MATH 1009 - Computer-Based Algebraic Problem Solving A laboratory-based problem solving course focused on personal computing applications. Topics include general problem solving techniques, deductive reasoning, elementary probability, computer algebraic software, optimization, graphical analysis, systems of equations, spreadsheets, functions, descriptive statistics, linear programming and elementary programming logic. Prereq: basic high school algebra and some familiarity with Microsoft Windows. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 1010 - Mathematics for the Liberal Arts Designed to give liberal arts students the skills required to understand and interpret quantitative information that they encounter in the news and in their studies, and to make quantitatively-based decisions in their lives. Topics include a survey of logic and analysis of arguments, identifying fallacies in reasoning, working with numbers and units, linear and exponential relations and essentials of probability and statistics. The emphasis is on applications with case studies in economics, finance, environmental sciences, health, music and science. Note: This course assumes that students have knowledge equivalent to three years of high school mathematics (two years of algebra). GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1 Semester Hours: 3 to 3

MATH 1011 - Math for Liberal Arts Workshop Prepares students for college-level mathematics. Students receive one-on-one and small-group instruction on mathematics topics related to college level mathematics success. Max hours: 1 Credit. Semester Hours: 1 to 1

MATH 1070 - College Algebra for Business Covers the same mathematical topics as College Algebra, MATH 1110, but with business applications. Note: Graphics calculator required. Note: Students may not receive credit for this course if they have already received credit for MATH 1110 or MATH 1130. Note: 24 on ACT-Math, 560 on SAT-Math or above average performance in intermediate algebra, algebraic literacy or integrated math are strongly recommended as preparation for this course. Max hours: 3 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1. Semester Hours: 3 to 3

MATH 1080 - Calculus for Social Sciences and Business A one-semester course in single-variable calculus. Topics include limits, derivatives, differentiation rules, integration and integration rules. Emphasis is on applications to business and social sciences. Note: No knowledge of trigonometry is required. Those planning to take more than one semester of calculus should take MATH 1401 instead of MATH 1080. MATH 1070 or MATH 1110 with a C- or higher is required for students to register for this course. No co-credit with MATH 1401. Max hours: 3 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1. Semester Hours: 3 to 3

MATH 1110 - College Algebra Topics in algebra designed for students who intend to take the calculus sequence. Functions, domains, ranges, graphs, data scatter plots and curve fitting, solving equations and systems of equations, polynomial, rational, exponential and logarithmic functions and other topics. Applications are emphasized. Note: Students may not receive credit for this course if they have already received credit for MATH 1070 or MATH 1130. Note: 24 on ACT-Math, 560 on SAT-Math or above average performance in intermediate algebra, algebraic literacy or integrated math are strongly recommended as preparation for this course. Max hours: 4 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1. Semester Hours: 4 to 4

MATH 1111 - First Year Seminar Restriction: Restricted to Freshman level students. Max hours: 3 Credits. Semester Hours: 1 to 3

MATH 1120 - College Trigonometry Topics in trigonometry, analytic geometry, and elementary functions designed for students who intend to take the calculus sequence. Angles and trigonometry functions of acute angles, analytic trigonometry, fundamental trigonometric functions and identities including hyperbolic trigonometry, parametric equations, and polar coordinate system. Graphic calculators and/or computer algebra systems are used extensively. Applications are emphasized. Note: This course assumes that students have mathematical knowledge equivalent to MATH 1110 or MATH 1070. Students with a grade of B- or better in MATH 1110 or MATH 1070 pass the course at a much higher rate. No co-credit with MATH 1130. Max hours: 3 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1. Semester Hours: 3 to 3

MATH 1130 - Precalculus Mathematics Condensed treatment of the topics in MATH 1110 and 1120. Note: This course assumes that students have mathematical knowledge equivalent to a grade of C- or better in College Algebra and Trigonometry. No co-credit with MATH 1070, 1110 or 1120. Max hours: 4 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1. Semester Hours: 4 to 4

