# Mathematics Courses

**MAT 100 Elementary Algebra (3)**

An introductory algebra course that prepares students to understand concepts such as the properties of real numbers, factoring, linear equations, inequalities, systems of linear equations, polynomials, rational expressions, exponents, radicals, quadratic equations, graphs and functions. Does not count towards graduation.

**MAT 105 Intermediate Algebra (3)**

A refresher in basic algebra necessary for success in the required mathematics courses. Includes the field properties, linear equations, relations and functions, polynomials, rational expressions, roots, radicals, exponents, quadratic equations, and systems of linear equations. Prerequisite: high school algebra or equivalent.

**MAT 114 Finite Mathematics (GE) (3)**

Prepares students for future statistics courses. Topics include linear equations, matrices, counting principles, probability, statistical measures, and normal curves. Prerequisite: high school algebra, MAT 105, or permission of instructor.

**MAT 115 College Algebra (GE) (3)**

Designed for students with a solid background in high school algebra. Provides a basis for further mathematical study. Students with a strong mathematical background should take MAT 241 rather than MAT 115. Topics include equations, inequalities, graphs, linear functions, polynomial functions, rational functions, exponential functions, logarithmic functions, and trigonometric functions. Prerequisite: strong background in high school algebra, MAT 105, or permission of instructor.

**MAT 175R Topics in Math (3)**

Topics in mathematics.

**MAT 206 Mathematics for Liberal Arts (GE) (4)**

Introduces students to some of the great ideas and achievements of mathematics. Topics may include properties of numbers, infinity, geometry, the fourth dimension, chaos and fractals, shape and topology, symmetry and patterns, probability and statistics, network theory, voting systems, and many more important mathematical ideas. Prerequisite: MAT 100 or equivalent, or consent of instructor.

**MAT 221 Statistics (GE) (3)**

Introduction to probability and statistics. Topics include measures of center, variability, correlation, experimental design, linear regression, probability, normal distributions, confidence intervals, hypothesis testing, chi-square distributions, F distributions, t distributions, and analysis of variance. Prerequisite: one of the following: MAT 114, 115, or permission of instructor.

**MAT 241 Calculus I (GE) (4)**

Topics include limits, continuity, derivatives, implicit differentiation, applications of derivatives, anti-derivatives, definite integrals and applications of anti-differentiation and the definite integral. Prerequisite: Strong background in high school algebra or above, MAT 115 or equivalent.

**MAT 242 Calculus II (GE) (3)**

The definite integral and infinite series and the associated applications. Topics include Rieman sums, definite integrals, indefinite integration, transcendental functions, applications of integration, integration techniques, L’hopital’s rule, improper integrals, and infinite series. Prerequisite: MAT 241 or equivalent.

**MAT 275R Topics in Mathematics (3)**

Topics in Mathematics.

**MAT 305 Basic Concepts of Mathematics I (3)**

Provides a broad background of number systems and operations for non-science students and prospective elementary school teachers. Includes development and applications of set theory; number systems, their structure, basic operations and properties; number theory; ratio; proportion and percent. Introduction to algebra including linear and nonlinear equations and functions; linear systems of equations and coordinate geometry. Prerequisite: MAT 115 or consent of instructor.

**MAT 306 Basic Concepts of Mathematics II (3)**

Provides a broad background in mathematics for non-science students and prospective elementary school teachers. Includes development and applications of number systems; number theory; introduction to geometric figures, their properties and relationships; Pythagorean theorem; measurement; probability and statistics. Prerequisite: MAT 115 or consent of instructor.

**MAT 321 Mathematical Statistics I (3) **

A study of probability theory relative to both discrete and continuous probability laws. Topics include independence and dependence, mean, variance and expectation, random variables, jointly distributed probability laws, Chebysheff’s Inequality and a version of the Central Limit Theorem. Applications of probability theory are approached through a variety of idealized problems. Prerequisite: MAT 241 and MAT 242.

**MAT 322 Mathematical Statistics II (3) **

A mathematical approach to statistical theory. Includes a study of distribution theory, important properties of estimators, interval estimation and hypothesis testing, regression and correlation, and selected topics from non-parametric statistics. Prerequisite: MAT 321. Note: MAT 221, 321 and 322 will provide the background knowledge for a prospective secondary teacher to teach AP Statistics in high school.

**MAT 332 Discrete Mathematics (3) **

An introduction to fundamental mathematical concepts used in mathematics as well as computer science, with an emphasis on writing mathematical arguments. The course presents the principles of mathematical logic and methods of proof such as direct and indirect proofs and mathematical induction. Other topics include sets, functions, relations, recursion, matrix algebra, and techniques from elementary combinatorics and graph theory. Prerequisite: MAT 115 or MAT 241.

