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**MAT 1000-1001 Essential Mathematical Skills I-II**

*1 credit each term; total 2 credits *

A modified tutorial program intended to improve the basic quantitative skills of freshmen and other students. The subject matter includes pre-algebra and elementary algebra. The mathematics skills inventory administered during orientations for new students provides one basis for this recommendation. Offered every Term I and Term II.

**MAT 1030 College Algebra**

*3 credits*

Development of facility in computational and problem-solving procedures by examining the fundamental operations of the real number system. Topics include a review of basic operations with real numbers, rules of exponents and scientific notation, combining and factoring polynomials, solving linear and quadratic equations, solving systems of linear equations, inequalities, and absolute values and exponential and logarithmic functions. Prerequisites: MAT 1000 or an adequate score on the departmental placement test. Distribution Requirement: MAT. Offered every Term I and Term II.

**MAT 1091 Pre-Calculus I**

*4 credits*

The first course in a two term sequence designed to prepare students for the study of calculus. Topics will include analytic geometry, polynomial and rational functions, exponential and logarithmic functions, graphing and problem solving. Course includes a computer lab. Fulfills Math Competency. Prerequisites: MAT 1030 or an adequate score on the departmental placement test. Offered every Term I.

**MAT 1092 Pre-Calculus II**

*4 credits*

A continuation of the sequence designed to prepare students for calculus. Topics will include angles and their measures, trigonometric and inverse trigonometric functions, triangle trigonometry and trigonometric identities. Course includes a computer lab. Prerequisites: MAT 1091 or an adequate score on the departmental placement test. Offered every Term II.

**MAT 2001 Mathematics for Elementary Educators**

*4 credits*

An overview of number systems and numerical operations, intended to give pre-service elementary school teachers and understanding of numbers and geometric figures. It is also intended to instill an ability to communicate that knowledge. Topics will include sets, historical and other numeration systems, arithmetic operations and problem solving. Prerequisites: MAT 1030 or an adequate score on the departmental placement test. Offered as needed.

**MAT 2003 Mathematical History: Ancient to Medieval**

*3 credits*

A survey of the historical development of mathematics from antiquity to the Twelfth Century. Contributions of mathematics to the sciences and interactions between mathematics and other aspects of human civilization (such as the arts or the social sciences). Considerable mathematical content, including problem-solving using historical and modern methods. Prerequisites: MAT 1092 or an adequate score on the departmental placement test. Distribution Requirement: GN. Offered every Term I.

**MAT 2009 Mathematical History: Renaissance to Modern**

*3 credits*

A survey of the historical development of mathematics from the Twelfth Century to the Nineteenth Century. Contributions of mathematics to the sciences and interactions between mathematics and other aspects of human civilization (such as the arts or the social sciences). Considerable mathematical content, including problem-solving using historical and modern methods. Prerequisites: MAT 1092 or an adequate score on the departmental placement test. Distribution Requirement: GN. Offered every Term II.

**MAT 2010 Calculus I**

*4 credits*

The first course in a unified three-term calculus sequence involving functions of one variable. Limits, continuity, and derivatives of algebraic, trigonometric, and exponential functions and their inverses. Applications of differentiation to geometry and to the natural and social sciences. Three hours of computer laboratory per week using mathematical and productivity software. Prerequisites: MAT 1092: or an adequate score on the departmental placement test. Offered every Term I.

**MAT 2020 Calculus II**

*4 credits*

The second course in a unified three-term calculus sequence involving functions of one variable. Antiderivatives and definite integrals of algebraic, trigonometric, and exponential functions and their inverses, and an introduction to differential equations, with applications to geometry and to the natural and social sciences. Three hours of computer laboratory per week using a mathematical programming language and a symbolic algebra system. Prerequisites: MAT 2010 or an adequate score on the departmental placement test. Offered every Term II.

