# Department of Mathematics

25 University Avenue, Room 101

610-436-2440

Department of Mathematics

Peter L. Glidden, *Chairperson*

Allison Kolpas*, Assistant Chairperson *

Sally Malarney*, Administrative Assistant*

The Department of Mathematics offers three different undergraduate programs: bachelor of arts degree in mathematics, bachelor of science degree in mathematics, and bachelor of science degree in education. All three programs require the same five core mathematics courses, and they share many upper-division courses, which gives students a great deal of flexibility in selecting their ultimate course of study.

**The B.A. in Mathematics**is designed to prepare students for graduate study in mathematics. The B.A. degree has a language requirement (French, German, or Russian are recommended), which makes it particularly appropriate for students who want to enroll in doctoral programs that require a language.**The B.S. in Mathematics**provides students with a wide choice of career-oriented concentrations that prepare graduates for careers in the private and public sectors. Current concentrations include: actuarial science, applied and computational mathematics, mathematical finance, pure mathematics, and statistics.**The B. S. in Education - Mathematics**provides students with the mathematical content, pedagogical content knowledge, and professional education preparation required for certification to teach mathematics at the middle school, junior high school, or senior high school levels.

The Undergraduate Handbook for Mathematics Majors should be consulted for current degree program requirements.

## Majors in Mathematics

- B.A. in Mathematics
- B.S.Ed. in Mathematics
- B.S. in Mathematics - Actuarial Science Concentration
- B.S. in Mathematics - Applied and Computational Mathematics Concentration
- B.S. in Mathematics - Computational Mathematics Concentration
**(no longer admitting new students)**- B.S. in Mathematics - Computational Mathematics Concentration to M.S. in Applied and Computational Mathematics Accelerated Program
**(no longer admitting new students)**

- B.S. in Mathematics - Computational Mathematics Concentration to M.S. in Applied and Computational Mathematics Accelerated Program
- B.S. in Mathematics - Mathematical Finance Concentration
- B.S. in Mathematics - Statistics Concentration
- B.S. in Mathematics - Mathematics Concentration

## Minors in Mathematics

## Graduate Opportunities

See the graduate catalog for more information on the Mathematics program.

All undergraduate students are held to the academic policies and procedures outlined in the undergraduate catalog. Students are encouraged to review departmental handbooks for program tips, suggested course sequences, and explanations of procedures. When applicable, additional policies for specific department program(s) may be listed below.

## Advanced Placement Policy

Course credit for success on AP exams in mathematics is awarded as follows:

AP Test | Score on AP Test 3 | 4 | 5 |
---|---|---|---|

Calculus AB | MAT 143 | MAT 161 | MAT 161 |

Calculus BC | MAT 161 | MAT 162 | MAT 162 |

Statistics | MAT 121 | MAT 121 | MAT 121 |

## Accelerated Program Policy

Refer to the Accelerated Programs page for more information.

**Admission to the Accelerated B.S. in Mathematics - Statistics Concentration and M.S. in Applied Statistics Program**

Students may conditionally enroll in the Accelerated Program at any point during their undergraduate career. If they are current West Chester students, or transfer students, they must have a minimum cumulative GPA of 3.0 in all MAT and STA courses for admission. While enrolled within the Accelerated Program, students must maintain this minimum cumulative GPA of 3.0 in their MAT and STA courses throughout their undergraduate career.

## Professors

Gail M. Gallitano (1992)

Graduate Coordinator, Mathematics

B.S., Monmouth College; M.S., Farleigh Dickinson University; M.A., M.Ed., Ed.D., Columbia University

Robert J. Gallop (2001)

B.S., Pennsylvania State University; M.S., Ph.D., Drexel University

Peter L. Glidden (1995)

Chairperson, Mathematics

B.A., College of Wooster; M.A., Ph.D., Columbia University

James McLaughlin (2005)

B.S., University of Ulster; M.S., Queen's University Belfast; Ph.D., University of Illinois

Viorel Nitica (2001)

B.S., M.S., University of Bucharest; Ph.D., Pennsylvania State University

Scott Parsell (2009)

B.S., Massachusetts Institute of Technology; M.S., Ph.D., University of Michigan

Randall H. Rieger (2000)

B.A., Bowdoin College; M.S., Ph.D., University of North Carolina

Lin Tan (1989)

B.S., M.A., Zhejian University; M.S., Ph.D., University of California, Los Angeles

## Associate Professors

Andreas Aristotelous (2016)

