Return to Mathematics | Courses Index

## [1] Courses in Mathematics (MATH)

**1150 MATHEMATICS DISCOVERY SEMINAR** The purpose of the seminar is to improve students’ analytical thinking and problem-solving skills early in their mathematics careers by introducing the logical foundations of mathematics and by developing and implementing group and individual problem-solving strategies. Seminar format. Prerequisite: MATH 1390 or equivalent. On demand.

**1191 MATHEMATICS SOFTWARE** This course is an elective for a major in applied mathematics. As an introduction to computer algebra software, such as Mathematica, Derive, and other current software, this course provides students with basic computer skills for applications throughout the mathematics curriculum and prepares students who are enrolled in calculus or pre-calculus to use technology to enhance their understanding of mathematics. Laboratory. Prerequisite: MATH 1390 or equivalent. Recommended Corequisite: MATH 1496. On demand.

**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 utilize the models to solve problems. Lecture/demonstration format. Prerequisite: Math ACT of 19 or higher or C or better in UNIV 1340. Fall, spring, summer. **[ 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. Prerequisite: MATH ACT of 19 or higher or C or better in UNIV 1340. Fall, spring, summer.**[ ACTS: MATH1103 ]**

**1392 PLANE TRIGONOMETRY** Coupled with College Algebra (MATH 1390), this course satisfies the prerequisites for Calculus I (MATH 1496) as an alternative to MATH 1580. Topics include angles and triangles and their measure, graphs and applications of trigonometric functions, and inverse trigonometric functions, vectors, polar coordinates, and complex numbers. Lecture/demonstration format. Prerequisite: MATH 1390 or equivalent. Fall, spring, summer. **[ ACTS: MATH1203 ]**

**1395 APPLIED CALCULUS FOR BUSINESS AND ECONOMICS** As a component of the business foundation, this course is a requirement for all majors in the College of Business Administration. The course is an introduction to calculus involving algebraic, exponential, and logarithmic functions including quantitative methods and applications used in business, finance, and economics. Calculus topics include limits, derivatives, optimization, and marginal analysis in business and economics. Problem solving and calculator technology will be emphasized. Lecture/demonstration format. Prerequisite: MATH 1390 (C grade or higher) or equivalent. Fall, spring, summer.

**1491 APPLIED CALCULUS FOR THE LIFE SCIENCES** This course is a brief introduction to calculus and includes differentiation and integration of polynomial, exponential, and logarithmic functions, solutions of basic differential equations, and the application of these techniques to solve physical problems particularly in the life sciences such as biology. Lecture/demonstration format. Prerequisite: MATH 1390 or equivalent. Fall, spring.

**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: C or better in MATH 1390 and C or better in MATH 1392, or C or better in MATH 1580, or equivalent . Fall, spring. **[ 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. Fall, spring. **[ ACTS: MATH2505 ]**

**1580 ALGEBRA AND TRIGONOMETRY** Designed for students who plan to study calculus, this course may be used to meet the general education requirement in mathematics and includes the study of concepts of algebra and trigonometry essential to the study of calculus. Technology such as the graphics calculator is used extensively. Meets five days a week. Lecture/Activity Format. Not open to students who already have credit for MATH 1390 or MATH 1392. Prerequisite: Math ACT of 19 or higher or C or better in UNIV 1340. Fall, spring. **[ ACTS: MATH1305 ]**

**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. On demand.

**2311 STATISTICAL METHODS I ** 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. The course introduces the basics of descriptive statistics, probability theory, and statistical inference. The use of appropriate technology is emphasized. Lecture/Activity format. Prerequisite: MATH 1390 or equivalent. Fall, spring, summer. **[ 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 sets, relations, functions, induction and recursion, graphs and digraphs, trees and languages, algebraic structures, groups, Boolean algebra, and finite state machines. Lecture and problem-solving activities. Prerequisite: CSCI 1470 and MATH 1491 or MATH 1496, or consent of instructor. Fall.

**2335 TRANSITION TO ADVANCED MATHEMATICS** This 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: MATH 1497. Fall, spring.

**2441 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. Topics will include applications of summations, iterative methods, recursion, polynomial approximations and trigonometric approximations. Lecture/Computer Lab format. Prerequisite: C or better in Math 1497. Fall.

**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. Fall, spring, summer. **[ 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. On demand.

**3311 STATISTICAL METHODS II **This course emphasizes intermediate and advanced statistical data analysis, including various hypothesis tests, multiple linear regression, experimental designs, and analysis of variance (ANOVA). Statistical software will be used for data analysis. Prerequisite: MATH 2441 or equivalent and consent of instructor. Spring.

