# Mathematics (MATH)

## [1] Courses in Mathematics (MATH)

1360 QUANTITATIVE LITERACY This course satisfies the general education aims of the university through the study of topics in contemporary mathematics. Upon completion of the course, students will be able to apply principles of mathematics to real-world situations, create mathematical and statistical models of the situations, and use the models to solve problems. Lecture/demonstration format. Placement in this course is guided by the university’s Mathematics Placement policy. [ACTS: MATH1113]

1365 MATHEMATICAL REASONING FOR HEALTH SCIENCE PROFESSIONS This course develops quantitative reasoning skills necessary for a career in health sciences. Topics include quantities and measurements, dosage calculations, dimensional analysis, exponential and logarithmic models, and an introduction to statistical studies and descriptive statistics. There is a focus on health science applications throughout. Placement in this course is guided by the university’s Mathematics Placement policy. [ACTS: MATH1113]

1390 COLLEGE ALGEBRA This course satisfies the general education aims of the university by providing a solid foundation of algebraic concepts. The course includes the study of functions, relations, graphing, and problem solving, and provides a knowledge of how to apply these concepts to real problem situations. Lecture/demonstration format. Placement in this course is guided by the university’s Mathematics Placement policy. [ACTS: MATH1103]

1392 PLANE TRIGONOMETRY Topics include angles and triangles and their measure, graphs and applications of trigonometric functions, and inverse trigonometric functions, vectors, polar coordinates, and complex numbers. This course can be coupled with College Algebra (MATH 1390) as an alternative prerequisite for Calculus I (MATH 1496). If one year has passed since successful completion of College Algebra, then Calculus Preparation (MATH 1486) is the preferred prerequisite for Calculus I (MATH 1496). Lecture/demonstration format. Prerequisite: MATH 1390 or equivalent. [ACTS: MATH1203]

1395 BUSINESS MATHEMATICS As a component of the business foundation, this course is a requirement for students seeking a Bachelor of Business Administration. The course develops quantitative reasoning skills necessary for business success. Topics include functions & linear modeling, an introduction to statistics & probability, and finance. Additional topics may also be covered. This course focuses on utilizing technology for problem-solving. Placement in this course is guided by the university’s Mathematics Placement policy. [ACTS: MATH1113]

1486 CALCULUS PREPARATION A conceptual approach to the algebra and trigonometry essential for calculus. Designed for students who plan to study calculus, this course is the preferred prerequisite for Calculus I (MATH 1496) and satisfies the general education requirement in mathematics. Lecture and problem-solving activities. Prerequisite: Math ACT score of 21 or higher; or MATH 1390 with a grade of C or higher; or consent of instructor. [ACTS: MATH1305]

1491 APPLIED CALCULUS FOR THE LIFE SCIENCES This course is a brief introduction to calculus and includes differentiation and integration of polynomial, exponential, trigonometric, and logarithmic functions, and applications in the life sciences. Lecture/demonstration format. Prerequisite: MATH 1390 or equivalent.

1496 CALCULUS I As a prerequisite for nearly all upper-division mathematics, this course is a requirement for majors and minors in mathematics and other majors in the natural sciences and engineering. The content includes the study of limits, continuity, derivatives, integrals, and their applications. Lecture and problem solving activities. Prerequisites: MATH ACT of 27 or higher, or C or better in MATH 1486, or C or better in both MATH 1390 and MATH 1392, or equivalent . [ACTS: MATH2405]

1497 CALCULUS II This course is required of all majors or minors in mathematics, chemistry, or physics. Topics include applications of the definite integral, techniques of integration, infinite series, conics, parametric equations, polar coordinates, vectors, and vector functions. This course is a prerequisite for Calculus III and most of the upper division mathematics courses. Lecture format. Prerequisite: C or better in MATH 1496. [ACTS: MATH2505]

2V25 INDEPENDENT STUDY IN MATHEMATICS (Variable credit: 1-3 credit hours.) The student will independently study a mathematical topic with a faculty mentor. Course may be repeated. Prerequisites: MATH 1496 and consent of instructor.

