## Mathematics

25 University Avenue, Room 101

West Chester University

West Chester, PA 19383

610-436-2440

Dr. Jackson, Chairperson

Dr. Johnston, Assistant Chairperson

Dr. Gallitano, Graduate Coordinator

610-436-2452

### Professors [top]

Gail M. Gallitano, Ed.D., Columbia University

Robert Gallop, Ph.D., Drexel University

Peter L. Glidden, Ph.D., Columbia University

Viorel Nitica, Ph.D., Pennsylvania State University

Randall H. Rieger, Ph.D., University of North Carolina

Waclaw Szymanski, D.Sc., Polish Academy of Sciences

Lin Tan, Ph.D., University of California, Los Angeles

Paul Wolfson, Ph.D., University of Chicago

### Associate Professors

Michael Fisher, Ph.D., Lehigh University

Shiv K. Gupta, Ph.D., Case Western Reserve University

Kathleen Jackson, Ed.D., Temple University

Clifford Johnston, Ph.D., Temple University

Lisa Marano, Ph.D., Lehigh University

Scott McClintock, Ph.D., University of Kentucky

James McLaughlin, Ph.D., University of Illinois

Joseph Moser, M.S., Purdue University

Scott Parsell, Ph.D., University of Michigan

### Assistant Professors

Brian Bowen, Ph.D., University of Delaware

Andrew Crossett, Ph.D., Carnegie Mellon University

Whitney George, Ph.D., University of Georgia

Daniel Robert Ilaria, Ph.D., Rutgers University

Kim Johnson, Ph.D., Pennsylvania State University

Allison Kolpas, Ph.D., University of California, Santa Barbara

Mark A. McKibben, Ph.D., Ohio University

Rosemary Sullivan, Ph.D., Lehigh University

Peter Zimmer, Ph.D., University of Kansas

### INSTRUCTOR

Joann H. Kump, M.A.T., Indiana University

## Programs of Study [top]

The Department of Mathematics offers the master of arts degree with options in mathematics and mathematics education, the master of science degree in applied statistics, and a certificate in applied statistics.

## Master of Arts in Mathematics

The mathematics option is for students interested in furthering their mathematical background. It provides the foundation for continued work in mathematics leading to the Ph.D. in mathematics.

The mathematics education option is directed to teachers of mathematics who wish to strengthen their background in mathematics and mathematics education; in addition, it provides the foundation for doctoral programs in mathematics education.

## Admission to the M.A. Program [top]

### Mathematics Education Option

In addition to meeting the basic admission requirement of the University, applicants must have a bachelor's degree with a mathematics major or related field. Applicants must schedule an interview with the graduate coordinator prior to enrollment. Deficiencies, as determined by the graduate coordinator, may be removed by successfully completing appropriate course(s). Applicants must submit scores for the general section of the Graduate Record Examination (GRE).

### Mathematics Option

In addition to meeting the basic admission requirements of the University, applicants must have a bachelor’s degree in mathematics or a related field. Applicants must schedule an interview with the graduate coordinator prior to enrollment. A full treatment of calculus along with an advanced undergraduate course in modern algebra, linear algebra, differential equations, and geometry is recommended. Deficiencies in these areas may be removed by successfully completing appropriate courses. Applicants must submit scores for the general section of the GRE.

## Requirements for the M.A. Degree

In addition to completing the course requirements shown below, candidates must either pass a comprehensive examination or submit a thesis.

### Mathematics Education Option (33 semester hours)

- One three-credit course in each (12 semester hours):

MTE 507, 508, 512, 604 - One three-credit course in each (15 semester hours):

MAT 515, 521, 532, 545, and STA 505 - Two three-credit electives (6 semester hours):

One to be a continuation of real analysis, algebra, or geometry.

One to be chosen from:

MAT 503, 514, 516, 533, 546, 570, 575, or STA 506

(Elective courses to be scheduled in advance on a rotating basis.)

### Mathematics Option (33 semester hours)

- One three-credit course in each (18 semester hours):

MAT 515, 516, 545, 546, 575, and an approved course in statistics or applied mathematics - MAT or STA electives (15 semester hours)

Chosen from MAT or STA course offerings (except MAT 503 and MAT 541)

After 27 credits have been completed, the student selects either two more courses or the thesis option (MAT 609 and 610).

