Department of Mathematics

West Chester University

Mathematics Information
Office: Room 101
25 University Avenue
West Chester, PA 19383
Phone (610) 436-2440
Fax (610) 738-0578
Email: Department Chair

Undergraduate Mathematics Courses

MAT 000 Fundamentals of Algebra (3 s.h.)

A preparatory course to remediate basic algebraic skills. Students obtaining a placement level less than 1 on the Mathematics Department placement test are required to take this course prior to any other mathematics course. Credits earned in 000-level courses do not count towards the 120 hours of credit needed for graduation. The course must be passed with a grade of C- or better.

MAT 001 Fundamental Skills in Arithmetic (3 s.h.)

A course designed to remediate basic arithmetic skills and to introduce elementary algebra. In general, students placed in MAT 001 have obtained a placement level less than 2 on the Mathematics Department placement test. Students are being prepared to take Fundamentals of Algebra (MAT 000) and must earn at least a C- to enroll in that course. A student in MAT 001 does not earn credit toward graduation for this course. Elementary and special education majors in need of algebraic and/or arithmetic remediation must enroll in MAT 001 and successfully pass with a grade of C- or better before being permitted to enroll in MAT 101.

MAT 101 Mathematics for Elementary Teachers I (3 s.h.)

Prerequisite: Placement level of 2, or above, on the Mathematics Department placement test, or successful completion of MAT001

Sets; functions; logic; development of whole numbers, integers, and rationals (including ratios, proportions, and percents); number theory; problem solving. For early childhood, elementary education, and special education majors only.

MAT 102 Mathematics for Elementary Teachers II (3 s.h.)

Prerequisite: MAT 101

Development of real numbers; geometry; measurement; probability and statistics; problem solving. For elementary education and special education majors only.

MAT 103 Introduction to Mathematics (3 s.h.)

Prerequisite: Placement level of 2, or above, on the Mathematics Department placement test, or successful completion of MAT 000

This course is designed to help prepare students to understand almost any quantitative issue 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.

MAT 105 College Algebra and Trigonometry (3 s.h.)

Prerequisite: Placement level of 3, or above, on the Mathematics Department placement test.

A unified course in algebra and trigonometry.

MAT 107 College Algebra (3 s.h.)

Prerequisite: Placement level of 3, or above, on the Mathematics Department placement test., or obtaining at least a C- in MAT 000

A thorough treatment of college algebra. Topics covered include the study of polynomial, exponential, and logarithmic functions, plus systems of linear equations..

MAT 108 Brief Calculus (3 s.h.)

Prerequisite: MAT105, MAT107, MAT110, or a placement level of 4, or above, on the Mathematics Department placement test.

An intuitive approach to the calculus of one and several variables with emphasis on conceptual understanding and practical application,

MAT 110 Precalculus (3 s.h.)

Prerequisite: Placement level of 4, or above, on the Mathematics Department placement test.

A preparation for MAT 161, Calculus I. Topics include polynomial and rational functions, algebra of functions, graphs of functions, transcendental functions, trigonometry, series, induction, and complex numbers.

MAT 121 Statistics I (3 s.h.)

Prerequisite: Placement level of 2, or above, on the Mathematics Department placement test. or successful completion of MAT 000.

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

MTL 121 Statistics Lab I (1 s.h.)

Prerequisite or Corequisite MAT 121

Introduces the student to using and programming the computer to solve statistical problems and to aid the student in understanding statistical concepts.

MAT 122 Statistics II (3 s.h.)

Prerequisite: MAT121

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

MAT 151 Introduction to Discrete Mathematics (3 s.h.)

Prerequisite: Placement level of 2, or above, on the Mathematics Department placement test. or successful completion of MAT 000.

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

MAT 161 Calculus I (4 s.h.)

Prerequisite: C or better in Mat 110 or placement level of 5 on the Mathematics Department placement test.

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

MAT 162 Calculus II (4 s.h.)

Prerequisite: MAT 161 with a grade of C or better.

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

MAT 200: The Nature of Mathematics

Prerequisite: Mat161

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.

Course should be taken by the end of the sophomore year and passed with a grade of at least a C before enrolling in higher-level mathematics course.

MAT 221 Applied Statistics (3 s.h.)

Prerequisite: CSC 141 (or equivalent) and MAT 162 (or equivalent).

Probabilities, discrete and continuous probability distributions, methods of estimation, and hypothesis testing.

MAT 209 Topics in Mathematics for the Elementary Teacher (3 s.h.)

Prerequisite: MAT 102

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 metric system with practice in the classroom. Additional topics in applied mathematics will be considered.

MAT 261 Calculus III (3 s.h.)

Prerequisite: MAT 162

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.

MAT 281 Discrete Mathematics (4 s.h.)

Prerequisite: MAT 162

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, modeling, cardinality, recursions and induction, graphs, and algebra..

MAT 301: The Scientific Revolution

This course addresses how modern science began in the seventeenth

century. It includes introductions to the heroes of science – Copernicus, Kepler, Galileo and Newton. By examining its origins in the seventeenth century, the course addresses the nature of modern science.

This course counts toward both the Interdisciplinary (I) and Writing Emphasis (W) requirements.

MAT 311 Linear Algebra (3 s.h.)

Prerequisite: MAT 110 or MAT 161

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

MAT 312 Algebra for Elementary Teachers (3 s.h)

Prerequisite: MAT 261

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.

MAT 325 Computational Mathematics (3 s.h.)

Prerequisite: C or better in MAT 162

This course is designed to introduce the student to the use of the computer as an investigative tool in the field of mathematics with emphasis on experimental techniques involving graphical and numerical displays, application of techniques from numerical analysis to data driven problems, and the use of computers in solution techniques.