2311 ELEMENTARY STATISTICS This course introduces the basics of descriptive statistics, probability theory, and statistical inference. This course may be used to satisfy the statistics requirement in several degree programs. No credit can be awarded for more than one introductory statistics course from the following: GEOG 2330, MATH 2311, PSCI 2312, PSYC 2330, CISA/QMTH 2330, and SOC 2321. The use of appropriate technology is emphasized. Lecture/Activity format. Prerequisite: Any 1000-level MATH course. [ACTS: MATH2103]

2330 DISCRETE STRUCTURES I This course provides a mathematical foundation for applications in computer science and for the development of more advanced mathematical concepts required for a major in computer science. Topics include Boolean operations, truth tables, set operations, mathematical induction, relations, functions, analysis of algorithms, and recursive algorithms. This course uses lecture and problem-solving activities. Prerequisite: Grade of C or higher in CSCI 1470 and either MATH 1491 or MATH 1496, or consent of instructor.

2335 TRANSITION TO ADVANCED MATHEMATICSThis course is an introduction to the language and methods of advanced mathematics. The student will learn the basic concepts of formal logic and its use in proving mathematical propositions. Specific topics that will be covered may vary depending upon the instructor, but will include basic number theory and set theory. Prerequisite/Corequisite: MATH 1497 or consent of instructor.

2341 INTRODUCTION TO MATHEMATICAL COMPUTATION This course focuses on the process of translating a mathematical concept, formula or algorithm into a form that is appropriate for investigation via computational tools, including common mathematical software and programming languages. The basic concepts of programming and their implementations (such as data types, arrays, conditional statements, loops, functions) will be discussed. Topics may include applications of summations, iterative methods, recursion, polynomial approximations, numerical approximations, and applications from other fields of science. Lecture/Computer Lab format. Prerequisite: MATH 1497 or concurrent enrollment in MATH 1497.

2471 CALCULUS III This course is a continuation of Calculus II and is required of all majors in mathematics, chemistry, and physics. Topics include vector valued functions, partial differentiation, multiple integrals, Green’s theorem, and Stokes’ theorem. Lecture format. Prerequisite: C or better in MATH 1497. [ACTS: MATH2603]

3V25 SPECIAL TOPICS IN MATHEMATICS (Variable credit: 1-3 credit hours.) This course is an elective lecture course that focuses on advanced topics in mathematics not covered in the current curriculum. Topics vary with instructors. Course may be repeated. Prerequisite: MATH 1497 and consent of instructor.

3311 STATISTICAL METHODS This course emphasizes statistical data analysis including descriptive statistics, discrete and continuous random variables, probability distributions, sampling distributions, estimation, hypothesis testing, and simple linear regression. Statistical computer software will be used. Prerequisites: MATH 2341, or MATH 1491 and CSCI 1470, or MATH 1496 and CSCI 1470, or consent of instructor.

3320 LINEAR ALGEBRA This course is required for all majors in mathematics, physics, and computer science. This course introduces matrix algebra, vector spaces, linear transformations, and Eigenvalues. Optional topics include inner product spaces, solutions to systems of differential equations, and least squares. Lecture format. Prerequisite: C or better in MATH 1497 or C or better in CSCI 2330. [UD UCA Core: I]

3330 COMBINATORICS AND GRAPH THEORY  This course covers two advanced topics in discrete mathematics. Graph theory topics may include connectivity, traversability, matchings, and coloring. Combinatorics topics may include permutations, combinations, recurrence relations, and generating functions. Prerequisite: C or better in either MATH 2330 or MATH 2335.

3331 ORDINARY DIFFERENTIAL EQUATIONS I  Topics include linear and nonlinear first order equations, linear, second, or higher order equations, the Cauchy-Euler equation, and systems of linear first order equations. Applications from the natural sciences and engineering are emphasized. Lecture/computer activities. Prerequisite: MATH 1497. [UD UCA Core: C]

3351 NUMBER SYSTEMS: INTEGERS This course is a professional development course required for elementary education majors. The course organizes mathematical knowledge of whole number and integer concepts and operations, and number theory. In this course, teacher candidates will be able to connect concepts to mathematical processes, learn models for mathematical ideas, and explore the mathematics from the perspective of a student and a teacher. The primary method of delivery is through activities involving manipulatives, technology and problem solving. MATH 3351 does not fulfill a Mathematics major, minor, or Bachelor of Science special degree requirement. Prerequisite: C or better in MATH 1360 or MATH 1390 or declared major in elementary education.