## Secondary Mathematics Certification Option

Some students pursue certification for Pennsylvania teaching after they graduate with bachelor’s degrees from West Chester or other universities. The Department of Mathematics normally accepts equivalent courses from colleges or universities accredited in the United States or their equivalent from schools in other countries. Students seeking post-baccalaureate certification should consult with the appropriate adviser in the Department of Mathematics to see which requirements they have already fulfilled in their undergraduate program and which they need to fulfill to get their teaching certificate. These students should also meet with their adviser to plan their academic progress and to ensure they are keeping up with requirements, and they should meet with an adviser in the Department of Professional and Secondary Education for information on required education courses. Students pursuing post-baccalaureate certification must meet all requirements for formal admission and student teaching.## Applied Statistics

Dr. Rieger, Program Director

Vital to a wide variety of disciplines, applied statisticians have found employment in pharmaceutical research and development, government public policy, economic forecasting and analysis, psychometrics, public health research, and many other areas. The mission of the program in applied statistics is to train students to possess the skills necessary for immediate employment and/or provide a course of study that would make further (doctoral) study in statistics, biostatistics, biomathematics, or other related fields feasible. The program provides strong training in statistical analysis and programming, design of scientific studies, and the ability to communicate statistical concepts.

### Admission to the M.S. Program

In addition to meeting the basic admission requirements of the University, applicants must have knowledge of calculus and linear algebra. Deficiencies, as determined by the program director, may be removed by successfully completing appropriate course(s). Borderline candidates for admission may be required to present GRE scores at the discretion of the program director.

### Admission to the Certificate Option

In addition to meeting the basic admission requirements of the University, applicants must have at least one undergraduate level (or higher) course in statistics. Deficiencies, as determined by the program director, may be removed by successfully completing an appropriate course.

## Master of Science in Applied Statistics

After admission to the program, students will be allowed to select the thesis or nonthesis track for the M.S. in applied statistics. The thesis option replaces one of the elective classes and STA 531 with a six-credit thesis, to be initiated after the completion of STA 505 and STA 506.

### Curriculum (32 semester hours)

**Nonthesis Option (32 semester hours)**

- Required (26 semester hours)

STA 505, 506, 507, 511, 512, 513, 514, and 531 - Electives (6 semester hours)

Two, three-credit electives from a selected area of concentration or STA 601 and one additional three-credit elective from a selected area of concentration

**Thesis Option (32 semester hours)**

- Required (29 semester hours)

STA 505, 506, 507, 511, 512, 513, 514, 609, and 610 - Electives (3 semester hours)

One three-credit elective from a selected area of concentration or STA 601

## Certificate in Applied Statistics

### Curriculum (19 semester hours)

- Required (13 semester hours)

STA 507, 511, 512, 514 - Electives (6 semester hours)

Two courses from a selected area of concentration

## Course Descriptions [top]

### Mathematics

Symbol: MAT

**503** History of Mathematics (3) Development of mathematics from prehistoric time to present. Emphasis on changes in
the mainstreams of mathematical thought through the ages.

**514** Theory of Numbers (3) Elementary number theory and selected topics in analytic number theory.

**515** Algebra I (3) Elements of abstract algebra, groups, commutative ring theory, modules, and associative algebras
over commutative rings.

**516** Algebra II (3) A continuation of MAT 515. Vector spaces, representation theory, and Galois theory. PREREQ: MAT 515.

**521** Discrete Mathematics and Graph Theory (3) Techniques of problem solving, including the use of binomial coefficients,
generating functions, recurrence relations, the principle of inclusion exclusion, and Polya's Theorem.

**532** Geometry I (3) This course is a rigorous introduction to geometry from a transformational point of view, emphasizing
Euclidean, hyperbolic, and/or projective geometry. Other topics such as Spherical geometry, symplectic geometry, or Affine geometry may be
included if time permits.

**533** Geometry II (3) A study of geometry using calculus as our main tool. The course covers the basics of differential
geometry - parametrizations, tangent spaces, curvature, geodesics - leading to Stokes theorem and the Gauss-Bonnett theorem. Several examples
will be studied in depth, including the sphere and the projective plane (which were introduced in the first course).

**535** Topology (3) A rigorous treatment of filters, nets, separation axioms, compactness, connectedness, and uniform spaces.

**541** Advanced Calculus (3) For students with background deficiencies in analysis. Ordinary and uniform limits; sequences
of functions; and the Riemann integral.

**545** Real Analysis I (3) A rigorous study of real-valued functions of real variables. PREREQ: MAT 541 or equivalent.

**546** Real Analysis II (3) Continuation of MAT 545. PREREQ: MAT 545.

**548** Industrial Mathematics – Continuous Models (3) This course is designed to provide a survey of mathematical concepts, techniques, and numerical algorithms used to study real-world continuous mathematical models. Application areas include population dynamics, climatology, feedback and control systems, traffic flow, diffusion, Black-Sholes model, fluids and transport, and epidemiology. Computer software packages such as Matlab, Mathematica, and Maple will be used in the analysis of the problems. PREREQ: MAT 261, 311, and 343.