Mat 330 Using Technology in Teaching Elementary School Mathematics (3 s.h.)

PREREQ: MAT 101 and 102

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

MAT 331 Foundations of Geometry (3 s.h.)

Prerequisite: MAT 161 or above

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

MAT 332 Differential Geometry (3 s.h.)

Prerequisite: MAT 261

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

MAT 333 Geometry for Elementary Teachers (3 s.h.)

Prerequisite: MAT 102

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

MAT 343 Differential Equations (3 s.h)

Prerequisite: MAT 261

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.

MAT 345 Applied Probability (3 s.h.)

Prerequisites: C or better in MAT 261

Upon completion of this course, a student should know the standard concepts and methods of stochastic modeling. In addition, the student should have a better understanding of the applications of stochastic processes to other disciplines, including biology, management, social sciences and statistics.

MAT 349 Teaching Mathematics in Early Childhood (3 s.h)

Prerequisite: MAT 101

Concepts, learning aids, syllabi, texts, and methods in early childhood mathematical teaching.

MAT 350 Foundations of Mathematics Education (3 s.h.)

Prerequisite: MAT 231 and MAT 261

Historical overview of mathematics education with emphasis on influential curricular programs, implications of learning theory, significance of research, identification of current issues, organizational alternatives for the classroom, and evaluation resources..

MAT 351 Teaching Mathematics in Elementary Schools I (3 s.h)

Prerequisite: MAT 101 and MAT102

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

MAT 352 Teaching Mathematics in Elementary Schools II (3 s.h.)

Prerequisite: MAT 351

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.

MAT 354 Techniques of Teaching Secondary School Mathematics (3 s.h.)

Prerequisite: MAT 350

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

MAT 357 Teaching to Diverse Learners (3 s.h.)

Prerequisite: MAT 102

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.

MAT 362 Calculus IV (3 s.h.)

Prerequisite: MAT 261

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.

**MAT 390 Seminar in Mathematics Education (3 s.h.)

Prerequisite: MAT 351

Typical topics are remedial programs, low achiever programs, materials for mathematics education, methodology in mathematics education, mathematics and the computer, theories of mathematics education, and analysis of research in mathematics education.

MAT 400 History of Mathematics for Elementary Teachers (3 s.h.)

Prerequisite: MAT 212 and MAT 233

History and development of elementary mathematics from primitive times to the discovery of calculus. Problems of the period are considered. Development of mathematics from the Babylonian era to the 18th century. Some modern topics included

MAT 401 History of Mathematics (3 s.h.)

Prerequisite: Mat 261 (C or better in Mat 261)

Development of mathematics from the Babylonian era to the 18th century. Some Modern topics included.

MAT 403 Fundamentals of Actuarial Science (3 s.h.)

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. Prerequisite: C or better in MAT 261

**MAT 405 Special Topics in Mathematics (3 s.h.)

Prerequisite: Consent of Department Chairman

Topics and prerequisites announced at the time of offering.

MAT 406 Mathematics of Finance (3 s.h.)

Prerequisite: C or better in MAT 261

Students completing this course will understand the mathematical theory of interest in a deterministic setting. They will become familiar with compound interest and the time value of money and learn how the two are used to compute the present value of future payments. Students will be able to calculate both the present and accumulated values of annuities and the price of bonds. They will be able to determine yield rates on investments and the time required to accumulate a given amount or repay a given loan amount. In addition, they should be able to apply interest theory to amortization of lump sums, fixed income securities, depreciation, mortgages, etc.

MAT 409 Financial Calculus (3 s.h.)

Prerequisite: C or better in MAT 261

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 pricing more complicated derivatives, such as call options on dividend-paying securities and exotic options.

MAT 411-412 Algebra I-II (3 s.h.) (3 s.h.)

Prerequisite: MAT 261. MAT 411 must precede 412.

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

MAT 413 Computer Algebra (3 s.h.)

Prerequisite: C or better in MAT 162 and MAT 311.

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

MAT 414 Theory of Numbers (3 s.h.)

Prerequisite: MAT 261

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

MAT 421-422 Mathematical Statistics I-II (3 s.h), (3 s.h)

Prerequisite: MAT 261. MAT 421 must precede 422.

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.

MAT 425 Numerical Analysis (3 s.h.)

Prerequisite: CSC 141 and MAT 261

Numerical methods for the approximate solution of applied problems. Interpolation theory, curve fitting, approximate integration, and numerical solution of differential equations

MAT 427 Introduction to Optimization Techniques (3 s.h.)

Prerequisite: CSC 141 and MAT 261.

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.

MAT 432 Topology (3 s.h.)

Prerequisite: Completion of a 400 level mathematics course with a C or better

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

MAT 441-442 Advanced Calculus I-II (3 s.h) (3 s.h)

Prerequisite: MAT 261. MAT 441 must precede 442.

A rigorous treatment of the calculus of a single real variable. Topics in several real variables and an introduction to Lebesque integration.

MAT 443-444 Applied Analysis I-II (3 s.h) (3 s.h.)

Prerequisite: MAT 261. MAT 443 must precede 444

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

MAT 445 Complex Variables (3 s.h.)

Prerequisite: MAT261

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

**MAT 490 Seminar in Mathematics (3 s.h.)

Prerequisite: Senior standing and consent of Department Chairperson.

Topics in mathematics selected for their significance and student/instructor interest. Independent study and student reports, oral and written.

** May be taken again for credit.

MAT 493 Mathematical Modeling (3 s.h.)

Prerequisite: MAT 261 and MAT 343.

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

**MAT 499 Independent Study (1-3 s.h.)

Prerequisite: Written Permission of the instructor

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

** May be taken again for credit

STA 311 Introduction to Statistical Computing and Data Management

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