MATH 1401 - Calculus I First course of a three-semester sequence (MATH 1401, 2411, 2421) in calculus. Topics covered include limits, derivatives, applications of derivatives, and the definite integral. Note: No co-credit with MATH 1080. Note: : To be able to register for this course, students must first be entered into the MATH 1401 Student Group. To be eligible, students must demonstrate that they have mathematical knowledge equivalent to MATH 1120 or MATH 1130. Students can demonstrate this proficiency 1) by having an SAT score of 620 or an ACT score of 27, taken within the last three years, or 2) by having completed and transferred in a course that is the exact equivalent of MATH 1401 at a different institution, or 3) by earning a score of 70% or higher on the prerequisite exam administered through the MERC lab. Some preparation is required before this prerequisite exam can be taken; contact the MERC lab or the Mathematics department for more information. Max hours: 4 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1 Semester Hours: 4 to 4

MATH 1840 - Independent Study. Max hours: 3 Credits. Semester Hours: 1 to 3

MATH 2411 - Calculus II The second of a three-semester sequence (MATH 1401, 2411, 2421) in calculus. Topics covered include exponential, logarithmic, and trigonometric functions, techniques of integration, indeterminate forms, improper integrals and infinite series. Prereq: C- or better in MATH 1401. Note: Students with a grade of B- or better in MATH 1401 pass this course at a much higher rate. Max hours: 4 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1. Semester Hours: 4 to 4

MATH 2421 - Calculus III The third of a three-semester sequence in Calculus (MATH 1401, 2411 and 2421). Topics include vectors, vector-valued functions, partial differentiation, differentiation, multiple integration, and vector calculus. Prereq: C- or better in MATH 2411. Note: Students with a grade of B- or better in MATH 2411 pass this course at a much higher rate. Max hours: 4 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1 Semester Hours: 4 to 4

MATH 2511 - Discrete Structures Covers the fundamentals of discrete mathematics, including: logic, sets, functions, growth of functions, algorithms, matrices, mathematical reasoning, proofs, induction, relations, graphs, trees and combinatorics. There is an emphasis on how discrete mathematics applies to computer science in general, and algorithm analysis in particular. Prereq: CSCI 2421. Cross-listed with CSCI 2511. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 2810 - Topics Topics in mathematics with various subtitles reflecting course content. Prereq: permission of instructor. Max hours: 6 Credits. Semester Hours: 1 to 3

MATH 2830 - Introductory Statistics Basic statistical concepts, summarizing data, probability concepts, distributions, confidence intervals, hypothesis testing. Note: This course assumes that students have knowledge equivalent to three years of high school mathematics (two years of algebra), intermediate algebra, or Algebraic Literacy at a Colorado Community College at the start of class. Students who have a grade of B- or better in one of these courses pass at a much higher rate. Max hours: 3 Credits. GT: Course is approved by the Colorado Dept of Higher Education for statewide guaranteed transfer, GT-MA1. Semester Hours: 3 to 3

MATH 2939 - Internship Experiences involving application of specific, relevant concepts and skills in supervised employment situations. Note: students must work with the Experiential Learning Center advising to complete a course contract and gain approval. Prereq: 15 hours of 2.75 GPA. Max hours: 9 Credits. Semester Hours: 1 to 3

MATH 3000 - Introduction to Abstract Mathematics Students learn to prove and critique proofs of theorems by studying elementary topics in abstract mathematics, including logic, sets, functions, equivalence relations and elementary combinatorics. Coreq: MATH 2421 or MATH 3191. Note: This course assumes that students have taken MATH 2411 or equivalent. Students who have a grade of B- or better in MATH 2411 pass at a much higher rate. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 3040 - Mathematics for Elementary Teachers Key mathematical concepts for K-6 teachers informed by NCTM & Common Core State Standards, such as place-value number systems, rational, proportional, & algebraic reasoning, geometrical concepts, & statistical/probability ideas. Students’ meaningful, enjoyable learning is promoted via problem solving activities. Cross-list with MTED 5400. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 3191 - Applied Linear Algebra Topics include systems of equations, Gaussian elimination with partial pivoting, LU–decomposition of matrices, matrix algebra, determinants, vector spaces, linear transformations, eigen values and applications. Note: No co-credit with MATH 3195. Note: This course assumes that students have taken MATH 2411 or equivalent. Students who have a grade of B- or better in MATH 2411 pass this course at a much higher rate. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 3195 - Linear Algebra and Differential Equations Presents the essential ideas and methods of linear algebra and differential equations, emphasizing the connections between and the applications of both subjects. The course is designed for students in the sciences and engineering. Note: No co-credit with MATH 3200 and MATH 3191. Note: This course assumes that students have taken MATH 2411 or equivalent. Students who have a grade of B- or better in MATH 2411 pass this course at a much higher rate. Max hours: 4 Credits. Semester Hours: 4 to 4