**MAT 341 Calculus III (3)**

Topics include conic, parametric equations, polar coordinators, vectors and the geometry of space, vector valued functions, function of several variables, multiple integration and vector analysis. Prerequisite: MAT 242.

**MAT 343 Linear Algebra (3)**

Includes vectors, dot and cross products, matrices, systems of equations, vector spaces, determinants, linear transformations, eigenvalues, and eigenvectors. Prerequisite or concurrent enrollment: MAT 241 or consent of instructor.

**MAT 344 Elementary Differential Equations (3)**

The analysis and applications of first and second order differential equations. Topics include separation of variables, integrating factors, numerical methods, homogeneous linear equations, non-homogeneous linear equations, variation of parameters, series solutions, Laplace Transforms, and linear systems of differential equations. Prerequisite: MAT 242 or equivalent.

**MAT 355 History of Mathematics (3) **

(For prospective secondary teachers.) Historical development of number theory, geometry, algebra, and analysis. Study of the significant mathematical contributions to these topics made by prominent mathematicians from ancient beginnings to modern times. Prerequisite: MAT 343.

**MAT 356 Number Theory (3) **

Unique factorization, arithmetic functions, linear and quadratic congruences, quadratic reciprocity law, quadratic forms, introduction to algebraic numbers. Prerequisite: MAT 343.

**MAT 360 Abstract Algebra I (3) **

An introduction to the theory of groups, rings and fields. Topics include normal subgroups, quotient groups, homomorphisms, Cayley’s theorem, permutation groups, ideals, the field of quotients of an integral domain, and polynomial rings. Prerequisite: MAT 343.

**MAT 365 Geometry (3) **

(For prospective secondary teachers.) A rigorous treatment of Euclidean geometry and an introduction to other geometry. Advanced approach to fundamental properties of Euclidean and other geometries. Writing intensive. Prerequisite: MAT 343.

**MAT 375R Topics in Mathematics (3)**

Topics in mathematics. Prerequisite: consent of instructor.

**MAT 385R Directed Study in Mathematics (3)**

Directed study in mathematics. Prerequisite: consent of instructor.

**MAT 399 Internship/Practicum in Mathematics (3)**

Internship or practicum in field of potential employment or advanced study. Internship proposal must be approved before registration. Prerequisite: consent of instructor.

**MAT 410 Introduction to Numerical Analysis (3) **

Survey of methods to approximate numerical solutions of problems in root-finding, differentiation, integration, curve-fitting, differential equations, and systems of equations. Derivations, limitations, and efficiency of different algorithms are considered. Prerequisite: MAT 343 and MAT 344.

**MAT 441 Real Analysis (3) **

A rigorous treatment of one-variable calculus including: limits, continuity, differentiation, the Riemann integral, metric spaces, sequences and series of functions. Prerequisite: MAT 343.

**MAT 444 Introduction to Partial Differential Equations (3) **

Introduces the solution of partial differential equations. Models arising from initial-boundary-value problems of mathematical physics and Sturm-Liouville problems are examined; solution techniques include separation of variables, Bessel functions, series expansions by orthogonal functions, and numerical methods. Prerequisite: MAT 344.

**MAT 446 Complex Analysis for Applications (3) **

Complex numbers, analytic functions, Cauchy-Riemann equations, conformal mapping, contour integration, Cauchy’s integral formula, infinite series, residue calculus, Fourier and Laplace transforms. Prerequisite: MAT 441 or consent of instructor.

**MAT 460 Abstract Algebra II (3) **

A continuation of Mathematics 360 including additional topics in group theory and ring theory, extension fields, straight-edge and compass constructions, Galois Theory and solvability by radicals. Prerequisite: MAT 360.

**MAT 498 Mathematics Capstone Course. (3) **

Prerequisite: Students must have senior standing. (1) Mathematics majors will write a senior thesis showing an understanding of a substantial area of modern mathematics. Students must have completed at least one of the one-year sequences of upper-level mathematics. (2) Mathematics majors with Secondary Education Certification: Students will write a senior thesis based on research of a current topic in mathematics education. We recommend that the Capstone course be taken over two semesters for 2 and 1 credit each.

**MAT 499 Senior Internship/Practicum in Math (3) **

Internship or practicum in field of potential employment or advanced study. Internship proposal must be approved before registration. Prerequisite: senior class standing and consent of instructor.