B.S., University of Cypress; M.S., Florida Institute of Technology; Ph.D., University of Tennessee, Knoxville

Brian Bowen (2010)

B.S.Ed., West Chester University; M.Ed., Ph.D., University of Delaware

Michael J. Fisher (2008)

B.S., Millersville University; M.S., Ph.D., Lehigh University

Shiv K. Gupta (1985)

B.S., M.S., Delhi University; M.S., University of Wisconsin; Ph.D., Case Western Reserve University

Daniel Robert Ilaria (2011)

B.A., Drew University; Ed.M., M.S., Ph.D., Rutgers University

Clifford A. Johnston (1992)

B.S.E., Mansfield University; M.A., Ph.D., Temple University

Allison Kolpas (2011)

Assistant Chairperson, Mathematics

B.A., Revelle College; M.A., Ph.D., University of California, Santa Barbara

Scott McClintock (2007)

B.S., San Jose State University; M.S., M.A., Ph.D., University of Kentucky

Mark A. McKibben (2013)

B.S., M.S., Ph.D., Ohio University

## Assistant Professors

Andrew Crossett (2012)

B.A., Canisius College; M.A., Ph.D., Carnegie Mellon University

Kim Johnson (2013)

B.S., MS.Ed., Millersville University; Ph.D., Pennsylvania State University

Premalatha Junius (2014)

B.S., M.S., University of Madras; M.A., Ph.D., University of Northern Colorado

Chuan Li (2016)

B.S., University of Science and Technology of China; M.S., Ohio University; Ph.D., University of Tennessee Knoxville

Kathleen M. McAneny (2014)

B.A., M.A., West Chester University of Pennsylvania; Ph.D., University of Delaware

Emily K. Miller (2016)

B.A., The College of New Jersey; M.S., Ph.D., University of Delaware

Rosemary Sullivan (2008)

B.S., Pennsylvania State University; M.S., Ph.D., Lehigh University

Peter Zimmer (2000)

B.S., M.S., University of Wisconsin; Ph.D., University of Kansas

## Instructors

Joann H. Kump (2013)

B.S., Florida State University; M.A.T., Indiana University

Thomas H. Short (2016)

B.S., John Carroll University; M.S., Ph.D., Carnegie Mellon University

#### MAT

**MAT Q20. Fundamental Skills in Arithmetic. 3 Credits.**

This course is designed to strengthen basic arithmetic skills and to introduce the elements of algebra. Mathematics placement required. Credits earned in Q00-level courses do not count toward the 120 hours of credit needed for graduation.

Pre / Co requisites: MAT Q20 requires a prerequisite of an appropriate score on the Mathematics Placement Examination.

Typically offered in Fall, Spring & Summer.

**MAT Q30. Fundamentals of Algebra. 3 Credits.**

This course is designed to strengthen basic algebraic skills. Credits earned in Q00-level courses do not count toward the 120 hours of credit needed for graduation.

Pre / Co requisites: MAT Q30 requires a grade of C- or better in MAT Q20 or an appropriate score on the Mathematics Placement Examination.

Typically offered in Fall, Spring & Summer.

**MAT 101. Mathematics for Teachers of Children I. 3 Credits.**

Sets; functions; logic; development of whole numbers, integers, and rationals (including ratios, proportions, and percents); number theory; problem solving. For students seeking Certification in Grades PK-4 or 4-8 only.

Pre / Co requisites: MAT 101 requires a grade of C- or better in MAT Q30 or an appropriate score on the Mathematics Placement Examination.

Typically offered in Fall, Spring & Summer.

**MAT 102. Mathematics for Teachers of Children II. 3 Credits.**

Development of real numbers; geometry; measurement; probability and statistics; problem solving. For students seeking Certification in Grades PK-4 or 4-8 only.

Pre / Co requisites: MAT 102 requires prerequisite of MAT 101.

Typically offered in Fall, Spring & Summer.

**MAT 103. Introduction to Mathematics. 3 Credits.**

This course is a liberal arts introduction to the nature of mathematics. Topics are chosen from among logic, graph theory, number theory, symmetry (group theory), probability, statistics, infinite sets, geometry, game theory, and linear programming. These topics are independent of each other and have as prerequisite the ability to read, reason, and follow a logical argument.

Pre / Co requisites: MAT 103 requires prerequisites of a grade of C- or better in MAT Q30 or an appropriate score on the Mathematics Placement Examination.

Distance education offering may be available.

Typically offered in Fall, Spring & Summer.