**549** Industrial Mathematics – Discrete Models (3) This course is designed to provide a survey of mathematical concepts, techniques, and numerical algorithms used to study real-world discrete mathematical models. Application areas include forestation, particle dynamics, image processing, genetics, queues, efficient call and traffic routing, and optimal scheduling. Computer software packages such as Matlab, Mathematica, and Maple will be used in the analysis of the problems. PREREQ: MAT 261, 311, and 343.

**570** Mathematical Models in the Life, Physical, and Social Sciences (3) Techniques and rationales of model building.
Applications to the life, physical, and social sciences.

**575** Complex Analysis I (3) A rigorous study of complex-valued functions of complex variables.

**595** Topics in Mathematics Education (1-3) Topics announced at time of offering. Offered as needed. PREREQ: Permission
of instructor.

**599** Independent Study (1-3) Offered as needed.

**609** Thesis I (3) Conduct literature search, develop thesis proposal, and begin research under the guidance of a
mathematics faculty member. Offered as needed.

**610** Thesis II (3) Carry out research proposal developed in MAT 609 and present results to committee. Develop a
graduate-level thesis under the guidance of the Department of Mathematics. Offered as needed.

### Mathematics Education

Symbol: MTE

**501** Fundamental Concepts of Mathematics I (3) Selected topics that reflect the spirit and the content of the modern
elementary school mathematics programs. Logic, sets, functions, number systems, integers, number theory, rational numbers, and problem
solving, including estimations and approximations, proportional thinking, and percentages.

**502** Fundamental Concepts of Mathematics II (3) A continuation of MTE 501. The real number system, probability,
statistics, geometry, measurement, and problem solving. PREREQ: MTE 501.

**507** Foundations of Secondary Mathematics Education (3) Research methods in mathematics education; forces which have
shaped mathematics education; classroom implications of 20th-century learning theorists; assessment in the classroom; methods of organizing
for instruction; cultural and gender considerations.

**508** Junior High School Mathematics - Curriculum, Instruction, and Assessment (3) This course will focus on the curricula,
methods of instruction, and assessment techniques used to teach mathematics in a junior high school setting. Course topics will include
elementary school mathematics from the perspective of a secondary school teacher, junior high school mathematics, algebra I, and
general/consumer mathematics. Teachers also will explore strategies that can be used to integrate the calculator and computer into the
mathematics classroom. PREREQ: MTE 507 for students in the M.A. program.

**510** Algebra for the Elementary Teacher (3) An introduction to modern algebra. A comparative study of mathematics
systems. PREREQ: MTE 501 or equivalent.

**512** Senior High School Mathematics - Curriculum, Instruction, and Assessment (3) This course will focus on the
curricula, methods of instruction, and assessment techniques used to teach mathematics in a senior high school setting. Course topics will
include geometries, algebra II, trigonometry, precalculus, and discrete mathematics. Teachers also will explore strategies that can be used
to integrate the scientific and graphing calculator and computer into the mathematics classroom. PREREQ: MTE 507 for students in the M.A.
program.

**530** Geometry for the Elementary Teacher (3) Basic concepts in geometry. Euclidean geometry and postulative systems.
PREREQ: MTE 501 or equivalent.

**551** Teaching Mathematics to Diverse Populations (3) Examination of current programs in mathematics for students with
special needs; discussion of the pertinent research literature; and development of materials and techniques for these students.

**553** Teaching Children Mathematics I (3) In-depth treatment of strategies, methods, and materials for teaching the following concepts in an elementary classroom: place value; addition, subtraction, multiplication, and division of whole numbers; measurement; elementary number theory; geometry; fractions; and integers. PREREQ: Chapter 354 requires two mathematics courses.

**555** Teaching Children Mathematics II (3) A continuation of MTE 553 that covers the strategies and methods for teaching such topics as real numbers, deeper concepts of geometry in the plane and space, percents, proportional thinking, and algebra. PREREQ: MTE 553; field clearances.

**560** Teaching Algebra in the Secondary School (3) Methods and materials for teaching the concepts of first- and
second-year algebra. Emphasis on relevant applications to real-life situations. Objectives and criterion-referenced test items are developed
for prealgebra as well as for the two algebra courses. Current textbooks achievement tests and audio-visual materials on algebraic topics
are reviewed.

**561** Calculus for Teachers (3) Analytic geometry of both the straight line and conics, and elements of the calculus of
functions of a single real variable are reviewed. Topics include limits, continuity, the derivative and integral and their applications,
curve sketching, and polar coordinates. Emphasis on methods of teaching these topics to secondary school students.

**595** Topics in Mathematics Education (1-3) Topics announced at time of offering. Offered as needed. PREREQ: Permission
of instructor.