MATH 3200 - Elementary Differential Equations First and second order differential equations, Laplace transforms, systems of equations, with an emphasis on modeling and applications. Coreq: MATH 3191. Note: No co-credit with MATH 3195. Note: This course assumes that students have taken MATH 2411 or an equivalent course. Students who have a grade of B- or better in MATH 2411 pass this course at a much higher rate. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 3210 - Higher Geometry I Studies the foundations of modern geometry by examining axiomatic systems for various geometrics, with an emphasis on non-Euclidean hyperbolic geometry. Prereq: C- or better in MATH 3000. Cross-listed with MCKE 5210. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 3250 - Problem Solving Tools Students learn and refine both problem solving techniques and computer programming skills. Examples, exercises, and projects are taken from a wide range of mathematical topics including algebra, calculus, linear algebra and probability. Note: This course will not count toward a graduate degree in applied mathematics. Prereq: MATH 2411. Coreq: either MATH 3191 or MATH 3195. Cross-listed with MCKE 5250. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 3301 - Introduction to Optimization in Operations Research Introduces a mathematical approach for decision-making in practice based on optimization. Students will learn to model, analyze and solve a variety of problems from deterministic operations using both continuous and discrete mathematical programming algorithms and software. Note: this course assumes that students have taken MATH 3191 or MATH 3195 or equivalent. Students who have received a grade of B- or better in MATH 3191 or 3195 pass this course at a much higher rate. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 3302 - Simulation in Operations Research Elementary stochastic processes and standard nondeterministic operations research models solved by simulation: Markov chains, Poisson process, Monte Carlo and discrete-event simulation, queuing theory, and inventory models. Note: This course assumes that students have programming experience (e.g. MATLAB), and have taken MATH 3191 and MATH 3800 or 4810 or equivalent. Students who have a grade of B- or better in MATH 3191 and MATH 3800 or 4810 pass this course at a much higher rate. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 3382 - Statistical Theory Probability, random variables, properties of distributions, bootstrap methods, maximum likelihood and method of moments estimation, properties of estimators, classical methods for confidence intervals and hypothesis testing. Note: This course assumes students have passed Math 2421 with a C- or better. Students who have a grade of B- or better in Math 2421 pass this course at a much higher rate. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 3440 - Introduction to Symbolic Logic Covers truth functional and quantificational logic through polyadic first order predicate calculus and theory of identity. Attention is given to such problems in metatheory as proofs of the completeness and consistency of systems of logic. Cross-listed with PHIL 3440. Max hours: 3 Credits. Semester Hours: 3 to 3

Multivariate functions, probability and statistics for chemistry, matrices and vectors, mathematics of reaction kinetics and symmetry point groups. Course covers mathematics needed for CHEM 4511 and 4521. Can also be an elective for the mathematics minor. Prereq: MATH 2411, CHEM 2031 or CHEM 2081, CHEM 2061 or CHEM 2091. Max hours: 4 Credits. Semester Hours: 4 to 4

MATH 3800 - Probability and Statistics for Engineers Basic probability theory, discrete and continuous random variables, point and interval estimation, test of hypotheses, and simple linear regression. Note: no co-credit with MATH 4810. Note: This course assumes that students have taken MATH 2411 and have either previously taken MATH 2421 or are taking MATH 2421 the same semester as MATH 3800. Students who have a grade of B- or better in MATH 2411 pass this course at a much higher rate. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 3939 - Internship Designed experiences involving application of specific, relevant concepts and skills in supervised employment situations. Note: students must work with the Experiential Learning Center advising to complete a course contract and gain approval. Prereq: Junior standing or higher. Max hours: 9 Credits. Semester Hours: 1 to 3

MATH 4010 - History of Mathematics A history of the development of mathematical techniques and ideas from early civilization to the present, including the inter-relationships of mathematics and sciences. Prereq: MATH 2411 with a C- or higher. Coreq: MATH 3000 or 3191. Cross-listed with MATH 5010. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4012 - An Advanced Perspective on Number and Operation “Advanced study of number and operation, including why the various procedures from arithmetic work and connections to algebraic reasoning. Focuses on using rigorous mathematical reasoning and multiple representations to explain concepts. Note: For undergraduate majors, this course only counts toward the mathematics education option. Note: This course assumes that students have taken MATH 3000 or an equivalent course. Students who have a grade of B- or better in MATH 3000 pass this course at a much higher rate. Cross-listed with MATH 5012. Max hours: 2 Credits. Semester Hours: 2 to 2