**MAT 104. Introduction to Applied Mathematics. 3 Credits.**

The course is designed to help prepare students to understand almost any quantitative issues they will encounter in contemporary society. Topics are selected from the following: principles of reasoning, problem-solving tools, financial management, exponential growth and decay, probability, putting statistics to work, mathematics and the arts, discrete mathematics in business and society and the power of numbers.

Pre / Co requisites: MAT 104 requires prerequisites of a grade of C- or better in MAT Q30 or an appropriate score on the Mathematics Placement Examination.

Typically offered in Fall, Spring & Summer.

**MAT 113. Algebra and Functions. 3 Credits.**

A review of basic algebra, followed by a thorough treatment of polynomial, rational, exponential, and logarithmic functions. Successful completion of this course prepares students for MAT 143.

Pre / Co requisites: MAT 113 requires a prerequisite of a grade of C- or better in MAT Q30 or an appropriate score on the Mathematics Placement Examination.

Typically offered in Fall, Spring & Summer.

**MAT 115. Algebra, Functions, and Trigonometry. 3 Credits.**

Topics include polynomial, rational, exponential, logarithmic, and trigonometric functions. An emphasis is placed on using technology to understand topics of importance in the life and earth sciences. Successful completion of this course prepares students for MAT 143 or MAT 145.

Pre / Co requisites: MAT 115 requires a grade of C- or better in MAT Q30 or an appropriate score on the Mathematics Placement Examination.

Typically offered in Fall, Spring & Summer.

**MAT 121. Introduction to Statistics I. 3 Credits.**

Basic concepts of statistics. Frequency distributions, measures of central tendency and variability, probability and theoretical distribution, significance of differences, and hypothesis testing.

Pre / Co requisites: MAT 121 requires a prerequisite of a grade of C- or better in MAT Q30 or an appropriate score on the Mathematics Placement Examination.

Distance education offering may be available.

Typically offered in Fall, Spring & Summer.

**MAT 122. Introduction to Statistics II. 3 Credits.**

Continuation of MAT 121. Inference about the means, standard deviations and proportions, goodness of fit, analysis of variance, regression analysis, correlation, and nonparametric tests.

Pre / Co requisites: MAT 122 requires a prerequisite of a grade of C- or better in MAT 121 or ECO 251.

Typically offered in Fall & Spring.

**MAT 131. Precalculus. 3 Credits.**

Topics include polynomial, rational, exponential, logarithmic, and trigonometric functions. An emphasis is placed on understanding function properties and graphs without the use of technology. Successful completion of this course prepares students for MAT 161.

Pre / Co requisites: MAT 131 requires a prerequisite of a grade of C- or better in MAT Q30 or an appropriate score on the Mathematics Placement Examination.

Typically offered in Fall, Spring & Summer.

**MAT 143. Brief Calculus. 3 Credits.**

An intuitive approach to calculus with emphasis on conceptual understanding and applications to business. Topics include differentiation, curve-sketching, optimization, integration, and partial derivatives.

Pre / Co requisites: MAT 143 requires a prerequisite of a grade of C- or better in MAT 113, MAT 115, or MAT 131; or an appropriate score on the Mathematics Placement Examination.

Typically offered in Fall, Spring & Summer.

**MAT 145. Calculus for the Life Sciences. 3 Credits.**

An overview of differential and integral calculus, motivated through biological problems. Topics include mathematical modeling with functions, limits, continuity, differentiation, optimization, and integration. Graphing calculators are used as an aid in the application of calculus concepts and methods to realistic biological problems.

Pre / Co requisites: MAT 145 requires a prerequisite of a grade of C or better in MAT 115 or MAT 131; or an appropriate score on the Mathematics Placement Examination.

Typically offered in Fall, Spring & Summer.

**MAT 151. Introduction to Discrete Mathematics. 3 Credits.**

Set theory, Boolean logic, elementary combinatorics, proofs, simple graph theory, and simple probability.

Pre / Co requisites: MAT 151 requires a prerequisite of a grade of C- or better in MAT Q30 or an appropriate score on the Mathematics Placement Examination.

Typically offered in Fall, Spring & Summer.

**MAT 161. Calculus I. 4 Credits.**

Differential and integral calculus of real-valued functions of a single real variable with applications.

Pre / Co requisites: MAT 161 requires prerequisites of a C or better in MAT 131 or an appropriate score on the Mathematics Placement Examination.

Typically offered in Fall, Spring & Summer.

**MAT 162. Calculus II. 4 Credits.**

Continuation of MAT 161 including the study of series, methods of integration, transcendental functions, and applications to the sciences.