**599** Independent Study (1-3)

**604** Research Seminar (3) This course will focus on the study of research in mathematics education. Contemporary topics
of research will be discussed and perused. Students will be expected to report on a topic of research of their choosing. In addition,
empirical study and design will be discussed along with data analysis and the reporting of results.

**610** Thesis (3-6)

### Applied Statistics

Symbol: SAT

**505** Mathematical Statistics I (3) A rigorous mathematical treatment of the underlying theory of probability and
statistical inference. Probability spaces, discrete and continuous distribution theory, functions of random variables, Central Limit
Theorem, and other topics.

**506** Mathematical Statistics II (3) Continuation of STA 505. Point estimation, hypothesis tests, confidence intervals,
asymptotic properties of estimators, and other topics.

**507** Introduction to Categorical Analysis (3) Data-driven introduction to statistical techniques for analysis of categorical data arising from a variety of studies. Contingency tables, logistic regression survival models, nonparametric methods, and other topics. PREREQ: STA 511 and 512 or permission of instructor.

**510** Statistical Methods for Research (3) This course provides the tools and methods for designing a research project,
conducting the research, managing and manipulating a dataset, and analyzing data. This course is for students not enrolled in the applied
statistics graduate degree program. It requires no prior course in statistics or computer science. Topics include research design, basic
statistics, introductory statistical programming using SAS and Excel, statistical analysis (including t-tests, linear regression, ANOVA,
and chi-squared tests), and writing a final report, including graphics, summarizing the results.

**511** Introduction to Statistical Computing (3) Course will give students the ability to effectively manage and
manipulate data, conduct statistical analysis, and generate reports and graphics, primarily using the SAS statistical software sackage.

**512** Principles of Experimental Analysis (4) Course provides technology-driven introduction to regression and other
common statistical multivariable modeling techniques. Emphasis on interdisciplinary applications.

**513** Intermediate Linear Models (4) Rigorous mathematical and computational treatment of linear models. PREREQ: STA
505, 506, 511, and 512 or permission of instructor.

**514** Modern Experimental Design (3) Focusing on recent journal articles, this course will investigate issues associated
with design of various studies and experiments. Pharmaceutical clinical trials, case-control studies, cohort studies, survey design,
bias, causality, and other topics. PREREQ: STA 511 and 512 or permission of instructor.

**521** Statistics I (3) For nonmathematics majors. Emphasis on applications to education, psychology, and the sciences.
Distributions, measures of central tendency and variability, correlation, regression and hypothesis testing, and other topics.

**531** Topics in Applied Statistics (3) Topics of current interest in research and industry announced at time of offering.

**532** Survival Analysis (3) This course provides students with the knowledge and tools to conduct a complete statistical
analysis of time-to-event data. Students will get experience using common methods for survival analysis, including Kaplan-Meier Methods,
Life Table Analysis, parametric regression methods, and Cox Proportional Hazard Regression. Additional topics include discrete time
data, competing risks, and sensitivity analysis.

**533** Longitudinal Data Analysis (3) Introduction to the application and theory for clustered and longitudinal data
models. Course addresses the analysis for both continuous and categorical response data. Course will be held in the statistics lab and
use the statistical software package SAS. Other software such as R, HLM, SPSS, MIXORMIXREG may be introduced. PREREQ: STA 507, 511, 512,
and 513 or permission of director.

**534** Time Series (3) Time series analysis deals with the statistical study of random events ordered through time.
This class focuses on the characteristics inherent in processes such as repetitive cycles and deteriorating dependence. Topics include
seasonal decomposition, exponential smoothing, and ARIMA models. Emphasis will be placed on real-life data analysis and statistical
communication. Data analysis will be done with a variety of programs such as SAS, R, and Excel. PREREQ: STA 511 and 512.

**599** Independent Study (1-3) Individual exploration of nine topics in statistics.

**601** Internship in Applied Statistics (1-6) In cooperation with a regional industrial company student will perform
an internship in applied statistics.

**609** Thesis I (3-6) Preliminary research under the guidance of a mathematics faculty member. Students must present
oral preliminary findings before proceeding to STA 610.

**610** Thesis II (3-6) Research project under the guidance of the mathematics faculty.

### Service Courses in Mathematics

Mathematics Education (MTE)

**501** Fundamental Concepts of Mathematics I

**502** Fundamental Concepts of Mathematics II

**510** Algebra for the Elementary Teacher

**553** Teaching Elementary School Mathematics I

**560** Teaching Algebra in the Secondary School

**561** Calculus for Teachers

**562** Computer Applications for Elementary School Mathematics

### Statistics (STA)

**521** Statistics I