MATH 4013 - An Inquiry-Based Approach to Geometry An inquiry-based approach to middle-level and Euclidean geometry. Topics include: polygons and the angle relationships, constructions, Pythagorean theorem and perimeter, area and volume, similarity and congruence, circles. Note: For undergraduate majors, this course only counts toward the mathematics education option. Note: This course assumes that students have taken MATH 3000 or an equivalent course. Students who have a grade of B- or better in MATH 3000 pass this course at a much higher rate. Cross-listed with MATH 5013. Max hours: 1 Credit. Semester Hours: 1 to 1

MATH 4014 - Statistical Knowledge for Teaching A problem-based statistics seminar aimed at secondary teachers. Topics include: the central limit theorem, the law of large numbers, probability, measures of central tendency and variability, sampling distributions, regression, and hypothesis testing. Note: For undergraduate majors, this course only counts toward the mathematics education option. Note: This course assumes that students have taken MATH 3800 or an equivalent course. Students who have a grade of B- or better in MATH 3800 pass this course at a much higher rate. Cross-listed with MATH 5014. Max hours: 1 Credit. Semester Hours: 1 to 1

MATH 4015 - Capstone Course for Secondary Teachers High school mathematics from an advanced perspective: analyses of alternative definitions, extensions and generalizations of familiar theorems; discussions of historical contexts in which concepts arose; applications of mathematics. Note: For undergraduate majors, this course only counts toward the mathematics education option. Note: this course assumes that students have taken MATH 3210, 4310 and 3140 or equivalent. Cross-listed with MATH 5015. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4027 - Topics in Mathematics Special topics in mathematics will be covered; consult ‘Schedule Planner’ for current topics and prerequisites. Max hours: 12 Credits. Semester Hours: 3 to 3

MATH 4110 - Theory of Numbers Every other year. Topics include divisibility, prime numbers, congruencies, number theoretic functions, quadratic reciprocity, and special diophantine equations, with applications in engineering. Prereq: Grade of C- or better in MATH 3000. Note: Students who have a grade of B- or better in MATH 3000 pass this course at a much higher rate. Cross-listed with MATH 5110. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4140 - Introduction to Modern Algebra Studies the fundamental algebraic structures used in modern mathematics. Topics include groups, rings, fields and polynomials. Note: This course assumes that students have taken MATH 3000 or equivalent and either MATH 3191 or MATH 3195. Students who have a grade of B- or better in these courses pass at a much higher rate. Cross-listed with MCKE 5140. Max hours: 3 Credits. Semester Hours: 3 to 3