Pre / Co requisites: MAT 162 requires prerequisite of C or better in MAT 161.

Typically offered in Fall, Spring & Summer.

**MAT 190. Topics in Mathematics. 3 Credits.**

Topics announced at time of offering.

Consent: Permission of the Department required to add.

**MAT 200. The Nature of Mathematics. 3 Credits.**

Topics include the role of mathematics in contemporary society, career opportunities, mathematical notation and argument, structure of proofs, basic facts about logic, mathematical proofs, problem-solving techniques, and introductions to mathematical software packages.

Pre / Co requisites: MAT 200 requires a prerequisite of C or better in MAT 161. Course should be taken by the end of sophomore year.

Typically offered in Fall, Spring & Summer.

**MAT 201. Elementary Functions Essential Calculus I. 3 Credits.**

Elementary functions from an advanced viewpoint with detailed discussion of formal manipulations. Special emphasis on applications and the use of technology. Open only to prospective Grade 4-8 certification students.

Pre / Co requisites: MAT 201 requires prerequisite MAT 102.

**MAT 202. Elementary Functions and Essential Calculus II. 3 Credits.**

Elementary functions from an advanced viewpoint with detailed discussions of formal manipulations. Special emphasis on applications and the use of technology. Open only to prospective Grade 4-8 certification students.

Pre / Co requisites: MAT 202 requires prerequisite MAT 201.

**MAT 203. Elementary Functions and Essential Calculus II. 3 Credits.**

Continued discussion of elementary functions. Introduction to the intuitive ideas of derivative and integral with applications.

Pre / Co requisites: MAT 203 requires prerequisite of MAT 202.

**MAT 261. Calculus III. 4 Credits.**

The calculus of several variables. Topics include polar coordinates, vectors and three-dimensional analytic geometry, differentiation of functions of several variables, multiple integrals, and line and surface integrals.

Pre / Co requisites: MAT 261 requires a prerequisite of MAT 162 with a C or better.

Typically offered in Fall, Spring & Summer.

**MAT 301. The Scientific Revolution. 3 Credits.**

This course addresses how modern science began in the 17th century by examining its origins and including introductions to the heroes of science - Copernicus, Kepler, Galileo, and Newton. This course counts toward the writing emphasis requirement.

Gen Ed Attribute: Interdisciplinary Requirement, Writing Emphasis.

Typically offered in Fall & Spring.

**MAT 302. Mathematics and Social Justice. 3 Credits.**

In this course we will explore several social issues and we will discuss methods which can quantitatively illustrate that are taking place. By doing so, the hope is that each student will learn mathematical skills and techniques. This tool kit of basic mathematical skills is often referred to as Quantitative Literacy (QL). Moreover as attainment of QL is itself a social justice issue, we will explore ways to carry these skills to historically marginalized groups through service learning projects.

**MAT 309. Topics in Math for Elementary Teachers. 3 Credits.**

Introduction to programming in BASIC; computer uses for the classroom teacher; descriptive statistics with applications for teaching; and measurements of length, area, volume, and temperature that focus on the SI metric system with practice in the classroom. Additional topics in applied mathematics will be considered.

Pre / Co requisites: MAT 309 requires prerequisite of MAT 102.

Repeatable for Credit.

**MAT 311. Linear Algebra. 3 Credits.**

An introduction to linear algebra. Topics covered include matrices, systems of linear equations, vector spaces, linear transformation, determinants, eigenvalues, spectral theorem, and triangulation.

Pre / Co requisites: MAT 311 requires Concurrent or Prerequisite of MAT 162.

Typically offered in Fall, Spring & Summer.

**MAT 312. Algebra for Teachers in Grades 4-8. 3 Credits.**

Formal structure of groups, rings, and fields with examples from the elementary curriculum. Topics from linear algebra including matrices, determinants, and linear programming.

Pre / Co requisites: MAT 312 requires prerequisite of MAT 102.

Typically offered in Fall & Spring.

**MAT 313. Geometry for Teachers in Grades 4-8. 3 Credits.**

Modern informal approach to two- and three-dimensional geometric figures, measurement, similarity, congruence, coordinate geometry, and the postulational method.

Pre / Co requisites: MAT 313 requires prerequisite of MAT 102.

Typically offered in Fall & Spring.

**MAT 319. Applied Statistics. 3 Credits.**

This course will cover simple and multiple linear regression methods and linear time series analysis with an emphasis on fitting suitable models to data and testing and evaluating models against data.