3352 NUMBER SYSTEMS: REALS This course is a professional development course required for elementary, special education, and middle level education majors. The course organizes mathematical knowledge of real numbers, operations and properties of real numbers, percents, proportional relationships, essential concepts in algebra and functions. In this course, teacher candidates will be able to connect concepts, learn models for mathematical ideas, and explore the mathematics from the perspective of a student and a teacher. The primary methods of delivery is through activities involving manipulatives, technology and problem solving. MATH 3352 does not fulfill a Mathematics major, minor, or Bachelor of Science special degree requirement. Prerequisite: MATH 3351 or declared major in elementary, special education, or middle level education. Open to elementary, special education, or middle level education majors only.

3354 CONCEPTS OF DISCRETE MATHEMATICS This course, a requirement for middle-level mathematics teacher candidates and an option for secondary teacher candidates, is the study of modeling and solving problems involving sequential change and decision-making in finite settings. Topics include graph theory, number theory, recursion, counting methods, optimization, probability, combinations, and algorithmic problem solving. The primary methods of delivery are discussion and activities. Prerequisite: MATH 1390 or a content course above 1390.

3360 INTRODUCTION TO RINGS AND FIELDS This course is designed to introduce students to abstract mathematics. Topics include binary operations, the integers, modular number systems, rings, and fields. Prerequisite: MATH 2335 or consent of instructor.

3362 INTRODUCTION TO GROUP THEORY This course is designed to introduce students to abstract mathematics. Topics include groups, subgroups, group homomorphism, and the classification of finite abelian groups. Additional topics vary but may include Lie groups, representation theory, group actions, or Galois groups depending on the makeup of the class. Prerequisite: MATH 3320 or MATH 2335, or consent of instructor.

3364 CONCEPTS OF GEOMETRY AND MEASUREMENT This course is a requirement for middle-level mathematics teacher candidates. The course will use both hands-on and computer activities such as concrete geometric models, virtual manipulatives, and other dynamic geometry tools. Geometric reasoning and constructions will be emphasized using introductory proofs and computer explorations. This course will also connect geometry and measurement to other topics such as probability and algebra using geometric models and coordinate geometry. Delivery will include discussions, computer labs, and problem solving activities. MATH 3364 does not fulfill a Mathematics major, minor, or Bachelor of Science special degree requirement. Prerequisite: MATH 1390 (College Algebra) and MATH 3351 (Number Systems).

3370 MATHEMATICS IN THE SECONDARY SCHOOLS The main goal of this course is to review the mathematics curriculum currently taught in secondary schools and the corresponding curricular materials and instructional strategies with an emphasis on content knowledge for teaching. Class discussions, presentations, task analysis, and state and national standards are central to the course. MATH 3370 does not fulfill a Mathematics major or Bachelor of Science special degree requirement. Prerequisite: MATH 1496.

3381 DATA CLEANING AND VISUALIZATION This course provides an intensive, hands-on introduction to Data Cleaning with a statistical programming language. Students will learn the fundamental skills required to import, tidy, transform, manipulate, visualize, and communicate data using statistical programming software. Prerequisite: MATH 3311 or consent of the instructor.

3391 NONPARAMETRIC STATISTICS This course focuses on nonparametric procedures with desirable properties that hold under relatively weaker assumptions. Topics include Binomial test, sign tests, Wilcoxon Signed Rank Test, Permutation test, Wilcoxon Rank-Sum Test, Mann-Whitney Test, Siegel-Tukey Test, Kolmogorov-Smirnov Test, Kruskal-Wallis Test, Friedman’s Test, Cochran’s Q Test, Kendall’s W test, Spearman Rank Correlation, Bootstrap Methods, Smoothing methods, and Robust Model fitting. Prerequisite: MATH 3311 or consent of the instructor.

3392 MULTIVARIATE ANALYSIS This course is an introduction to multivariate analysis in data science and shows how multivariate statistical techniques can be applied to analyze datasets with many variables. Topics may include data visualization, principal components analysis, multidimensional scaling, exploratory and confirmatory factor analyses, structural equation models, and analysis of repeated measures data. Prerequisites: MATH 3311 and 3320, or consent of the instructor.

