 with a grade of "C" or better.

• 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 1320 or MATH 1350 with a grade of "C" or better.

• 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 with a grade of "C" or better.

• MATH 2650 - Intro to Computational Math. (1 credit) 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 2810 - Introduction to Basic Statistics. Study of the elementary statistical measures. Introduction to probability, statistical distributions, statistical inference and hypothesis testing. Prer., MATH 1040 or equivalent.

### 3000 Level Courses

• 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. Approved for Compass Curriculum requirement: Explore-Physical and Natural World.

• 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. Approved for Compass Curriculum requirement: Explore-Physical and Natural World.

• 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 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.

• 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 - Introduction to Analysis. An introduction to proofs in analysis, with the main focus on completeness of the real numbers, infinite sequences, numerical series, power series, and related topics. This course is strongly recommended for students planning to take MATH 4310. Prer., MATH 2150 and MATH 2350.

• MATH 3480 - Functions and Modeling. 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.

• 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, machining and optimization. Prer., MATH 2150.

• MATH 3650 - Advanced Computational Math. (2 credits) Continuation of MATH 2650: 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 and MATH 3400.

• MATH 3670 - Scientific Computation I. 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 and MATH 3400.

• 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.

### 4000/5000 Level Courses

• MATH 4040 - Senior Math Seminar. 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.
• 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. Meets with MATH 5050.

• 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. Meets with MATH 5100.

• MATH 4130/5130 - Linear Algebra I. Vector spaces, linear transformations and matrices, determinants, eigenvalues, similarity transformations, orthogonal and unitary transformations, normal matrices and quadratic forms. Prer., MATH 3130. Meets with MATH 5130.

• 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 4140. The relationship between groups and fields is explored via a thorough investigation of Galois theory. Prer., MATH 4140. Meets with MATH 5150.

• MATH 4210/5210 - Higher Geometry. Axiomatic systems. The foundations of Euclidean and Lobachevskian geometries. Prer., MATH 3110 or MATH 3130. Meets with MATH 5210.

• 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. Meets with MATH 5230.

• 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. Meets with MATH 5250.

• 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. Meets with MATH 5320.

• 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. Meets with MATH 5420.

• 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. Meets with MATH 5450.

• MATH 4470/5470 - Methods of Applied Mathematics. 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.

• MATH 4480/5480 - Mathematical Modeling. 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 3130, MATH 3400, and MATH 3100 or MATH 3810 or ECE 3610. MATH 2650 or adequate experience with computer programming. Meets with MATH 5480.

• 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. Meets with MATH 5650.

• MATH 4670/5670 - Scientific Computation II. Description and analysis of algorithms used for numerical solutions of partial differential equations of importance in science and engineering. Practical computations are included. Prer., MATH 3130, MATH 3400, and CS 1150 or equivalent. Meets with MATH 5670.

• 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. Meets with MATH 5810.

• 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. Meets with MATH 5820.

• 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 computation. Prer., MATH 3810 or ECE 3610, or MATH 3100 and MATH 3130. Meets with MATH 5830.

• 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 2650 or adequate experience with computer programming. Meets with MATH 5850.

• MATH 4900 - Advanced Topics Seminar. Various advanced topics in mathematics. Prer., Vary depending on course content. Consent of instructor required. Meets with MATH 5900.

### 5000/6000 Level Courses

• MATH 5010 - Topology I. Elements of general topology,, algebraic topology and differentiable manifolds. Prer., MATH 4130/5130, 4140, 4310, and 4320/5320.

• MATH 5050 - Topics in Mathematics for the 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. Meets with MATH 4050.

• MATH 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. Meets with MATH 4100.

• 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 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. Meets with MATH 4130.

• MATH 5150 - Modern Algebra II. 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.

• 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 or MATH 6170.

• MATH 5210 - Higher Geometry. Axiomatic systems. The foundations of Euclidean and Lobachevskian geometries. Prer., MATH 3110 or MATH 3130. Meets with MATH 4210.

• MATH 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. Meets with MATH 4230.

• MATH 5250 - Introduction to Chaotic Dynamical Systems. 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.

• MATH 5270/6270 - Algebraic Coding Theory. 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.

• MATH 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. Meets with MATH 4320.

• MATH 5330/6330 - Real Analysis I. 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.

• 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 4320 or MATH 5320. Meets with MATH 6350. Graduate students only.

• MATH 5420 - Optimization. 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.

• MATH 5430/6430 - Ordinary Differential Equations. Existence and uniqueness theorem, linear systems, Floquet theory, stability analysis of equilibrium solutions of two-dimensional systems, series solutions at regular singular points, Sturm-Liouville problems. Req., MATH 3130, MATH 3400, and MATH 4310. Meets with MATH 6430. Grad level only.

• 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 MATH 5610/6610. Graduate students only. Meets with MATH 6440.

• MATH 5450 - Complex Variables. Theory of functions of one complex variable, including integrals, powering series, residues, conformal mapping and special functions. Meets with MATH 4450.

• MATH 5470 - Methods of Applied Mathematics. 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.

• MATH 5480 - Mathematical Modeling. 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.

• 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-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.

• MATH 5620/6620 - Complex Analysis II. 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.

• MATH 5650 - Numerical Analysis. Error analysis, root finding, numerical integration and differentiation, numerical methods for ordinary differential equations, numerical linear algebra and eigenvalue problems. Meets with MATH 4650.

• MATH 5670 - Scientific Computation II. Description and analysis of algorithms used for numerical solutions of partial differential equations of importance in science and engineering. Practical computations are included. Prer., MATH 3130, MATH 3400, and CS 1150 or equivalent. Meets with MATH 4670.

• MATH 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. Meets with MATH 4810.

• MATH 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 3100 or MATH 3810. Meets with MATH 4820.

• MATH 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. Meets with MATH 4830.

• 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 C S 5840.

• MATH 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 2650 or adequate experience with computer programming. Meets with MATH 4850.

• MATH 5900 - Graduate Seminar. Various topics in mathematics at the graduate level. Prer., Consent of instructor. Meets with MATH 4900.

• MATH 5910/6910 - Theory of Probability I. 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.

• 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. Graduate students only. Meets with MATH 6920.

• 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.

### 7000 - 9000 Level Courses

• 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 9000 - Fundamentals of 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 the Department of Mathematics. Pass/fail grading only. Does not count toward BA or BS degree.

• 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.