MATH - Mathematics

This institutional credit course is required for all first-year students, with a declared major in mathematics. By providing an overview of academic policies, campus resources, and general graduation guidelines, the seminar is designed to help students succeed in their university endeavors. In addition, the seminar will focus on building skills in preparation for completing the major requirements. This course does not count toward the total hours required for graduation.

This course is an alternative in Area A of the Core Curriculum and is not intended to supply sufficient algebraic background for students who intend to take Precalculus or the calculus sequences for mathematics and science majors. This course places quantitative skills and reasoning in the context of experiences that students will be likely to encounter. It emphasizes processing information in context from a variety of representatives, understanding of both the information and the processing, and understanding which conclusions can be reasonably determined.

Prerequisite: Four years of high school mathematics. Students who have completed a course in calculus in high school with a grade of B or better may not enroll for credit in this course without permission of the chair of the Department of Mathematics. This course is an introduction to mathematical modeling using graphical, numerical, symbolic, and verbal techniques to describe and explore real world phenomena. Emphasis is on the use of elementary functions to investigate and analyze applied problems and questions, supported by the use of appropriate technology, and on effective communication of quantitative concepts and results.

This course is a symbolically intensive, functional approach to algebra that incorporates the use of appropriate technology. Emphasis will be placed on the study of functions and their graphs, inequalities, and linear, quadratic, piece-wise defined, rational, polynomial, exponential, and logarithmic functions. Appropriate applications will be included.

Prerequisites: Grade of C or better in MATH 1111 or equivalent. This course is designed to prepare students for calculus, physics, and related technical subjects. Topics include an intensive study of algebraic and transcendental functions accompanied by analytic geometry.

Prerequisite: Four years of high school mathematics. Topics covered will include the basic trigonometric functions, graphs of trigonometric functions, identities, triangles, the law of sines and the law of cosines. Also covered are the conic sections and their graphs. Students may not receive credit for both MATH 1113 and MATH 1114.

Prerequisite: C or better in Area A mathematics. This course introduces the concepts of differential and integral calculus useful to students in business, economics, biology, and the social sciences. Topics include: the derivative, methods of finding derivatives, applications of derivatives, the integral, methods of integration, applications of integrals, and elementary multivariable calculus. A student may not receive credit for MATH 1260 and MATH 1261. MATH 1260 does not substitute for MATH 1261 in any course that has MATH 1261 as a prerequisite or in any degree program that requires MATH 1261.

Prerequisite: C or better in MATH 1113 or MATH 1114 or an average of B or better in four years of high school mathematics including a course in trigonometry or permission of the instructor. This course introduces the fundamental concepts of calculus: limits, continuity, differentiation, transcendental functions, and Riemann Integration. Applications of these topics are included.

Prerequisite: C or better in MATH 1261. This course covers further topics in calculus: techniques of integration, analytic geometry and vectors, infinite series, and polar coordinates.

Prerequisite: Completion of Area A mathematics with a grade of C or higher. This course is an Area F introductory mathematics course that may only be taken by pre-early childhood and special education majors. This course will emphasize the understanding and use of the major concepts of number and operations. As a general theme, strategies of problem solving will be used and discussed in the context of various topics. A student may not receive credit for both MATH 2008 and MAED 3001. Enrollment is restricted to early childhood education majors and special education majors.

Prerequisite: C or better in MATH 1261. An introduction to the algebra and geometry of Euclidean 2-space and 3-space and its generalization to n-space and also a transition to the study of abstract vector spaces. Topics include systems of linear equations, matrix algebra, determinants, vector spaces, linear transformations, and an introduction to eigenvectors and eigenvalues.

Prerequisite: C or better in MATH 1262. Multi-variable and vector calculus. Topics include vectors, functions of several variables, partial derivatives, multiple integration, Green's and Stoke's Theorem.

Completion of Area A2 mathematics requirement. This course will introduce students to selected topics in advanced mathematics with the aim of conveying to students that mathematics deals with large and universal questions, that it does so in a unique and compelling way, and that mathematics has much to contribute to other areas of thought. The topics covered will be selected from number theory, set theory, graph theory, abstract algebra, and geometry.

Prerequisite: C or better in Area A mathematics. This course is an overview of descriptive and inferential statistics, with topics in exploratory data analysis, basic experiment design, probability distributions and elementary statistical inference.

Prerequisite: C or better in MATH 1261 or MATH 2600 and permission of instructor. This course is an introduction to the mathematics of the Incas in pre-Columbian Latin America. Inca engeneering and astronomy are investigated and their mathematical framework is compared with earlier pre-Columbian cultures and modern western cultures. Topics also include quipus and the geometry of Inca textiles and ceramics.

Prerequisite: C or better in MATH 1262. This course is an introduction to abstract mathematics and the nature of a mathematical proof. Topics include: methods of proof, symbolic logic, set theory, relations and functions, countable and uncountable sets.