4V25 UNDERGRADUATE RESEARCH IN MATHEMATICS (Variable credit: 1-3 credit hours.) The student will engage in mathematical research under the supervision of a faculty mentor. Course may be repeated. Prerequisites: MATH 2471 and consent of instructor.

4200 INTRODUCTION TO EDUCATIONAL TESTING AND ASSESSMENT IN STEM This course is is designed to study the purpose, development, use, and analysis of assessments in teaching within STEM disciplines. Assessment policies and issues that impact teaching will also be discussed. Prerequisites: Admission to Teacher Education.

4301 SECONDARY MATHEMATICS METHODS Topics include innovative curricula for secondary mathematics topics, state and national standards, planning and organization in the classroom, strategies, methods, materials, technology, and other topics related to teaching and learning mathematics. Class discussions, presentations, and papers such as summaries and critiques are central to the course. Prerequisite: MATH 1497. [UD UCA Core: C]

4305 ORDINARY DIFFERENTIAL EQUATIONS II This course is an elective course for majors in mathematics and applied mathematics. The topics include ordinary and partial differential equations, Fourier series, and numerical analysis with modeling applications in physics, biology, and other sciences. Lectures, computer labs, and projects are central to the course. Prerequisite: MATH 3320 and 3331.

4306 MODELING AND SIMULATION This project-oriented capstone course applies techniques and methods in mathematics (such as differential equations, probability, statistics) to solve realistic problems from science, business, and industry. Lectures, computer labs, and projects. Prerequisites: MATH 2341 and 3331; and pre-/corequisites: MATH 3320 and 4371. [UD UCA Core: Z]

4310 GEOMETRY AND MEASUREMENT TOPICS FOR ELEMENTARY TEACHERS This course is a professional development course required for elementary education majors. Mathematical topics include geometry and measurement concepts, probability, and statistics. In this course, teacher candidates will be able to connect concepts to mathematical processes, learn models for mathematical ideas, and explore the mathematics from the perspective of a student and a teacher. The primary method of delivery is through activities involving manipulativcs, technology and problem solving. MATH 4310 does not fulfill a Mathematics major, minor, or Bachelor of Science special degree requirement. Prerequisite: C or better in MATH 3351 or equivalent.

4312 THE METRIC SYSTEM AND OTHER TOPICS FOR ELEMENTARY AND MIDDLE SCHOOL TEACHERS This course is a professional development course for elementary and middle school preservice teachers. Topics include converting in the metric system, measurement, geometry, and number systems. This activity-oriented course includes numerous hands-on materials for measuring and converting, presentations, article critiques, NCTM standards, and cooperative learning. MATH 4312 does not fulfill a Mathematics major, minor, or Bachelor of Science special degree requirement. Prerequisite: C or better in MATH 3351 or equivalent.

4313 FUNCTIONS AND MODELING This course is designed to strengthen and expand students’ knowledge of the mathematical modeling process and understanding of the use of cognitive, physical, and mathematical models in teaching. Students will model a variety of real-world situations using function models, geometric modeling, and data modeling, among others. Activities are designed to illuminate the connections between secondary and college mathematics and connections between various areas of mathematics; to illustrate effective uses of technology in teaching; and to engage in non-routine problem solving, problem-based learning, and applications of mathematics. Prerequisite: MATH 1497.

4314 APPLICATIONS OF MIDDLE LEVEL MATHEMATICS This course is required for the middle level mathematics/science education majors. The primary goal is to provide preservice teachers with the opportunity to learn mathematics and science as integrated content and pedagogy. Candidates enroll in this course concurrent with the middle level Teaching Internship I. The primary method of delivery is through activities, problem solving, projects, and presentations. MATH 4314 does not fulfill a Mathematics major, minor, or Bachelor of Science special degree requirement. Prerequisite: MATH 3352 and SCI 3320

4315 INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS  Topics in this course include solving first order linear, non-linear partial differential equations using the method of characteristics, and solving second order linear partial differential equations using separation of variables. Applications include heat conduction, steady state temperatures, and vibrating strings and membranes. Lecture. Prerequisites: MATH 2471 and 3331.