Metric spaces and topological spaces, compactness, separation properties, and connectedness. Note: This course assumes that students have taken MATH 3000. Students who have a grade of B- or better in MATH 3000 pass this course at a much higher rate. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4220 - Higher Geometry II Studies affine and projective geometries. Coordinates are introduced in this framework. Planes and higher dimensional spaces are examined. Note: This course assumes that students have taken MATH 3191. Students who have a grade of B- or better in MATH 3191 pass this course at a much higher rate. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4310 - Introduction to Real Analysis I Calculus of one variable, the real number system, continuity, differentiation, integration theory, sequence and series. Prereq: Prereq: Grade of C- or better in MATH 2421 and 3000. Note: Students who have a grade of B- or better in MATH 2421 and 3000 pass this course at a much higher rate. Cross-listed with MCKE 5310. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4320 - Introduction to Real Analysis II Convergence, uniform convergence; Taylor’s theorem; calculus of several variables including continuity, differentiation and integration; Picard’s theorem in ordinary differential equations and Fourier series. Note: This course assumes that students have taken MATH 4310 or an equivalent course. Students who have a grade of B- or better in MATH 4310 pass this course at a much higher rate. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4387 - Applied Regression Analysis Topics include simple and multiple linear regression, model diagnostics and remediation, and model selection. Emphasis is on practical aspects and applications of linear models to the analysis of data in business, engineering and behavioral, biological and physical sciences. Prereq: Grade of C- or better in MATH 3191 and MATH 3800 or 4820. Note: Students who have a grade of B- or better in MATH 3191, an A in MATH 3800 or a B- or better in MATH 4820 pass this course at a much higher rate. Cross-listed with MATH 5387. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4390 - Game Theory Zero-sum and non-zero-sum games; Nash equilibrium and the principle of indifference; Shapley value and other concepts of fair division; Evolutionary game theory, ESS, and evolutionary population dynamics. Applications in economics, business, and biology. Note: This course assumes that students have programming experience (e.g. MATLAB), and have taken MATH 2421, 3191 and 3200 or MATH 3195, MATH 3800 or 4810, or equivalent. Students who have a grade of B- or better in these courses pass this course at a much higher rate. Cross-listed with MATH 5390. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4394 - Experimental Designs Designs covered will include: completely randomized, complete block, split plot, incomplete block, factorial and fractional factorial designs. Additionally, power and study design for non-experimental studies will be covered. Prereq: Grade of C- or better in MATH 4387 or 5387. Cross-listed with MATH 5394. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4408 - Applied Graph Theory Introduces discrete structures and applications of graph theory to computer science, engineering, operations research, social science, and biology. Topics include connectivity, coloring, trees, Euler and Hamiltonian paths and circuits, matching and covering problems, shortest route and network flows. Note: This course assumes that students have taken MATH/CSCI 2511 or MATH 3000. Students who have a grade of B- or better in MATH/CSCI 2511 or MATH 3000 pass this course at a much higher rate. Cross-listed with CSCI 4408 and MCKE 5408. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4409 - Applied Combinatorics Every other year. Major emphasis is on applied combinatorics and combinatorial algorithms, with applications in computer science and operations. Topics include general counting methods, generating functions, recurrence relations, inclusion-exclusion, and block designs. Note: This course assumes that students have taken MATH 3000. Students who have a grade of B- or better in MATH 3000 pass this course at a much higher rate. Cross-listed with MCKE 5409. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4450 - Complex Variables Infrequent. Topics include complex algebra, Cauchy-Riemann equations, Laurent expansions, theory of residues, complex integration, and introduction to conformal mapping. Note: This course assumes that students have taken MATH 2421 and MATH 3000. Students who have a grade of B- or better in MATH 2421 and MATH 3000 pass this course at a much higher rate. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4650 - Numerical Analysis I Methods and analysis of techniques used to resolve continuous mathematical problems on the computer. Solution of linear and nonlinear equations, interpolation and integration. Prereq: MATH 2411, 3191 or 3195, and programming experience. Cross-listed with CSCI 4650, 5660, and MATH 5660. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4660 - Numerical Analysis II Numerical differentiation and integration, numerical solution of ordinary differential equations, and numerical solutions of partial differential equations as time allows. Prereq: MATH 3195 or both 3191 and 3200; MATH or CSCI 4650 or 5660; or programming experience. Cross-listed with MATH 5661, CSCI 4660 and 5661. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4733 - Partial Differential Equations Infrequent. Initial/Boundary value problems for first-order, wave, heat and Laplace Equations; maximum principles; Fourier Series and applications. Note: This course assumes that students have taken MATH 2421 and MATH 3200, and either have taken MATH 3000 or have experience with partial differential equations in engineering or physics. Students who have a grade of B- or better in MATH 2421 and MATH 3200 pass this course at a much higher rate. Cross-listed with MATH 5733. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4779 - Math Clinic The clinic is intended to illustrate the applicability and utility of mathematical concepts. Research problems investigated originate from a variety of sources–industry, government agencies, educational institutions, or nonprofit organizations. Prereq: consult Schedule Planner or instructor. Cross-listed with MATH 5779. Max hours: 99 Credits. Semester Hours: 3 to 3