**MAT 2090 Statistical Methods**

*4 credits*

A survey of the principal means of providing and evaluating quantitative data. Topics include descriptive statistics, design and sampling in statistical studies, probability and probability distributions, estimation and hypothesis testing, and correlation and regression. Prerequisites: MAT 1030 or an adequate score on the departmental placement test. Offered every Term I and Term II.

**MAT 2100 Discrete Mathematics**

*4 credits*

Discrete mathematics includes a number of topics which do not belong to the traditional calculus sequence, but which are important to future educators and all wishing to deepen their understanding of mathematics. This course is an introductory survey. Topics include sets, number systems, logic, and proof techniques, combinatorics (counting arguments), and introductory graph theory. This course includes laboratory time where students work together to study the theory and practice of these topics Prerequisites: MAT 1092 or an adequate score on the departmental placement test. Offered every Term I.

**MAT 3010 Calculus III**

*4 credits*

The third course in a unified three-term calculus sequence involving functions of one variable. Sequences and series of numbers, power series and Taylor’s theorem. Polar coordinates, vectors in two and three dimensions, and parametric equations. Three hours of computer laboratory per week using a mathematical programming language and a symbolic algebra system. Prerequisites: MAT 2020 or an adequate score on the departmental placement test. Offered every Term I.

**MAT 3020 Ordinary Differential Equations**

*4 credits*

Methodology and theory for solving linear and non-linear ordinary differential equations using analytic, numerical and graphical techniques. Various applications to real world problems discussed. Includes computer lab using specialized software designed to solve and analyze differential equations. Prerequisite: MAT 3010. Offered alternate years beginning 2012-2013.

**MAT 3030 Vector Calculus**

*4 credits*

An introduction to the calculus of functions of several variables and vector analysis—the mathematical framework for modern physics. Topics include an introduction to the geometry of Euclidean space, vector valued functions (divergence, gradient and curl), line and surface integrals, Green’s Theorem, Stokes’ Theorem, and applications to physics. Prerequisite: MAT 3010. Offered alternate years beginning 2011-2012.

** MAT 3045 Introduction to Probability**

*3 credits*

A calculus-based introduction to probability theory, including axiomatic probability theory, random variables and functions of random variables, conditional probability, moments and moment-generating functions, and the Central Limit Theorem. Prerequisites: MAT 2100 and MAT 3030. Offered alternate years beginning 2012-2013.

** MAT 3050 Linear Algebra**

*4 credits*

A transition from computational mathematics to more theoretical mathematics, but also some powerful mathematical tools that can be applied in the natural and social sciences. Specific topics include matrix algebra and linear transformations, determinants, systems of linear equations, finite-dimensional vector spaces, eigenvalues and eigenvectors, and the geometry of Euclidean spaces. This course includes lab component. Prerequisites: MAT 2100 and MAT 2020. Offered alternate years beginning 2011-2012.

**MAT 3060 Abstract Algebra**

*4 credits*

An introduction to the study of abstract algebraic structures. Algebraic properties of familiar number systems are formalized into axiomatic systems, and abstract theory is then developed on the basis of the axioms alone. Topics include groups, rings, fields, isomorphisms and homomorphisms, and quotient structures. This course includes labs to study the theory of algebraic structures. Prerequisite: MAT 3050. Offered alternate years beginning 2012-2013.

**MAT 3155 Numerical Methods**

*3 credits*

An introduction to numerical methods of solving problems for which analytic solutions are either too cumbersome or nonexistent. Emphasis will be placed on the mathematical development of algorithms suitable for computer application. Various classes of problems common in the natural sciences and economics will be considered. Prerequisite: MAT 2020. Offered alternate years beginning 2011-2012.

**MAT-MGT 3200 Operations Analysis and Modeling**

*3 credits*

An introduction to operations research. It includes an examination of the nature of mathematical models and their role in choosing the “best” of several possible courses of action. The primary tool in this course will be linear programming, its derivatives and applications. Other topics include PERT, queueing theory, and inventory analysis. The course also includes an introduction computer software that is appropriate for solving problems with these techniques. Prerequisite: MAT 2090. Offered every Term II.

