MAT 090 Basic Algebra (3 Institutional Credit Hours)

This course is intended to develop those ideas, computational techniques, and methods of reasoning used in college mathematics, with an emphasis on algebra needed to formulate and solve first and second degree equations, constructing models using linear and quadratic functions; and concepts of coordinate geometry. Only for students entering Fall 1999 or later who have not passed either the Accuplacer Elementary Algebra Test or the College Level Math Test or for those students who entered before Fall 1999 who have not satisfied the Basic Mathematics Competency Requirement. Does not give degree credit. Three lecture hours per week.

MAT 108 Finite Mathematics (3 Credit Hours) DII

Prerequisite: Completion of the Basic Mathematics Competency Requirement.

MAT 110 Precalculus (3 Credit Hours) DII

Prerequisite: Completion of the Basic Mathematics Competency Requirement.

This course is intended to prepare the student for the study of Calculus. Topics include: properties of the real number systems; absolute values, inequalities; detailed study of linear and quadratic equations; polynomial and rational functions and their graphs; exponential, logarithmic, and trigonometric functions.  Three lecture hours per week.  Not open to students who have received credit for MAT 202N.

MAT 120 Mathematics for the Liberal Arts (3 Credit Hours) DII

Prerequisite: Completion of the Basic Mathematics Competency Requirement.

This course is designed to give the liberal arts student, as well as other interested students, an introduction to some mathematical topics usually reserved for specialists. Topics are selected on the basis of their role in solving mathematical problems. Such topics include probability and descriptive statistics, graph theory, cryptography, game theory, chaos, and problems relating to the environment. Classroom lectures and discussions cover the basics theories. These are followed by writing assignments which form an essential component of the course.  Not open to math majors without the permission of the Department Chairperson.

MAT 123 Mathematics for the Elementary Teacher I (3 Credit Hours) DII

Prerequisite: Completion of the Basic Mathematics Competency Requirement.

This course is designed for prospective elementary teachers. Those mathematical concepts which school teachers will be teaching are stressed. Topics include: Numeration systems, algorithms and estimation for the arithmetic operations on different sets of numbers, number theory, and probability concepts. Use of manipulatives and relevant technology including graphing calculators and computer software may be integrated into the course.  Three lecture hours per week. Not open to those who received credit for MAT 123A

MAT 124 Mathematics for the Elementary Teacher II (3 Credit Hours) DII

Prerequisite: Completion of the Basic Mathematics Competency Requirement.

This course is designed for prospective elementary teachers. Those mathematical concepts which school teachers will be teaching are stressed. Topics include: geometric figures and solids, congruence, similarity, constructions, measurement including perimeter, area, surface area and volume, geometric transformations, descriptive statistics. Use of manipulatives and relevant technology including graphing calculators and computer software may be integrated into the course. Not open to students who have received credit for MAT 223A. Three lecture hours per week.

MAT 205 Analytic Geometry (3 Credit Hours) DII

Properties of straight lines, conic sections and other algebraic curves, transcendental curves, polar coordinates, introduction to vectors and elementary 3-dimensional geometry. Not open to Math majors without permission of the Department Chairperson. Three lecture hours per week.

MAT 208 Business Calculus (3 Credit Hours) DII Q

Prerequisite: Completion of the Basic Mathematics Competency Requirement.

Introduction to calculus as applied to business. Differentiation, integration, and their applications are considered in conjunction with polynomial, algebraic, exponential, and logarithmic functions. Three lecture hours per week.

MAT 214A Discrete Structures (4 Credit Hours) DII

Prerequisite: MAT 220 Calculus I.

A study of discrete mathematical structures of interest in computer science and other applied fields. Applications-oriented study of: formal logic, algebra of sets, permutations and combinations, mathematical induction, recursion, graphs, trees, logic gates and circuits and finite state machines. Three lecture hours per week. Not open to students who have already completed MAT 314.

MAT 218 Introduction to Mathematical Computing (1 Credit Hours)

Prerequisite: MAT 220.

An introduction to a computer algebra system. Topics include the application of a computer algebra system to plotting functions, solving equations, simplifying expressions, and the creation of clear and attractive mathematical reports. One lecture hour per week.

MAT 220 Calculus I (4 Credit Hours) DII

Prerequisite: Knowledge of algebra and trigonometry is assumed.

This course includes functions and their limits, slopes and tangent lines, differentiation rules (including those for trigonometric functions), Chain Rule, linearizations, approximations, Newton's Method, extreme values and curve sketching, optimization, and the Mean Value Theorem and its applications. Also included is an introduction to integration with applications to area between curves, the Fundamental Theorems of Integral Calculus and the basic integration techniques.  Four lecture hours per week.