MATH 4791 - Continuous Modeling Every other year. Surveys mathematical problems that arise in natural sciences and engineering. Topics may include population models, epidemic models, mechanics, heat transfer and diffusion, tomography, pharmaco-kinetics, traffic flow, fractal models, wave phenomena, and natural resource management. Most models discussed are based on differential and integral equations. Emphasis is formulation and validation of models as well as methods of solution. Note: This course assumes that students have taken MATH 3191 and MATH 3200. Students who have a grade of B- or better in MATH 3191 and MATH 3200 pass this course at a much higher rate. Cross-listed with MATH 5791. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4792 - Probabilistic Modeling Every other year. Markov chains; Poisson processes, continuous time Markov chains, elementary topics in queuing theory, and some mathematical aspects of Monte Carlo simulation, including random variate generation, variance reduction, and output analysis. Note: This course assumes that students have taken MATH 4810 or 5310 and have some programming experience. Students who have a grade of B- or better in MATH 4810 or 5310 pass this course at a much higher rate. Cross-listed with MATH 5792. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4793 - Discrete Math Modeling Every other year. Focuses on the use of graph theory and combinatorics to solve problems in a wide variety of disciplines. Applications are selected from computer science, communication networks, economics, operations research, and the social, biological and environmental sciences. Note: This course assumes that students have taken MATH 3191 and MATH 4408. Students who have a grade of B- or better in MATH 3191 and MATH 4408 pass this course at a much higher rate. Cross-listed with MATH 5793. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4794 - Optimization Modeling Every other year. Principles of model formulation and analysis are developed by presenting a wide variety of applications, both for natural phenomena and social systems. Examples of optimization models to represent natural phenomena include principles of least time and energy. Examples in social systems include resource allocation, environmental control and land management. Specific applications vary, but are chosen to cover a wide scope that considers dichotomies, such as discrete vs. continuous, static vs. dynamic, and deterministic vs. stochastic. Some computer modeling language (like GAMS) is taught. Note: This course assumes that students have taken MATH 2421 and MATH 3191. Students who have a grade of B- or better in MATH 2421 and MATH 3191 pass this course at a much higher rate. Cross-listed with MATH 5794. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4810 - Probability Examines elementary theory of probability, including independence, conditional probability, and Bayes’ theorem; random variables, expectations and probability distributions; joint and conditional distributions; functions of random variables; limit theorems, including the central limit theorem. Note: No co-credit with MATH 3800. Note: This course assumes that students have taken MATH 3191 or equivalent and have either previously taken MATH 2421 or are taking MATH 2421 the same semester as MATH 4810. Students who have a grade of B- or better in MATH 3191 pass this course at a much higher rate. Cross-listed with MATH 5310. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4820 - Introduction to Mathematical Statistics Sampling distributions, maximum likelihood and method of moments estimation, properties of estimators, classical methods for confidence intervals and hypothesis testing, simple linear regression. Prereq: Grade of C- or better in MATH 3800 or MATH 4810 (preferred). Note: Students who have a grade of A in MATH 3800 or a B- or better in MATH 4810 pass this course at a much higher rate. Cross-listed with MATH 5320. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4830 - Applied Statistics Review of estimation, confidence intervals and hypothesis testing; Anova; categorical data analysis; non-parametric tests; linear and logistic regression. Note: this course assumes that students have mathematical knowledge equivalent to an introductory course in statistics (e.g., MATH 2830). No co-credit with MATH 4387 or 5387 and doesn’t count for Math degrees. Cross-listed with MATH 5830. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 4840 - Independent Study Variable credit depending on the student’s needs. Offered for the advanced student who desires to pursue a specific topic in considerable depth. Note: Supervision by a full-time faculty member is necessary, and the dean’s office must concur. Students may register for this course more than once with departmental approval. Max hours: 12 Credits. Semester Hours: 1 to 3

MATH 4880 - Directed Research Students will engage in original research projects supervised and mentored by faculty. Students must work with faculty prior to registration to develop a proposal for their project and receive permission to take this course. Max hours: 6 Credits. Semester Hours: 1 to 6

MATH 5010 - History of Mathematics A history of the development of mathematical techniques and ideas from early civilization to the present, including the inter-relationships of mathematics and sciences. Note: this course assumes that students have mathematical knowledge equivalent to MATH 1401. Prereq: Graduate standing. Not open to students who have had MATH 4010. No credit for applied math graduate students. Cross-listed with MATH 4010. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5012 - An Advanced Perspective on Number and Operation Advanced study of number and operation, including why the various procedures from arithmetic work and connections to algebraic reasoning. Focuses on using rigorous mathematical reasoning and multiple representations to explain concepts. Note: Does not count toward graduate degrees in applied mathematics. Note: this course assumes that students have taken MATH 3000 or an equivalent course. Prereq: Graduate standing. Cross-listed with MATH 4012. Max hours: 2 Credits. Semester Hours: 2 to 2