**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: MATH 1497 or 2330. Fall, spring, summer. [UD UCA Core: I]

**3330 DISCRETE STRUCTURES II** This course in discrete mathematics is designed for mathematics and computer science majors. The topics include recursion, graph theory, matrices, algorithms, basics of formal languages and automata theory. Applications leading to the development of algorithms are emphasized. Lecture format. Prerequisite: MATH 2330 or MATH 2335. Spring.

**3331 ORDINARY DIFFERENTIAL EQUATIONS I** This course is required for applied mathematics majors and is an elective for all other mathematics majors. Topics include linear and nonlinear first order equations, linear second 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. Fall, spring. [UD UCA Core: C]

**3351 NUMBER SYSTEMS: INTEGERS** This course is a professional development course required for elementary education majors. A primary goal is to organize mathematical knowledge of the real number system so that teacher candidates connect concepts to processes, learn models for mathematical ideas, and experience the construction of mathematics through problem solving. The primary method of delivery is through activities involving manipulatives 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 1390 or higher and intent to apply for admission to Teacher Education. Fall, spring, summer.

**3352 NUMBER SYSTEMS: REALS** This course is a professional development course required for elementary and middle-level education majors. The primary goal is to organize mathematical knowledge of the Real Number system, operations and algebraic thinking and supporting content including data analysis so that candidates can develop the six types of knowledge that research has identified as necessary for teachers: common content knowledge, specialized content knowledge, knowledge on the mathematical horizon, knowledge of content and students, knowledge of content and teaching and knowledge of curriculum. The primary methods of delivery will be investigation (including use of models), problem solving, and discussion. MATH 3352 does not fulfill a Mathematics major, minor, or Bachelor of Science special degree requirement. Prerequisite: MATH 3351 and declared major in teacher education. This course is not open to non-education majors. Fall, spring and summer as needed.

**3354 CONCEPTS OF DISCRETE MATHEMATICS** This course, required for middle level mathematics/science 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. MATH 3354 does not fulfill a Mathematics major, minor, or Bachelor of Science special degree requirement. Prerequisite: MATH 1390 (College Algebra) and MATH 3351 (Number Systems). Spring.

**3360 INTRODUCTION TO RINGS AND FIELDS** A required course for majors in pure mathematics, UCA STEMteach Pure Mathematics, and UCA STEMteach Mathematics Education tracks. This course is designed to introduce students to abstract mathematics. Topics include binary operations, the integers, modular number systems, rings, and fields. Lecture format. Prerequisite: MATH 2335. Fall.

**3362 INTRODUCTION TO GROUP THEORY** A required course for majors in pure mathematics. The 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. Lecture format. Prerequisites: MATH 2335, and **either** MATH 3320 **or** PHYS 3341. Spring.

**3364 CONCEPTS OF GEOMETRY AND MEASUREMENT** This course is designed for middle level teacher candidates that will use both hands-on and computer activities such as concrete geometric models, virtual manipulatives, and Geometer’s Sketchpad software. 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). Fall.

**3370 MATHEMATICS IN THE SECONDARY SCHOOLS** This course is designed for secondary mathematics education majors and minors. The main goal is to review the mathematics curriculum currently taught in secondary schools and the corresponding curricular materials and instructional strategies. Class discussions, presentations, curriculum critiques, and the NCTM standards are central to the course. MATH 3370 does not fulfill a Mathematics major, minor, or Bachelor of Science special degree requirement. Prerequisite: Admission to Secondary Teacher Education or the intent to register for MATH 4301 in the subsequent semester. Spring.

**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. On demand.

**4200 INTRODUCTION TO EDUCATIONAL TESTING AND ASSESSMENT IN MATHEMATICS** This course is required for majors and minors in mathematics education who plan to seek teacher licensure. The course is designed to study the purpose, analysis, and construction of various assessments and the assessment policies and issues that impact teaching. Class discussions, projects, and presentations are central to the course. Prerequisites: MATH 3370 and Admission to Teacher Education. Corequisite: MATH 4301. Fall.

**4301 SECONDARY MATHEMATICS METHODS** This course is required for majors in mathematics education who plan to seek teacher licensure. Topics include innovative curricula for secondary mathematics topics, NCTM 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 2471, 3370. Fall. [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. Fall.

**4306 MODELING AND SIMULATION** This is a capstone course required for majors in applied mathematics, STEMteach applied mathematics track, and serves as an elective course for other tracks in mathematics. This project-oriented course applies techniques of differential equations and other methods to solve realistic problems from science, business, and industry. Lectures, computer labs, and projects. Prerequisites: MATH 2441, 3320, 3331, and 4371. Spring. [UD UCA Core: Z]

**4310 GEOMETRY AND MEASUREMENT TOPICS FOR ELEMENTARY TEACHERS** This course is a professional development course required for early childhood pre-service teachers. Mathematical topics include geometry, probability, statistics, measurement, NCTM standards, and technology. Class discussions, presentations, article critiques, discovery and cooperative learning are central to the course. 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. Fall, spring, summer.