4316 FUNDAMENTALS OF APPLIED MATHEMATICS FOR FLUID MECHANICS AND GRANULAR MATERIALS This course is an introduction to applied mathematics in fluid mechanics and granular materials. It is an elective for all mathematics majors. Topics include dimensional analysis, perturbation methods for algebraic equations and differential equations, basic concepts and methods for fluid mechanics as well as granular materials. Prerequisite: MATH 4315.

4320 CONCEPTS OF CALCULUS This course is required for middle level teacher candidates in the mathematics/science track. The primary goal is to connect middle school mathematics content with advanced mathematics. Topics include the concepts of derivative, integral, Pick’s Theorem, Monte Carlo method, rates of change, and partitioning methods. In addition to the mathematics content, the course focuses on instructional methods, strategies, and connections to science topics. Delivery is mainly through discussion and problem solving activities. Prerequisite: MATH 3354 or MATH 3364.

4330 MATHEMATICAL MODELING IN BIOLOGY This elective course is an introduction to mathematical modeling and analysis in biology and life sciences. Topics include dynamic system theory, feedback control, enzyme kinetics, Michaelis-Menten equation, the Hodgkin-Huxley model, mathematical models for calcium dynamics and blood glucose regulation, numerical solutions and mathematical analysis of the models. A contemporary textbook, research papers on this subject, and MATLAB will be used. Primary methods of delivery are lecture, student presentations, and discussion. Prerequisite: C or better in MATH 2341 and 3331.

4335 CONCEPTS OF ADVANCED MATHEMATICS This course is required in the middle level mathematics/science degree and is designed to demonstrate the connections among all the strands in the middle school curriculum and to develop the algebra and number strands through standards-based materials. The course emphasizes the middle level transition from arithmetic to algebraic thinking and formal reasoning. Standards-based activities and assessments, critiques, and curriculum analysis are central to the course. MATH 4335 does not fulfill a Mathematics major, minor, or Bachelor of Science special degree requirement. Prerequisites: MATH 3354 or MATH 3364.

4340 NUMERICAL METHODS This course is a mathematics elective that introduces methods of numerical analysis with modern high speed computers. Topics include methods of solving nonlinear equations, linear and nonlinear systems, polynomial approximation, curve fitting, numerical differential equations, numerical optimization. Lecture and computer activities. Prerequisites: MATH 3320 and either MATH 2341 or MATH 1491, CSCI 1470, and CSCI 1480. Each prerequisite must have a grade of C or better.

4345 COLLEGE GEOMETRY This course is required for all mathematics majors with an education minor. The course focuses on the elementary theory in foundations of geometry, advanced Euclidean geometry, and introduces transformations and non-Euclidean geometries. Problem solving, discovery, computer activities, and lecture. Prerequisite: MATH 1496.

4350 INTRODUCTION TO THE HISTORY OF MATHEMATICS This course is required for all mathematics majors with an education minor. The course traces the historical development of topics encountered in the secondary mathematics curriculum from the rise of civilization through the eighteenth century. Explorations of historical problems are emphasized. The purpose of the course is to provide an understanding of the evolution of mathematical concepts and the contributions of diverse cultures. Lecture, research, and discussion. Prerequisite: MATH 1497. [UD UCA Core: D]

4360 TEACHING INTERNSHIP I This internship is required of secondary mathematics education majors. In the form of a one 8-hour day per week practicum, this course combines the study of discipline-specific teaching methods and materials with the study of secondary school curriculum. Candidates enroll in this internship concurrent with courses in methods, assessment, literacy, and the history of mathematics. Prerequisite: MATH 3370 and admission to Secondary Teacher Education. Required corequisites: MATH 4301, 4350, MSIT 4320 and 4325.

4362 ADVANCED CALCULUS I This rigorous theoretical treatment of calculus includes completeness, compactness, connectedness, sequences, continuity, differentiation, integration, and series. Prerequisites: MATH 2471 and MATH 2335 or consent of instructor. [UD UCA Core: Z]

4363 ADVANCED CALCULUS II  This course is a multivariable treatment of Advanced Calculus topics that include a rigorous study of partial differentiation, multiple integrals, Implicit Function Theorem, Fubini’s Theorem, line integrals, and surface integrals. Prerequisite: MATH 4362 or consent of instructor.