**MAT 3260 Introduction to Classical and Modern Geometry**

*3 credits*

A systematic and axiomatic study of Euclidean and Non-euclidean geometries. Topics will include Euclid’s geometry and the controversy about the fifth postulate; alternatives such as the taxicab geometry, hyperbolic geometry, and elliptic geometry. Prerequisite: MAT 2100. Offered every Term II.

**MAT-ECO 3350 Game Theory**

*3 credits*

Game Theory is the tool used to study the strategic interaction between players in a game. Used first in military strategy during World War II, it currently dominates economic theory and is beginning to be used in other fields such as Political Science, Biology, Law and Anthropology. This course is designed to be a thorough introduction to Game Theory. Emphasis will be put on applications in Economics, Political Science and Biology. Prerequisites: ECO 2010 and ECO 2020, or permission of the instructor. Offered Term I and Term II.

**MAT 3610 Introduction to Real Analysis**

*3 credits*

In this course, students are introduced to the analytical techniques of mathematics that depend upon the topology of the real numbers. The course covers: set theory, including cardinality; the axioms of the real number system and their consequences; the concept of the limit and its applications in calculus, including integration theory; the convergence of sequences and series of functions of a real variable; and an introduction to metric spaces as a generalization of real analysis. Prerequisites: MAT 2100 and MAT 3010. Offered Term II.

**MAT 4590 Mathematics Seminar**

*1.5 credits each term; total 3 credits*

A capstone experience for senior mathematics students requiring an extension of their mathematical knowledge into more advanced areas of study. Oral and written presentations by students are an integral part of this experience. Fulfills W-Course Requirement. Offered every Term I and Term II.

**MAT 4601 Topology**

*3 credits*

An introduction to the study of geometric properties that are independent of the concepts of shape and size. Topics include set theory, metric spaces, continuity of functions in general topological spaces, compactness, connectedness, and separation properties, with applications to Euclidean space. Prerequisites: MAT 2100 and MAT 3010. Offered as needed.

**MAT 4605 Theory of Numbers**

*3 credits*

An investigation of the properties of integers. Topics include divisibility, unique prime factorization, the Euclidean algorithm, linear congruences and linear Diophantine equations, multiplicative number-theoretical functions, and primitive roots. Prerequisites: MAT 2100 and MAT 2020. Offered as needed.

**MAT 4610 Real Analysis**

*3 credits*

An in-depth study of fundamental concepts and theorems of calculus. Topics include fundamental theorems on limits and continuity, differentiation, integration, implicit functions, and convergence. Prerequisite: MAT 3610. Offered as needed.

**MAT 4620 Complex Analysis**

*3 credits*

A survey of the theory and selected applications of classical complex analysis. Topics include the arithmetic of complex numbers, analytic function theory, differentiation and integration of complex functions, complex power series, and the theory of residues. Prerequisites: MAT 2100 and MAT 3010. Offered as needed.

**MAT 4630 An Introduction to Field Theory and The Classical Problems of Antiquity**

*3 credits*

An overview of the ideas from introductory level field theory that lead to the study of Galois Theory. Topics will be traced historically, beginning with the three classical problems of antiquity, squaring the circle, doubling the cube and trisecting an angle. Discussions will proceed through some extremely important ideas and mathematical results such as the transcendental nature of e and π and investigations of constructible numbers and solving polynomials by radicals. Prerequisite: MAT 3050 or 3060 or permission of the instructor. Offered as needed.

**MAT 4650 Applied Combinatorics**

*3 credits*

An investigation of advanced counting techniques that are useful in fields such as computer science, discrete operations research, and probability. Enumerative methods will be developed and their logical structure investigated. Topics may include graph theory, generating functions, recurrence relations, combinatorial modeling, and combinatorial proofs. Prerequisites: MAT 2100 and MAT 2020. Offered as needed.