# 4000

## MATH 4000 Methods of Math Modeling

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.

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## MATH 4010 History of Mathematics

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.

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## MATH 4081 Abstract Algebra I

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.

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## MATH 4100 Linear Regression

Prerequisite: C or better in MATH 2600, or permission of the instructor. 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.

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## MATH 4110 Number Theory

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.

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## MATH 4150 Linear Algebra: A 2nd Course

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.

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## MATH 4261 Mathematical Analysis I

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.

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## MATH 4300 Complex Variables

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.

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## MATH 4340 Differential Equations

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.

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## MATH 4510 Geometry

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

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## MATH 4600 Probability

Prerequisite: C or better in MATH 1262. 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.

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## MATH 4620 Mathematical Statistics

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.

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## MATH 4650 Numerical Analysis

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.)

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## MATH 4680 Introduction to Graph Theory

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.

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## MATH 4900 Directed Readings

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.

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## MATH 4940 Independent Study

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.

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## MATH 4950 Special Topics

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

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## MATH 4960 Internship

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.

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## MATH 4989 Intro to Research in Math

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.

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## MATH 4990 Senior Project

Prerequisite: MATH 4989 with a grade of C or higher and permission of faculty advisor. This course is a continuation of research in the discipline of mathematics. Students will write a paper and orally present the results of the inquiry to the Department of Mathematics. This course is one component of the Senior Capstone Requirement for Mathematics majors.

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## MATH 4999 Undergraduate Research

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.

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