4371 INTRODUCTION TO PROBABILITY This course presents a calculus-based probability theory. Topics include axioms of probability, probability rules, conditional probability and Bayes theorem, discrete/continuous random variables with their distribution functions, expected values and variances, joint distribution, conditional distribution, covariance and conditional expectation. Prerequisite: MATH 1497. [UD UCA Core: R]

4372 INTRODUCTION TO STATISTICAL INFERENCE This course is an introduction to the core theory of statistical inference. Topics include review of probability/distribution theory, sampling distributions, limiting distributions and modes of convergence, methods of estimation such as MME, MLE, and UMVUE with their properties. Prerequisite: MATH 4371.

4373 REGRESSION ANALYSIS This course is an introduction to both the theory and practice of regression analysis. Topics include simple and multiple linear regression, linear models with qualitative variables, inferences about model parameters, regression diagnostics, variable selection, and the regression approach to analysis of variance (ANOVA). Prerequisite: MATH 3311 with a grade of C or higher, or consent of the instructor.

4374 INTRODUCTION TO STOCHASTIC PROCESSES This course is an introduction to applied mathematics in stochastic processes, computer science, management science, the physical and social sciences, and operations research. Topics include review of probability, Markov chains, continuous-time Markov chains, and stationary processes. Prerequisite: MATH 4371 or consent of instructor.

4375 INTRODUCTION TO TOPOLOGY   This course starts by asking, “What are the most general conditions that guarantee a function has a maximum value?” This requires generalizing the definition of “continuous” and leads to the definitions of a “topology” and of “compact.” This generalization process is then reversed, yielding a metrization theorem. Further topics may include brief introductions to differential manifolds, homology, and non-commutative geometry. Prerequisite: MATH 2471 or consent of instructor.

4380 SPECIAL PROBLEMS IN MATHEMATICS This course is an independent study or research project in a selected area of advanced mathematics. Prerequisite: Consent of instructor.

4381 SPECIAL PROBLEMS IN MATHEMATICS This course is an independent study or research project in a selected area of advanced mathematics. Prerequisite: Consent of instructor.

4385 COMPLEX ANALYSIS  The content of this course includes the arithmetic and geometry of the complex numbers, extension of transcendental functions to the field of complex numbers, analytic function theory, contour integration, and the Cauchy Integral Theorem, series, calculus of residues, and harmonic functions. This course is fundamental to physics and engineering as well as an extensive source of problems in pure mathematics. Prerequisite: MATH 2471 or consent of instructor.

4391 MACHINE LEARNING  This course is an introduction to common methods and algorithms used in machine learning. Content is broken down into supervised and unsupervised learning with an emphasis on using current cross-validation methods in either setting. Supervised topics include a variety of linear regression methods, classification and regression trees, and support vector machines. Unsupervised methods include cluster analysis and principal components. Students learn not only the theoretical underpinnings of learning, but also gain the practical know-how needed to quickly and powerfully apply these techniques to new problems using statistical software. Prerequisite: MATH 4373 or consent of the instructor.

4392 TIME SERIES AND FORECASTING This course is an introduction to time series analysis and forecasting in data science. Time series data are analyzed to understand the past and to predict the future. Topics include autocorrelation analysis, filtering time-series data, basic stochastic models, univariate time-series models, stationary models, non-stationary models, and long-memory processes. Prerequisite: MATH 4373 or consent of the instructor.

4395 PRACTICUM IN DATA SCIENCE The practicum serves as the capstone course for the Data Science track within the BS degree. Each student will be assigned a project under the supervision of a departmental faculty member. The products of the practicum will be a detailed, technical paper that details databases, methods of analyses, findings, and an oral presentation that summarizes the paper. Each student’s work should demonstrate a synthesis of the skills taught in the various classes within the data science curriculum. Prerequisite: MATH 4391.[UD UCA Core: Z]

4T90 INTERNSHIP II This course is designed for secondary pre-service teachers. The primary goal is to provide teaching experience under supervision in a school setting. Full-day involvement at a school site and in seminars is required. Prerequisites: Admission to the Internship and completion of all professional education courses. [UD UCA Core: Z]