**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. On demand.

**4313 FUNCTIONS AND MODELING** This course includes explorations and lab activities designed to strengthen and expand students’ knowledge of secondary education mathematics topics. Students collect data and explore a variety of situations that can be modeled using linear, exponential, polynomial, and trigonometric functions. Activities are designed to engage students in a deeper look at topics to which they have been previously exposed, to illuminate the connections between secondary and college mathematics, to illustrate good uses of technology in teaching, to illuminate the connections between various areas of mathematics , and to engage in serious, non-routine problem solving, problem-based learning, and applications of mathematics. This course is required for mathematics majors who are completing the STEM education minor. Prerequisite: MATH 1497. Fall and spring.

**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 3351 and SCI 3320 and admission to Middle Level Teacher Education. Required corequisite: MSIT 4411. Fall.

**4315 INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS** This course introduces techniques for solving first and second order linear partial differential equations. Topics include quasi-linear first order partial differential equations, and the method of characteristics, second order linear partial differential equations separation of variables of the heat equation, wave equations, and Laplace’s equations. Applications include heat conduction, steady state temperatures, and vibrating strings and membranes. Lecture. Prerequisites: MATH 2441, 2471 and 3331. Fall.

**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. Spring.

**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. Fall.

**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 2441 and 3331. Fall.

**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 and admission to Middle Level Teacher Education. Spring.

**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. Prerequisite: MATH 2441 and 3320, both with a grade of C or better. Fall.

**4345 COLLEGE GEOMETRY** This course is required for majors in mathematics education who plan to seek teacher licensure. 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. Spring, summer.

**4350 INTRODUCTION TO THE HISTORY OF MATHEMATICS** This course is required for majors in mathematics education who plan to seek teacher licensure. The course traces the historical development of topics encountered in the secondary mathematics curriculum from the rise of civilization through the eighteenth century. The purpose of the course is to provide the prospective teacher with an understanding of the evolution of mathematical concepts and a pedagogical appreciation for the problems involved in the development of the concepts. Lecture, research, and discussion. Prerequisite: MATH 1497. Fall. [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 course is required for mathematics majors and serves a mathematics elective for applied mathematics majors. This rigorous theoretical treatment of calculus includes completeness, compactness, connectedness, sequences, continuity, differentiation, integration, and series. Lecture format and problem solving. Prerequisite: MATH 2471. Fall. [UD UCA Core: Z]

**4363 ADVANCED CALCULUS II** This course is an elective for mathematics and applied mathematics majors. 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. Spring.

**4371 INTRODUCTION TO PROBABILITY** This course is required for all majors in mathematics, mathematics education, and applied mathematics. This calculus-based introduction to probability and the distributions and properties of several discrete random variables includes hypergeometric, geometric, binomial, negative binomial, Poisson, and the distributions and properties of several continuous random variables, including normal, gamma, uniform, chi-squared, t, and F. Lecture format. Prerequisite: MATH 1497. Fall. [UD UCA Core: R]

**4372 INTRODUCTION TO STATISTICAL INFERENCE** This course is required for majors in applied mathematics and serves as an elective for majors in mathematics. This introduction to the theory of statistical inference includes sampling distributions, point and interval estimation, hypothesis testing, and linear models. Lecture and projects. Prerequisite: MATH 2441 and 4371. Spring.

**4373 REGRESSION ANALYSIS** This course is an elective course for majors in mathematics and applied mathematics. This introduction to simple and multiple linear models and the analysis of variance (ANOVA) includes estimating the parameters of linear models and testing estimates. Students will learn basic designs of experiments and data analysis using ANOVA and examine applications in science, business, and industry. Lecture and projects. Prerequisite: MATH 4372. Fall.

**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. It is an elective course for all mathematics majors. Topics include review of probability; conditional probabilities and conditional expectations. Markov chains, continuous-time Markov chains, renewal theory, queuing theory, reliability theory, Brownian motion and stationary processes. Prerequisite: MATH 4371 or consent of instructor. Fall.

**4375 INTRODUCTION TO TOPOLOGY I** This course is an elective for all mathematics majors and minors. This course is an introduction to the study of the properties of continuous functions, including applications to knots, surfaces, and function spaces. Lecture/seminar format. Prerequisite: Consent of instructor. On demand.

**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. Fall, summer.

**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. Spring, summer.

**4385 COMPLEX ANALYSIS** This course is an elective for majors and minors in mathematics. The content of the 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. Lecture and discussion. Prerequisite: MATH 2471. On demand.

**4680, 4681 TEACHING INTERNSHIP II** This course is designed for secondary preservice 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. Student is required to enroll in MATH 4680 and 4681 simultaneously. Spring. [UD UCA Core: Z]