Pre / Co requisites: MAT 319 requires a prerequisite of MAT 143 or MAT 145 or MAT 161.

Typically offered in Fall & Summer.

**MAT 321. Combinatorics and Graph Theory. 3 Credits.**

Introduction to set theory, graph theory, and combinatorial analysis. Includes relations, cardinality, elementary combinatorics, principles of inclusion and exclusion, recurrence relations, zero-one matrices, partitions, and Polya's Theorem.

Pre / Co requisites: MAT 321 requires prerequisites of C or better in MAT 162 and MAT 200.

Typically offered in Fall.

**MAT 325. Numerical Analysis I. 3 Credits.**

A basic introduction to numerical analysis and scientific computing. Topics which will be studied include: Computer arithmetic, approximation and interpolation of functions, numerical quadratures, solutions of linear systems by direct methods, numerical solutions of nonlinear scalar equations, numerical differentiation, introduction to one step methods for the numerical solution of ordinary differential equations.

Pre / Co requisites: MAT 325 requires a prerequisite of MAT 162 with a "C" or better.

Typically offered in Spring.

**MAT 330. Using Technology Teaching Elementary School Mathematics. 3 Credits.**

Using computer software, calculators, and the Internet as aids in teaching elementary school mathematics.

Pre / Co requisites: MAT 330 requires prerequisites of MAT 101 and MAT 102.

Typically offered in Fall & Spring.

**MAT 331. Foundations of Geometry. 3 Credits.**

Geometric foundations from an advanced viewpoint. Topics are chosen from euclidean and noneuclidean geometrics.

Pre / Co requisites: MAT 331 requires prerequisite of C or better in MAT 162.

Typically offered in Spring.

**MAT 332. Differential Geometry. 3 Credits.**

Classical differential geometry from a modern viewpoint. Curves and surfaces and shape operators. Introduction to Riemann geometry.

Pre / Co requisites: MAT 332 requires prerequisites of C or better in MAT 200, MAT 261 and MAT 331.

**MAT 343. Differential Equations. 3 Credits.**

The general theory of nth order, and linear differential equations including existence and uniqueness criteria and linearity of the solution space. General solution techniques for variable coefficient equations, series solutions for variable coefficient equations, and study of systems of linear equations.

Pre / Co requisites: MAT 343 requires a prerequisite of C or better in MAT 162.

Typically offered in Fall, Spring & Summer.

**MAT 350. Techniques of Teaching Middle School Mathematics. 3 Credits.**

Techniques of Middle School Mathematics (3) Learning theory-based techniques for teaching children mathematical concepts in the middle school including: pedagogical content knowledge; techniques used to present specific mathematical concept; associated materials, including methods for exceptional students; levels of questioning; and motivational devices. Topics covered include number, measurement, algebra, geometry, and probability, and statistics.

Pre / Co requisites: MAT 350 requires prerequisites of MAT 261, EDA 304, Field Clearances, and Formal Admission to Teacher Education. MAT 350 requires a co-requisite of MAT 360.

Gen Ed Attribute: Writing Emphasis.

Typically offered in Fall.

**MAT 351. Methods for Teaching Children Math. 3 Credits.**

Concepts, learning aids, syllabi, texts, and methods in elementary school mathematics.

Pre / Co requisites: MAT 351 requires prerequisites of MAT 101 and MAT 102.

Typically offered in Fall, Spring & Summer.

**MAT 352. Methods for Teaching Children Mathematics II. 3 Credits.**

Techniques for teaching children concepts such as geometry in two and three dimensions, number sentences, graphing, ratios and percentages, quantifiers, etc. Use of laboratory materials will be emphasized.

Pre / Co requisites: MAT 352 requires prerequisites of MAT 351, Field clearances and Formal Admission to Teacher Education.

Typically offered in Spring.

**MAT 353. Methods for Teaching Middle School Mathematics. 3 Credits.**

Techniques for teaching children mathematical concepts in the middle school standards. Topics covered include number, algebra, geometry, and probability and statistics.

Pre / Co requisites: MAT 353 requires prerequisites of MAT 121, MAT 312, MAT 313, MAT 351, field clearances, and FATE.

Typically offered in Fall & Spring.

**MAT 354. Techniques of Teaching Secondary School Mathematics. 3 Credits.**

Techniques used in the presentation of specific mathematical concepts, associated materials, including methods for exceptional students; levels of questioning, and motivational devices. Scope and sequence of secondary mathematics topics. Criteria for text evaluation. Preview of student teaching.