MAT 221 Calculus II (4 Credit Hours) DII

Prerequisite: MAT 220

This course is a further development of the calculus of functions of one variable. Topics include logarithmic and exponential functions and their derivatives and integrals, exponential growth and decay, inverse trigonometric functions, techniques of integration, numerical integration with error estimates, applications of the integral, indeterminate forms and l'Hospital's rule. Infinite sequences and infinite series with error estimation.  Four lecture hours per week.

MAT 234 Introduction to Mathematical Proof (3 Credit Hours)

Prerequisite: MAT 220.

An introduction to mathematical proof and the fundamental notions of higher mathematics. Topics include the basics of propositional logic, set theory, mathematical induction, functions, equivalence relations, and cardinality with an emphasis on writing proofs. Three lecture hours per week.

MAT 247 Statistics I (3 Credit Hours) DII Q

Prerequisite: Completion of the Basic Mathematics Competency Requirement.

An elementary introduction to statistical concepts, probability, frequency distributions, sampling testing of hypothesis, and linear regression. The emphasis is on practical and usable results, rather than on mathematical derivations. This course can prepare the student for the use of statistics in business, economics, the social sciences, or education. Not open to Math majors without permission of the Department Chairperson. Three lecture hours per week.

MAT 303A Abstract Algebra I (3 Credit Hours) DII

Prerequisite: MAT 214 or MAT 221

This course provides a systematic study of the most common and useful rings and groups: integers, rational numbers, real numbers, complex numbers, residue classes, polynomials, and matrices. Both computational and structural aspects are treated. Three lecture hours per week. Not open to students who have received credit for MAT 303.

MAT 304A Linear Algebra I (3 Credit Hours) DII

Prerequisite: MAT 214 or MAT 221

A systematic study of vector spaces and linear transformations including the algebra of matrices, determinants, inner products, eigenvalues, and eigenvectors. Three lecture hours per week.

MAT 306 Number Theory (3 Credit Hours)

Prerequisite: MAT 303

An introduction to divisibility theory, prime numbers, congruences, Diophantine equations, number-theoretic functions, primitive roots, and indices, and quadratic residues. Three lecture hours per week.

MAT 308 Linear Programming (3 Credit Hours) DII

Prerequisite: MAT 220 or equivalent

Topics studied: linear equations and inequalities, convex regions, the simplex algorithm, duality and minimax theorems, matrix games, transportation and assignment problems. Experience is provided in the computer solution of linear programming problems and in applications to business and the sciences. Three lecture hours per week.

MAT 314 Discrete Mathematics (3 Credit Hours)

Prerequisite: MAT 303

Topics include finite-state machines, feedback, partially ordered sets, lattices, recursion and iteration with applications to logic, circuit design, and computer systems. Three lecture hours per week.

MAT 316 Combinatorial Mathematics (3 Credit Hours)

Prerequisite: MAT 214 or MAT 221

A survey of combinatorial methods including graphs, networks, permutations and combinations, partitions, and enumeration theory. Three lecture hours per week.

MAT 320 Calculus III (4 Credit Hours)

Prerequisite: MAT 221

This course extends important ideas of single variable calculus to higher dimensional settings. Topics include polar coordinates and calculus using polar coordinates, vector algebra and vector valued functions, cylindrical and spherical coordinates, calculus of multivariable functions (partial derivatives, limits, continuity, directional derivatives, gradients, Chain Rule), tangent planes and approximation, maxima and minima, double and triple integrals in Cartesian, cylindrical, and spherical coordinates. Four lecture hours per week.

MAT 323 Numerical Analysis (3 Credit Hours)

Prerequisite: MAT 221

A study of numerical methods. Topics include root finding for non-linear equations, polynomial interpolation, series methods, numerical integration, finite differences, and solutions of linear systems. Efficiency, accuracy and round off and truncation errors are considered. Computer implementation of selected methods is included. Three lecture hours per week.

MAT 403 Abstract Algebra II (3 Credit Hours)

Prerequisite: MAT 303A

Topics include normal subgroups, ideals, morphisms of groups and rings, fields and field extensions with examples and applications. Three lecture hours per week.  Not open to students who have received credit for MAT 404.

MAT 406 Modern Geometry (3 Credit Hours)  W   

Prerequisite:  MAT 304A

A study of topics in advanced geometry from three perspectives: synthetic, analytic, and transformational. Topics include advanced results in Euclidean geometry, axiomatic development of Euclidean and non-Euclidean geometries, the use of coordinates, transformations, and symmetries.  Writing, primarily in the form of mathematical proof, is an essential component of the course. Three lecture hours per week.  Required of all Mathematics Majors with a Secondary Education Minor. Not open to students who have received credit for MAT 405.

MAT 407 Probability and Mathematical Statistics I (3 Credit Hours)

Prerequisite: MAT 221

Topics include: probability models, random variables and their probability distributions, expectation, variance, moment and moment generating functions, regression and correlation. The binomial, Poisson, exponential, normal, chi-square, t and F distributions will also be studied. Three lecture hours per week. Required of all Mathematics Majors with a Secondary Education Minor.