MATH 5013 - An Inquiry-based Approach to Geometry An inquiry-based approach to middle-level and Euclidean geometry. Topics include: polygons and the angle relationships, constructions, Pythagorean theorem and perimeter, area and volume, similarity and congruence, circles. Note: Does not count toward a graduate degree in applied mathematics. Note: this course assumes that students have taken MATH 3000 or an equivalent course. Prereq: Graduate standing. Cross-listed with MATH 4013. Max hours: 1 Credit. Semester Hours: 1 to 1

MATH 5014 - Statistical Knowledge for Teaching A problem-based statistics seminar aimed at secondary teachers. Topics include: the central limit theorem, the law of large numbers, probability, measures of central tendency and variability, sampling distributions, regression, and hypothesis testing. Note: Does not count toward a graduate degree in applied mathematics. Note: this course assumes that students have taken MATH 3800 or an equivalent course. Prereq: Graduate standing. Cross-listed with MATH 4014. Max hours: 1 Credits. Semester Hours: 1 to 1

MATH 5015 - Capstone Course for Secondary Teachers High school mathematics from an advanced perspective: analyses of alternative definitions, extensions and generalizations of familiar theorems; discussions of historical contexts in which concepts arose; applications of mathematics. Note: Does not count toward a graduate degree in applied mathematics. Note: this course assumes that students have taken MATH 3210, 4310 and 3140 or equivalent. Prereq: Graduate standing. Cross-listed with MATH 4015. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5016 - RM-MSMSP Research Experience for Teachers - Math Cohort The Research Experience for Teachers (RET) program is a five-week research exploration in which twelve RM-MSMSP teachers will raise their level of relevant mathematics understanding by engaging in a “hands on” workshop, transforming what they have learned into new curricular materials that will improve the mathematics abilities of their students and hopefully stimulate them to consider a STEM career. Note: Credit may not apply toward any CLAS degree. Max hours: 6 Credits. Semester Hours: 1 to 6

MATH 5017 - Topics in Mathematics for Teachers Topics vary from semester to semester. Designed for professional mathematics teachers. Note: This course will not count toward a degree in applied mathematics. Prereq: permission of instructor. Max hours: 50 Credits. Semester Hours: 0 to 50