Pre / Co requisites: MAT 354 requires prerequisites of MAT 350 and Formal Admission to Teacher Education. MAT 354 requires a co-requisite of MAT 364.

Gen Ed Attribute: Writing Emphasis.

Typically offered in Spring.

**MAT 357. Teaching Mathematics to Diverse Learners. 3 Credits.**

Methods and materials associated with the presentation of mathematics to the handicapped. Emphasis on individualization and involving thinking skills at the concrete level. Evaluative and interpretive techniques are included.

Pre / Co requisites: MAT 357 requires prerequisites of MAT 101 and MAT 102 and formal admission into teacher education.

**MAT 360. Field Experiences in Middle School Mathematics. 1 Credit.**

The objective of this course is to apply the skills, techniques, and dispositions required to be an effective middle and secondary mathematics teacher. This course will allow you to work in a classroom setting to examine how the curriculum is delivered in a middle and high school setting. You will work with students on an individual or group basis, work cooperatively with teachers, and participate in the lesson and assessment planning process. By the end of the course, you should teach at least one lesson in a classroom setting.

Pre / Co requisites: MAT 360 requires a prerequisite of Formal Admission to Teacher Education. MAT 360 requires a co-requisite of MAT 350.

Typically offered in Fall.

**MAT 362. Calculus IV. 3 Credits.**

The calculus of vector-valued functions of a vector variable. Derivatives and properties of the derivative including the chain rule, fields and conservative fields, integration, and Green's, Stokes', and Gauss' theorems.

Pre / Co requisites: MAT 362 requires prerequisite of C or better in MAT 261 and C or better in MAT 311.

**MAT 364. Field Experiences in Secondary School Mathematics. 1 Credit.**

The objective of this course is to apply the skills, techniques, and dispositions required to be an effective secondary mathematics teacher. This course will allow you to work in a classroom setting to examine how the curriculum is delivered in a middle and high school setting. You will work with students on an individual or group basis, work cooperatively with teachers, and participate in the lesson and assessment planning process. By the end of the course, you should teach at least one lesson in a classroom setting.

Pre / Co requisites: MAT 364 requires prerequisites of MAT 360 and Formal Admission to Teacher Education. MAT 364 requires a co-requisite of MAT 354.

Typically offered in Spring.

**MAT 371. Mathematics of Finance. 3 Credits.**

The purpose of this course is to introduce the mathematical theory behind the concepts of: measurement of interest, annuities, yield rates, amortization of loans, sinking funds, and yield rates. Understanding the fundamental concepts of financial mathematics, and how these concepts can be applied to calculate present and future values of various financial instruments, is the prevailing theme of the course.

Pre / Co requisites: MAT 371 requires prerequisite of MAT 162 with a "C" or better.

Typically offered in Fall.

**MAT 381. Discrete Mathematics. 4 Credits.**

This course is designed to provide a foundation for the mathematics used in the theory and application of computer science. Topics include mathematical reasoning, the notion of proof, logic, sets, relations and functions, counting techniques, algorithmic analysis, modelling, cardinality, recursions and induction, graphs, and algebra.

Pre / Co requisites: MAT 381 requires prerequisite of C or better in MAT 162.

**MAT 390. Seminar in Mathematics Education. 3 Credits.**

This course is the capstone course for grades 4-8 certification students completing the 30-credit mathematics certification option. Topics selected from mathematics, statistics, the history of mathematics, and mathematics education for their significance and interest. Field experience may be required.

Pre / Co requisites: MAT 390 requires prerequisite of Formal Admission to Teacher Education.

Repeatable for Credit.

**MAT 400. History of Mathematics for Elementary Teachers. 3 Credits.**

History and development of elementary mathematics from primitive times to the discovery of calculus. Problems of the period are considered.

Pre / Co requisites: MAT 400 requires prerequisites of MAT 312 and MAT 313.

**MAT 401. History of Mathematics. 3 Credits.**

Development of mathematics from the Babylonian era to the 18th Century. Some modern topics included.

Pre / Co requisites: MAT 401 requires prerequisite of C or better in MAT 261.

Gen Ed Attribute: Writing Emphasis.

Typically offered in Fall, Spring & Summer.

**MAT 405. Special Topics in Mathematics. 3 Credits.**

Topics announced at the time of offering.

Consent: Permission of the Department required to add.

Repeatable for Credit.

**MAT 411. Algebra I. 3 Credits.**

Abstract algebra. Algebraic systems, groups, rings, integral domains, and fields.