Prerequisite: C or better in MATH 2600. This course is a continuation of MATH 2600. It introduces correlation, simple and multiple linear regression, logistic regression. Topics include: correlation, estimation via least squares, inference for the intercept and coefficients of a linear model, binary response variables and log-linear models.

Prerequisite: C or better in MATH 3030 and permission of the instructor. This course consists of directed readings in mathematics under the supervision of a faculty member. Material may be drawn from classical and modern texts as well as the literature. This course is repeatable for credit.

Prerequisite: C or better in both MATH 2263 and MATH 2150. This course will concentrate on the bridge between a variety of mathematical ideas and their applications to problems in the natural and social sciences through the techniques of mathematical modeling. The course will emphasize out-of-class project work and the written presentation of modeling results and conclusions.

Prerequisite: C or better in MATH 3030. This course is a review of the origins and development of the great ideas of classical and modern mathematics. The emphasis will be on mathematics as a living organism, constantly being invented, improved, and expanded. Important theorems and important mathematicians will be studied, as well as the historical and cultural contexts in which they arose.

Prerequisite: C or better in MATH 3030. An introduction to the basic structures of algebra including groups, rings, and fields along with their substructures as well as the ideas of homomorphism and isomorphism.

Prerequisite: C or better in MATH 3030. An introduction to the basic problems, terminology, and methods of elementary number theory. Topics include: division algorithm, Euclidean algorithm, Diophantine equations, fundamental theorem of arithmetic, prime numbers and their distribution, perfect numbers, congruences, Fermat's Little Theorem, Wilson's Theorem, Euler's Phi Function, Euler's Theorem, primitive roots, and quadratic reciprocity.

Prerequisite: C or better in MATH 2150. A rigorous study of vector spaces and linear transformations over arbitrary fields. Topics include linear maps and dual spaces, inner products and orthogonality, eigenvalues and eigenvectors, triangulation and canonical forms.

Prerequisite: C or better in both MATH 2263 and MATH 3030. Basic properties of the real numbers, limits, continuity of functions, formal definitions of derivative and integral.

Prerequisite: C or better in both MATH 2263 and MATH 3030. An introduction to functions of a complex variable. Topics include the Cauchy-Riemann equations, line integrals, the Cauchy integral formulas, Laurent series, harmonic functions and conformal mapping.

Prerequisite: C or better in MATH 2263. Ordinary differential equations with applications are the primary focus. Some consideration is given to existence and uniqueness theorems.

Prerequisite: C or better in MATH 3030. An axiomatic development of Euclidean geometry and an introduction to non-Euclidean geometry.

Prerequisite: C or better in MATH 2263 and (C or better in MATH 2150 or C or better in MATH 3030). A calculus-based first course in probability theory. Topics include combinatorial analysis, probability axioms, conditional probability, independence, discrete and continuous random variables, jointly distributed random variables, expectation, and limit laws such as the weak and strong laws of large numbers and the central limit theorem.

Prerequisite: C or better in MATH 4600. A calculus-based introduction to the theory and applications of statistical methods. Topics include estimation and prediction, inference and hypothesis testing, linear and multiple regression, analysis of variance, and nonparametric statistical methods.

Prerequisite: C or better in MATH 2150, MATH 1262, and CSCI 1302 or equivalents. A general algorithmic approach to numerical analysis with emphasis on concrete numerical methods. (This course is equivalent to CSCI 4650.)

Prerequisite: C or better in both MATH 2263 and MATH 2150. A basic introduction to operations research. Linear, integer and dynamic programming will be considered. The theory of queues is presented and the idea of stochastic simulation is introduced.

Prerequisite: C or better in MATH 3030 and permission of the instructor. This course consists of directed readings in mathematics under the supervision of a faculty member. Material may be drawn from classical and modern texts as well as the literature. This course is repeatable for credit.

Prerequisite: Permission of the instructor. Investigation of a topic of special interest under the supervision of a faculty member. This course is repeatable for credit.

Prerequisite: Permission of the instructor. Selected topics not available in other departmental courses. This course is repeatable for credit.

Prerequisite: Selection for participation in a University-approved Internship program. An individually designed course involving off-campus study, research, and/or work in a governmental agency or business organization. This course is repeatable for credit.

Prerequisite: Completion of all area F courses, MATH 3030, and at least one MATH 4000 level course with a C or better and permission of the faculty advisor. This course is an introduction to research in the discipline of mathematics. Students will explore a topic in-depth and develop basic research skills in mathematics. This course is one component of the Senior Capstone Requirement for Mathematics majors.

Prerequisite: MATH 4989 with a grade of C or higher and permission of faculty advisor. Research, writing, and presentation of a scholarly project. This course is a component of the Senior Capstone Experience for Mathematics majors.

Prerequisites: Completion of all Area F mathematics requirements with a grade of B or better and permission of the instructor. This course affords interested junior and senior students an opportunity to participate in a basic research experience with a member of the Department faculty. This course is repeatable for credit.