MATH 5027 - Topics in Applied Mathematics Selected topics in mathematical problems arising from various applied fields such as mechanics, electromagnetic theory, economics and biological sciences. Prereq: Graduate standing in Applied Mathematics, or permission of the instructor. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5070 - Applied Analysis Metric spaces, uniform convergence, elements of Banach spaces, elements of functions of complex variable. Problem solving and independent proof writing. Review of selected advanced topics in analysis for the PhD preliminary examination. Prereq: Graduate standing in Applied Mathematics or permission of the instructor. Note: This course assumes that students have the equivalent of two semesters of undergraduate real analysis (e.g., MATH 4310 and MATH 4320). Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5110 - Theory of Numbers Every other year. Topics include divisibility, prime numbers, congruences, number theoretic functions, quadratic reciprocity, and special diophantine equations, with applications in engineering. Prereq: Graduate Standing in Applied Mathematics or permission of the instructor. Note: This course assumes that students have the equivalent of an undergraduate-level course in mathematical proof (e.g. MATH 3000). Cross-listed with MATH 4110. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5135 - Functions of a Complex Variable Infrequent. The complex plane, infinite series and products, elementary special functions, Cauchy-Riemann equations, conformal mapping, complex integration, Cauchy integral theory, and residue theory. Prereq: Graduate standing in Applied Mathematics or permission of the instructor. Note: This course assumes that students have mathematical knowledge equivalent to two semesters of undergraduate-level real analysis (e.g. MATH 4310, MATH 4320) or to a semester of graduate-level real analysis (e.g., MATH 5070). Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5198 - Mathematics for Bioscientists Infrequent. Develops mathematical reasoning: introduces linear algebra, discrete structures, graph theory, probability, and differential equations, using applications to molecular biology. Note: No credit for mathematics or engineering students. Prereq: Graduate standing in Applied Mathematics or permission of the instructor. Note: This course assumes that students have mathematical knowledge equivalent to two semesters of calculus (e.g., MATH 1401, MATH 2411). Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5310 - Probability Examines elementary theory of probability, including independence, conditional probability, and Bayes’ theorem; random variables, expectations and probability distributions; joint and conditional distributions; functions of random variables; limit theorems, including the central limit theorem. Prereq: Graduate standing in Applied Mathematics or permission of the instructor. Note: This course assumes that students have the equivalent of differential and integral calculus (e.g., MATH 2411). Cross-listed with MATH 4810. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5320 - Introduction to Mathematical Statistics Sampling distributions, maximum likelihood and method of moments estimation, properties of estimators, classical methods for confidence intervals and hypothesis testing, simple linear regression. Prereq: Graduate standing in Applied Mathematics or permission of the instructor. Note: This course assumes that students have the equivalent of an undergraduate-level course in probability (e.g., MATH 3800 or 4810). Cross-listed with MATH 4820. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5350 - Mathematical Theory of Interest Rates of interest, term structure of interest rates, force of interest, yield rate, principal, equation of value, annuity, perpetuity, stocks, bonds, other financial instruments. Prereq: Graduate standing in Applied Mathematics or permission of the instructor. Note: This course assumes that students have the equivalent of an undergraduate-level course in probability (e.g., MATH 4810). Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5351 - Actuarial Models Severity models, frequency models, aggregate models, risk measures, ruin theory, construction and selection of empirical models, credibility, simulation. Prereq: Graduate standing in Applied Mathematics or permission of the instructor. Note:This course assumes that students have the equivalent of undergraduate-level courses in probability and statistics (e.g., MATH 4810, MATH 4820). Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5387 - Applied Regression Analysis Topics include simple and multiple linear regression, model diagnostics and remediation, and model selection. Emphasis is on practical aspects and applications of linear models to the analysis of data in business, engineering and behavioral, biological and physical sciences. Prereq: Graduate standing in Applied Mathematics or permission of the instructor. Note: This course assumes that students have the equivalent of an undergraduate-level course in statistics (e.g., MATH 4320). No co-credit with MATH 4830/5830. Cross-listed with MATH 4387. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5390 - Game Theory Zero-sum and non-zero-sum games; Nash equilibrium and the principle of indifference; Shapley value and other concepts of fair division; Evolutionary game theory, ESS, and evolutionary population dynamics. Applications in economics, business, and biology. Note: this course assumes that students have the equivalent of MATH 2421, 3191 and 3800 or 4810. Prereq: Graduate standing in Applied Mathematics. Cross-listed with MATH 4390. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5394 - Experimental Designs Designs covered will include: completely randomized, complete block, split plot, incomplete block, factorial and fractional factorial designs. Additionally, power and study design for non-experimental studies will be covered. Prereq: Graduate standing in Applied Mathematics or permission of the instructor. Note: This course assumes that students have the equivalent of an undergraduate-level course in regression analysis (e.g., MATH 4387). Cross-listed with MATH 4394. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5410 - Modern Cryptology Every other year. Deals with the mathematics that underlies modern cryptology. Topics include: classical cryptology, public and private key cryptosystems, secret sharing schemes, authentication schemes, linear feedback shift registers, discrete logarithm and elliptic curve-based schemes. Note: this course assumes that students have the equivalent of a course in linear algebra (e.g., MATH 3191). Prereq: Graduate standing in Applied Mathematics. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5432 - Computational Graph Theory Infrequent. Algorithmic techniques in graph theory and other discrete mathematics areas. Typical topics include: branch-bound algorithms, matching, colorings, domination, min-plus algebra, simulated annealing and related heuristics, NP-completeness theory. Prereq: Graduate standing in Applied Mathematics or permission of the instructor. Note: This course assumes that students have the equivalent of an undergraduate-level course in graph theory (e.g., MATH 4408). Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5446 - Theory of Automata Infrequent. Studies the relationships between classes of formal languages (regular, context-free, context-sensitive, phrase-structure) and classes of automata (finite-state, pushdown, Turing machines). Additional topics include decidability and computability issues. Prereq: Graduate standing in Applied Mathematics or permission of the instructor. Note: This course assumes that students have the equivalent of an undergraduate-level course in abstract algebra (e.g., MATH 4140). Cross-listed with CSCI 5446. Max hours: 3 Credits. Semester Hours: 3 to 3

MATH 5490 - Network Flows Every other year. Begins with the classical min-cost flow problem, defined on an ordinary network. Other problems, such as shortest path, are also shown in this class. Both theory and algorithms are presented. Extensions include generalized networks, nonlinear costs, fixed charges, multi-commodity flows and additional applications, such as in communications networks. Prereq: Graduate standing in Applied Mathematics or permission of the instructor. Max hours: 3 Credits. Semester Hours: 3 to 3