Pre / Co requisites: MAT 411 requires prerequisites of C or better MAT 200, MAT 261, and MAT 311.

Typically offered in Fall.

**MAT 412. Algebra II. 3 Credits.**

Abstract algebra. Algebraic systems, groups, rings, integral domains, and fields.

Pre / Co requisites: MAT 412 requires prerequisite of C or better in MAT 411.

Typically offered in Spring.

**MAT 413. Computer Algebra. 3 Credits.**

The focus of this course is to introduce students to computer algebra packages and review important topics in algebra, calculus and linear algebra.

Pre / Co requisites: MAT 413 requires prerequisites of MAT 162 and MAT 311 with a "C" or better.

Typically offered in Fall.

**MAT 414. Theory of Numbers. 3 Credits.**

Properties of integers; primes, factorization, congruences, and quadratic reciprocity.

Pre / Co requisites: MAT 414 requires prerequisites of C or better in MAT 200 and MAT 261.

Typically offered in Spring & Summer.

**MAT 415. Introduction to Cryptography. 3 Credits.**

An introduction to the mathematics behind various aspects of modern cryptography, including matrix cryptosystems, quadratic ciphers such as the Rabin cipher, exponential ciphers such as the Diffie-Hellman Key Exchange, the RSA algorithm and DES encryption.

Pre / Co requisites: MAT 415 requires prerequisites of MAT 161 and MAT 151 OR MAT 161 and MAT 200.

Typically offered in Spring.

**MAT 421. Mathematical Statistics I. 3 Credits.**

Probability theory, discrete and continuous random variables, distributions, and moment generating functions. Statistical sampling theory, joint and interval estimation, test of hypothesis, regression, and correlation.

Pre / Co requisites: MAT 421 requires a prerequisite of C or better in MAT 261.

Typically offered in Fall.

**MAT 422. Mathematical Statistics II. 3 Credits.**

Probability theory, discrete and continuous random variables, distributions, and moment generating functions. Statistical sampling theory, joint and interval estimation, test of hypothesis, regression, and correlation.

Pre / Co requisites: MAT 422 requires prerequisite of C or better in MAT 421.

Typically offered in Spring.

**MAT 423. Applied Probability. 3 Credits.**

Standard Concepts and methods of stochastic modeling and applications of stochastic processes.

Pre / Co requisites: MAT 423 requires prerequisites of MAT 261, MAT 311, and MAT 421 with a "C" or better.

Typically offered in Spring.

**MAT 425. Numerical Analysis II. 3 Credits.**

An examination of advanced topics in numerical analysis and scientific computing. Topics include: Approximation and interpolation of functions, numerical quadratures, matrix norms, iterative methods of numerical linear algebra, numerical solution of nonlinear systems of equations, and methods for the numerical solution of ordinary differential equations.

Pre / Co requisites: MAT 425 requires a prerequisite of C or better in MAT 325.

Typically offered in Fall.

**MAT 427. Introduction to Optimization Techniques. 3 Credits.**

Nature of optimization problems: deterministic and stochastic, and discrete and continuous. Computer methods of solution, systematic and random search, linear quadratic, dynamic programming, and others.

Pre / Co requisites: MAT 427 requires prerequisites of C or better in MAT 261 and C or better in MAT 311.

**MAT 432. Topology. 3 Credits.**

Elements of point set topology. Separation axioms. Connectedness, compactness, and metrizability.

Pre / Co requisites: MAT 432 requires prerequisites of C or better in MAT 200 and MAT 261.

**MAT 441. Real Analysis I. 3 Credits.**

Introduces the real line, limits of sequences, Cauchy sequences, limits of real functions, continuous functions, intermediate value theorem, the derivative, mean value theorems and Riemann integral.

Pre / Co requisites: MAT 441 requires prerequisites of C or better in MAT 200 and MAT 261.

Typically offered in Fall & Spring.

**MAT 442. Real Analysis II. 3 Credits.**

A continuation of MAT 441. Introduces infinite series, sequences and series of functions, Taylor's Theorem with applications and topics from integration theory.

Pre / Co requisites: MAT 442 requires prerequisite of C or better in MAT 441.

Typically offered in Fall.

**MAT 443. Applied Analysis I. 3 Credits.**

The techniques of analysis applied to problems in the physical sciences. Topics include partial differential equations, orthogonal functions, complex integration, and conformal mapping.

