# Course offerings

Mathematics
Mathematics

#### MATH 102 - Basic Algebra

Topics include numbers and their properties, operations with rational numbers, fundamental operations in algebra, linear equations in one variable, special products and factoring, algebraic fractions, systems of linear equations, exponents and radicals and quadratic equations. Required of students whose placement test indicates a need for further preparation in mathematics. A student who has received credit for MATH 115, MATH 123, or MATH 131 may not take MATH 102 for credit without the registrar’s consent.

#### MATH 115 - Pre-Calculus Mathematics

Primarily for students intending to take MATH 131 but who need more preparation. Topics include basic concepts of set theory, algebraic operations, functions, systems of equations, exponents, logarithms, trigonometry and an introduction to graphing software. Prerequisite: MATH 102 or placement. A student who has received credit for MATH 131 may not take MATH 115 for credit without the registrar’s consent. Spring semester.

#### MATH 120 - Numbers and Operations

Intended for elementary education majors, this course examines the mathematical content knowledge underlying the numbers and operations taught in elementary school. Students explore content in the Common Core State Standards, such as place value; algorithms for addition, subtraction, multiplication and division; and arithmetic properties of counting numbers, integers, fractions and decimals. This course focuses on mathematical content, not teaching methods. Prerequisite: MATH 102 or placement.

#### MATH 123 - Applications of Contemporary Mathematics

This course is designed to help students recognize the place of mathematics and mathematical reasoning in society. Students are given the opportunity to enhance their ability to see the relevance of mathematics behind many current topics and to use mathematical techniques to address those topics. Topics include: mathematics of finance, logic, probability, statistics and counting techniques, graph theory, and additional topics at the instructor’s discretion. Prerequisite: MATH 102 or placement.

#### MATH 128 - Introductory Statistics for Business

Intended for business administration majors, this course offers a background in combinatorics, probability, descriptive statistics, inferential statistics and basic calculus to prepare students to succeed in their business courses and especially BUAD 228. Students apply quantitative thinking to practical problems in business and economics. Prerequisite: MATH 102 or placement.

#### MATH 131 - Calculus and Analytic Geometry 1

Pre-calculus mathematics are presumed but reviewed as needed. Topics include limits and continuity of functions; the derivative, its meaning, computation and applications; the definite integral, its meaning, computation and applications; differentiation and integration of logarithmic, exponential and trigonometric functions; and the fundamental theorem of calculus. Prerequisite: four years of college preparatory math in high school or MATH 115.

#### MATH 132 - Calculus and Analytic Geometry 2

Topics include applications of integration, methods of integration, indeterminate forms and improper integrals, elementary differential equations, and series. Prerequisite: MATH 131.

#### MATH 203 - Linear Algebra

The course covers systems of linear equations and their solutions, matrix algebra, determinants, vector spaces and linear transformations, eigenvalues and eigenvectors, and inner product spaces. While linear algebra can be studied at a more theoretical level (e.g. MATH 303), this course focuses on the problem-solving capabilities and applications of linear algebra. Prerequisites: MATH 131 or placement in MATH 132.

#### MATH 212 - Principles of Algebra and Data

Intended for elementary education majors, this course examines the mathematical content knowledge underlying the algebra, number theory, statistics and probability taught in elementary and middle school mathematics. Students explore ratio and proportion, number theory, algebra, statistics, and probability. This course focuses on mathematical content, not teaching methods. Prerequisite: grade of C or better in MATH 120 or MATH 250. Spring semester.

#### MATH 220 - Principles of Geometry

Intended for elementary education majors, this course examines the mathematical content knowledge underlying the geometry taught in elementary and middle school mathematics. Students explore measurement including length, area and volume; polygons; constructions; similar and congruent figures; and symmetry. This course focuses on mathematical content, not teaching methods. Prerequisite: grade of C or better in MATH 120 or MATH 250. Fall semester.

#### MATH 221 - Statistics in the Sciences

The course covers both descriptive and inferential statistics and how they are used in science and engineering. Major topics include discrete and continuous random variables, probability and density functions, statistical inference and sample statistics, confidence intervals, hypothesis testing, analysis of variance (ANOVA), and regression analysis. Students will learn to implement these topics in the R programming language for statistical computing. Prerequisite: MATH 131 or placement in MATH 132.

#### MATH 233 - Calculus and Analytic Geometry 3

Topics include parametric equations, polar coordinates, matrices and determinants, vectors and curves in two- and three-dimensional space, partial derivatives, multiple integrals, further applications of differentiation and integration, and line integrals. Prerequisite: MATH 132. Every semester.

#### MATH 250 - Advanced Foundations of Mathematics

This course is intended to be a transition to abstract mathematics. Topics include logic, the axiomatic method and the nature of proof, sets, relations, functions and 1-1 correspondences, countability, and selected topics in discrete mathematics. Prerequisites: CSCI 110 (or instructor’s consent), MATH 132 and MATH 203.