MAT 409 Complex Variables (3 Credit Hours)

Prerequisite: MAT 221

Functions of a complex variable. Cauchy-Riemann equations, Cauchy's integral theorem and formula, the calculus of residues, series expansions of analytic functions, singularities, and contour integration will be discussed. Three lecture hours per week.

MAT 410 History of Mathematics (3 Credit Hours)

Prerequisite: MAT 303

A survey of the fundamental developments in mathematics from ancient to modern times, with special attention to the historical and logical bases of geometry, algebra, and analysis. Three lecture hours per week.

MAT 411 Real Analysis (3 Credit Hours)

Prerequisite: MAT 221

A rigorous treatment of the theorems on sequences, limits, continuity, derivatives, and integrals which are fundamental to all of real analysis. Three lecture hours per week.

MAT 412 Topology (3 Credit Hours)

Prerequisite: MAT 221

Topics include topological spaces, metric spaces, connectedness, compactness, and product and quotient spaces: additional topics as time permits.  Three lecture hours per week.

MAT 413 Ordinary Differential Equations (3 Credit Hours)

Prerequisite: MAT 221

The methods of solving linear and elementary nonlinear ordinary differential equations: variation of parameters, series solutions, Laplace transforms and applications. Three lecture hours per week.

MAT 414 Linear Algebra II (3 Credit Hours)

Prerequisite: MAT 304A

A continuation of Linear Algebra I. Topics include inner product spaces, canonical forms, quadratic forms, and similarity, Hermitian, Unitary, and normal transformation. Three lecture hours per week.

MAT 415 Geometric Structures (3 Credit Hours)

Prerequisite: MAT 303

An analysis of various geometric structures, especially projective geometry and its relation to certain algebraic structures. Three lecture hours per week.

MAT 417 Probability and Mathematical Statistics II (3 Credit Hours)

Prerequisite: MAT 407

Introduction to statistical inference, sampling distributions, decision theory, theory of estimations, tests of hypotheses, analysis of variance. Three lecture hours per week.

MAT 420 Special Problems Seminar (3 Credit Hours)

Prerequisite: MAT 303

Topics to be selected by the instructor

MAT 421 Advanced Calculus (3 Credit Hours)

Prerequisite: MAT 320

Functions of several variables, implicit functions and Jacobian determinants, line and surface integrals, and the theorems of Green and Stokes will be discussed. Three lecture hours per week.

MAT 424 Operations Research (3 Credit Hours)

Prerequisite: MAT 308 and knowledge of a scientific programming language

Theory of games, functional equations, dynamic programming, simulation, models, optimization, with applications to system design, economics, engineering and management. Three lecture hours per week.

MAT 427 Statistical Experimental Design (3 Credit Hours)

Prerequisite: MAT 247 or MAT 407

An overview of the fundamental designs used to analyze experimental data. Topics include simple and multiple linear regression, analysis of variance, two-group discriminant analysis, factor analysis, time series analysis, and the analysis of categorical data. There will be extensive use of statistical software packages on the computer. No open to students who have previously completed MAT 347. Three lecture hours per week.

MAT 500 Directed Study in Mathematics (3 Credit Hours)

Prerequisite: At least one 400 level math course (with a grade of C or above), Junior or Senior standing, agreement of a Department faculty member to act as supervisor and permission of the Mathematics Department Chairperson

The purpose of this course is to provide the student with an opportunity to explore in depth an area of mathematics that would not ordinarily be encountered in the program of required courses. It is recommended that the student take as many of the required courses as possible before enrolling in Directed Study. Credit for this course may not be applied toward Major requirements.

MAT 520 Mathematics Internship (3 credit hours)

Prerequisite: Permission of the faculty supervisor and of Department Chairperson.

An opportunity for students to gain practical or technical training in an industrial/commercial/research environment. The student makes the necessary arrangements with the chosen facility, in consultation with an appropriate faculty member. The internship must meet College Academic Policies (described elsewhere in this Catalog) and Mathematics Department Policy (available in the Mathematics Department). Open only to Junior/Senior Mathematics Majors who have obtained a faculty sponsor for this internship.

MAT 572 Mathematics Research I (3 credit hours)

Prerequisite: Permission of the faculty supervisor and of Department Chairperson.

This course provides qualified students with research direction and the opportunity to participate in independent work in any area of mathematics of special interest to them, provided that a faculty supervisor is available. A paper and poster presentation are required at the end of the course. Open only to Junior/Senior Mathematics Majors.

MAT 573 Mathematics Research II (3 credit hours)

Prerequisite: Permission of the faculty supervisor and of Department Chairperson.

This course builds on MAT 572, continuing with the same project or starting with a new project. Students in this course will be expected to present their results in a professional setting. Open only to Junior/Senior Mathematics Majors.