Students in both upper and lower level mathematics courses receive highly individualized attention from faculty members. Approximate class sizes are:

These small class sizes allow faculty members to easily and effectively address student needs both inside and outside the classroom.

**MAT 102**

**Topics in Mathematics**

This course provides a general survey of mathematical topics that are useful in a variety of fields. Topics include: set theory and logical operators; topics in number theory including graph theory, Euler circuits, Hamiltonian circuits, and search algorithms; voting methods; and topics in interest rate theory.

**MAT 103**

Discrete Mathematics I

This is an introduction to the theory and application of discrete mathematics. Topics include logic, sets, functions and relations, combinations and elementary probability.

**MAT 104**

Discrete Mathematics II

A continuation of MAT 103, this course includes trees and graphs, recurrence relations, elementary group theory and selected topics in computer science.

**MAT 110**

Elementary Statistics

This course gives students a general overview of modern statistics. Topics include: organization of data; probability and probability distributions; measures of central tendency and variability; normal distributions; sampling; hypothesis testing; correlation and regression. A TI-89 graphing calculator is highly recommended.

**MAT 120**

Pre-Calculus Mathematics

This is a review of algebra and trigonometry intended to be taken before 131 or 125 by those students whose background in algebra and trigonometry is insufficient. The major emphasis is on the function concept. Elementary analytic geometry is discussed, along with algebra, composition of functions, inverse functions, trigonometry, and logarithmic and exponential functions.

**MAT 125**

Calculus with Business/Economics Applications

Designed as a one-semester course for concentrators in business administration or economics, topics such as linear functions and models; matrices and matrix algebra; linear systems; functions and graphs; derivatives and integrals; and extremization are included. Partial differentiation also is introduced.

**MAT 131**

Calculus and Analytic Geometry I

This course involves fundamental concepts of functions of one variable. Topics include: limits, continuity differentiation, derivative applications, curve sketching, related rates and maxima-minima problems. Introduction to indefinite and definite integration including the fundamental theorems, and numeric approximation techniques are also covered. This is normally the first mathematics course taken by students entering a math or math-related curriculum.

**MAT 132**

Calculus and Analytic Geometry II

A continuation of MAT 131. Topics include transcendental functions, applications of integration including volume, surface area, arc length and work. Also covered are integration techniques, indeterminate forms, improper integrals, sequences and series, and Taylor’s theorem.

Prerequisite: MAT 131 with at least a C- grade.

**MAT 233**

Calculus III

A continuation of MAT 132. Topics include polar coordinates, parametric representation, vectors, analysis of functions of two (or more) variables, multiple integration, line and surface integrals. Normally taken by mathematics concentrators in the first semester of the sophomore year.

Prerequisite: MAT 132

**MAT 250**

Foundation of Mathematics

This is an introduction to abstract mathematics. Topics include symbolic logic, methods of proof (direct, contradiction and induction), set theory, relations, functions, countable and uncountable sets. Normally taken by mathematics concentrators in the first semester of the sophomore year.

Prerequisite: MAT 132 or permission of the department

**MAT 300**

Discrete Mathematics

In this course students will study counting and finite structures. Topics from combinatorics include: permutations and combinations, binomial and multinomial coefficients, recursion, generating functions, and the twelvefold way. Topics from graph theory include graphs, trees, Eulerian and Hamiltonian cycles, planarity, and coloring. Additional topics may include but are not limited to Catalan numbers, Sterling numbers, partitions, Ramsey theory, Latin squares, design theory, and coding theory. Proof techniques, especially proof by induction, will be used throughout the course.

Prerequisite: MAT 250 or permission of the department

**MAT 310**

Probability and Mathematical Statistics

This course introduces probability and mathematical statistics at the level presupposing knowledge of calculus. Descriptive and inferential statistics are included, along with hypothesis testing, estimation and analysis of variance.

Prerequisite: 132 & 250 or permission of the department

**MAT 320**

Linear Algebra

This is an introduction to matrix algebra; linear equations; linear dependence; determinants; vector spaces; linear transformations, eigenvalues, eigenvectors and diagonalization.

Prerequisites: MAT 132 & 250 or permission of the department

**MAT 325**

Abstract Algebra

This is an introduction to groups, rings and fields with topics selected from number theory, ideals and polynomial rings.

Prerequisite: MAT 250 or permission of the department

**MAT 334**

Differential Equations

This course is a study of solution techniques for ordinary differential equations. Topics include the principal types of equations of first and second order, linear equations with constant coefficient, higher order linear and non-linear equations, series solutions, operational methods, systems of equations and modeling problems. Runge- Kutta and other numerical approximation methods are also covered.

Prerequisite: MAT 233 & 320 or permission of the department

**MAT 340**

Geometry

This course is intended primarily for those students planning to enter the field of secondary education. It begins with a study of the most important ideas of Euclidean plane geometry, but also considers the historical significance of Euclid's original postulates. Special attention is given to the notion of parallelism of lines and the resulting non-Euclidean geometries when the axiom of parallelism is altered. Differential geometry also is introduced as a means of studying curves, surfaces and curves on surfaces.

Prerequisites: MAT 233 & 250 or permission of the department

**MAT 360**

Numerical Analysis

This is a study of numerical methods used in interpolation, differentiation and integration, solutions of equations and systems of equations, solutions of differential equations, fitting of empirical data and error estimation. Some computer or calculator programming will be employed and a basic level of programming is assumed. Applications are made to the sciences and engineering.

Prerequisite: MAT 233 & 250 or permission of the department

**MAT 431**

Real Analysis

This course is designed to take a rigorous look at definitions, theorems and concepts taken from the foundational calculus courses. Rigorous treatment is given to topics such as continuity, mean-value theorems, analysis of functions of several variables, extremization and limits. Other topics include sequences, series, the Heine-Borel covering theorem and the Riemann Integral.

Prerequisites: MAT 233 & 250 or permission of the department

**MAT 435**

Partial Differential Equations

Topics include: Orthogonal functions; Sturm-Liouville system; initial and boundary value problems; Fourier series; higher transcendental functions; separation-of-variables method; and other methods of solution of equations of mathematical physics.

Prerequisite: MAT 233, 250 & 334 or permission of the department

**MAT 438**

Complex Analysis

This is an introduction to the theory of functions of complex variables: derivatives and integrals; Cauchy's theorem; power series; theory of residues; and conformal mappings.

Prerequisite: MAT 233 & 250 or permission of the department

**MAT 440**

Introduction to Topology

This course introduces definitions and properties of topological spaces, metric spaces, continuity, homeomorphisms, separation axioms, compactness, connectedness, and fundamental group.

Prerequisites: MAT 233 & 250 or permission of the department

**MAT 480**

Advanced Topics in Mathematics

Designed to cover topics of interest that are not covered in other courses.

Prerequisites: Permission of the department

**MAT 491**

Seminar I (W)

A seminar in topics selected by the course instructor in which independent learning is stressed. The student is expected to present both oral and written reports on topics covered in the seminar.

Prerequisite: Junior standing and permission of the department

**MAT 492**

Seminar II (W)

A seminar in which each student selects a topic with the approval of the course instructor. The student is expected to present both oral and written reports. This seminar is to be taken in the final semester of the student's course work. Exceptions require the approval of the department. Prerequisite: Senior standing and permission of the department

The Raymond Mest mathematics scholarship is awarded each fall semester to a sophomore, junior, and senior mathematics major in accordance with the following criteria.