Pre / Co requisites: MAT 443 requires prerequisite of C or better MAT 261, MAT 311 and MAT 343.

Typically offered in Fall.

**MAT 444. Applied Analysis II. 3 Credits.**

The techniques of analysis applied to problems in the physical sciences. Topics include partial differential equations, orthogonal functions, complex integration, and conformal mapping.

Pre / Co requisites: MAT 444 requires prerequisite of C or better in MAT 443.

**MAT 445. Complex Variables. 3 Credits.**

Introduction to functions of a complex variable. Analytic functions, mappings, differentiation and integration, power series, and conformal mappings.

Pre / Co requisites: MAT 445 requires prerequisite of C or better in MAT 261.

Typically offered in Fall.

**MAT 455. Industrial Mathematics Practicum. 3 Credits.**

This is a case study, team problem-solving based course focused on solving real-world problems that can be modeled using discrete or continuous mathematics techniques and which emanate from industry. Ideally, the problems would be obtained from partnerships with local industry. Until these relationships develop, extant problems or problems arising in WCU faculty research (in math, physics, biology, geology, finance, etc.) will be used.

Pre / Co requisites: MAT 455 requires prerequisites of MAT 319, MAT 425, and MAT 413 and any one of MAT 493 or MAT 427.

Typically offered in Fall & Spring.

Repeatable for Credit.

**MAT 478. Fundamentals of Actuarial Science. 3 Credits.**

Students completing this course will have a better understanding of actuarial models of life contingencies, more specifically, students will understand that life insurance payments, life annuity payments, pension payments, etc. are determined by financial random variables dependent on human life.

Pre / Co requisites: MAT 478 requires prerequisite of MAT 371 and MAT 421 with a "C" or better.

Typically offered in Spring.

**MAT 479. Financial Calculus. 3 Credits.**

This course aims to provide the undergraduate mathematics major with an introduction to the mathematics behind derivative pricing and portfolio management. Pricing theory is first developed through the typical binomial model and then is extended to continuous time via the Black-Scholes model. In addition, the student will be exposed to how arbitrage can be used to aid in the pricing more complicated derivatives, such as call options on dividend-paying securities and exotic options.

Pre / Co requisites: MAT 479 requires prerequisite of MAT 371 and MAT 421 with a "C" or better.

Typically offered in Spring.

**MAT 491. Internship in Applied Mathematics. 2-4 Credits.**

In cooperation with regional businesses and industrial companies, student will perform an internship in applied mathematics.

Repeatable for Credit.

**MAT 493. Mathematical Modeling. 3 Credits.**

The idea of a mathematical model of a real situation. Techniques and rationales of model building. Examples from the life, physical, and social sciences.

Pre / Co requisites: MAT 493 requires prerequisites of C or better in MAT 261 and C or better in MAT 343.

**MAT 499. Independent Study in Mathematics. 1-3 Credits.**

Independent investigation of an area of mathematics not covered in the department's course offerings.

Consent: Permission of the Department required to add.

Repeatable for Credit.

#### MTE

**MTE 340. Using Technology Teaching Elementary Mathematics. 3 Credits.**

Using computer software, calculators, and the Internet as aids in teaching elementary school mathematics.

Pre / Co requisites: MTE 340 requires prerequisites of MAT 101 and MAT 102.

#### STA

**STA 311. Intro Statistical Computing and Data Management. 3 Credits.**

Course will give students the ability to manage and manipulate data effectively, conduct basic statistical analysis, and generate reports and graphics primarily using the SAS Statistical Software Program.

Typically offered in Spring.

**STA 320. Experimental Design. 3 Credits.**

The purpose of this course is to guide students in learning how to design, conduct and analyze the results of scientific studies so that valid and objective inferences about the population are obtained. It will cover ANOVAs, block, factorial, and split plot designs, as well as response surface analysis.

Pre / Co requisites: STA 320 requires a prerequisite of C or better in MAT 319.

Typically offered in Spring.

**STA 321. Topics in Advanced Statistics. 3 Credits.**

Course will cover select topics in categorical analysis, nonparametrics and time series analysis. Emphasis will be placed on statistical programming, particularly simulations.

Pre / Co requisites: STA 321 requires prerequisites of STA 311, STA 320, and MAT 421.

Typically offered in Spring.

**STA 490. Capstone Course in Statistics. 3 Credits.**

Course will synthesize lessons learned throughout the students career with the goal of preparing students for work as professional statisticians. Topics will include report writing, presentations, statistical consulting, sampling design, and resume writing.

Typically offered in Spring.