#### MATH 289 - Special Topics

The course topic and title are announced at the time the course is offered. This course is intended for students at the first-year/sophomore level.

#### MATH 303 - Advanced Linear Algebra

Topics include vector spaces and inner product spaces, linear transformations, matrices and determinants, and eigenvalue problems. Although linear algebra can be studied with an emphasis on computational techniques and column vectors (e.g. MATH 203), this course focuses on proof-writing and the theory of abstract vector spaces. Prerequisite: MATH 250. Spring semester, alternate years.

#### MATH 306 - Abstract Algebra

Topics include groups, cyclic groups, permutation groups, quotient groups, Lagrange’s theorem, homomorphism theorems, rings, ideals, polynomial rings, elementary number theory, integral domains and fields. Prerequisite: MATH 250. Fall semester.

#### MATH 310 - Differential Equations

Topics include solutions of first order linear and nonlinear ordinary differential equations including separable variables, exact, homogeneous, and autonomous. Includes higher order linear differential equations, systems of ordinary differential equations, variation of parameters, Laplace transforms, power series, numerical solutions, and applications of differential equations. Prerequisite: MATH 203 and MATH 233. Spring semester, alternate years.

#### MATH 313 - Mathematical Modeling

This course introduces the construction and investigation of mathematical models for real-world problems. Techniques explored involve dimensional analysis; difference, ordinary differential and partial differential equations; fixed point, stability, and phase-plane analysis; deterministic and stochastic processes; and computer packages as needed. Applications may include, but are not limited to, mechanical vibrations, population dynamics, traffic flow, chemical kinetics, cell biology and geophysical fluid dynamics. Prerequisite: MATH 203 and MATH 233. Fall semester, alternate years.

#### MATH 315 - Numerical Analysis

This course introduces algorithms for numerical solutions to mathematical problems, error analysis and computer packages. Topics include power series, roots of equations, linear and nonlinear systems, numerical differentiation and integration, differential equations, interpolation and difference equations, and curve fitting. Prerequisites: CSCI 110, MATH 132, and MATH 233 or instructor’s consent. Spring semester, alternate years.

#### MATH 317 - Operations Research

Topics include linear programming, duality, sensitivity analysis, transportation and assignment problems. The course also deals with computer implementation of selected algorithms. Selected topics from the following: game theory, network analysis, integer programming and decision theory. Prerequisite: MATH 233 and MATH 250.

#### MATH 318 - Methods of Applied Mathematics

This course offers an introduction to the methodologies and classical techniques in applied mathematics. Topics include scalar and vector field theory (line integrals, Stoke’s theorem, Green’s theorem, irrotational fields); Fourier methods (series, integral, transform); partial differential equations (characteristics, Laplace equation, the wave equation, potential theory); and complex variable theory (conformal mapping, Taylor series, Laurent series, residues). Prerequisite: MATH 203 and MATH 233. Fall semester, alternate years.

#### MATH 319 - Financial Mathematics

This course introduces students to principles of financial mathematics. Specific topics include time value of money, annuities, loans, bonds, general cash flows and portfolios, immunization, interest rate swaps, and determinants of interest rates. Offered Fall semester, every other year. Prerequisite: MATH 250.

#### MATH 321 - Probability and Statistics

Topics include probability, discrete and continuous random variables, discrete and continuous distributions, statistical inference and sample statistics, hypothesis testing and selection of procedures, and correlation and regression. Prerequisite: MATH 233 and MATH 250. Fall semester, alternate years.

#### MATH 350 - Modern Geometry

Topics include postulational systems, Euclidean and non-Euclidean geometries, and the role of geometry in the history of mathematics. Prerequisite: MATH 250. Spring semester, alternate years.

#### MATH 355 - Topology

Topics include metric spaces and general topological spaces, separation properties, compactness, connectedness, convergence, completeness, continuous functions and homeomorphisms. Prerequisite: MATH 250. Offered by special arrangement with a member of the mathematics faculty.

#### MATH 373 - Real Analysis

Topics include introduction to the theory of functions of a real variable, topology, limits, continuity, differentiability, the Riemann integral, sequences and series. Prerequisite: MATH 250. Spring semester, alternate years.

#### MATH 376 - Complex Analysis

Topics include elementary functions of a complex variable, differentiation, topology, integration, calculus of residues and series. Prerequisite: MATH 250. Spring semester, alternate years.

#### MATH 489 - Special Topics

A course designed for the study of subject material of special interest. The organization, methodology and objectives of the course are determined by the instructor. Prerequisites: instructor’s consent and junior or senior standing.

#### MATH 490 - Independent Study

A course that allows a talented student to pursue an area of study on an individual basis, with consultation and evaluation. The objectives, organization, methodology and means of evaluation are mutually agreed upon by a faculty member and the student. Prerequisites: instructor’s consent and junior or senior standing.