Graduate Catalog

2012 – 2013

Office of Graduate Studies and Extended Education
McKelvie Hall, 102 W. Rosedale Avenue
West Chester University
West Chester, PA 19383
Phone: 610-436-2943
Fax: 610-436-2763
gradstudy@wcupa.edu


Revised August 2012

Mathematics


25 University Avenue, Room 101
West Chester University
West Chester, PA 19383
610-436-2440
Dr. Jackson, Chairperson
Dr. Marano, 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
Frank Grosshans, Ph.D., University of Chicago
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

Shiv K. Gupta, Ph.D., Case Western Reserve University
Daniel Robert Ilaria, Ph.D., Rutgers University
Kathleen Jackson, Ed.D., Temple University
Clifford Johnston, Ph.D., Temple University
Lisa Marano, Ph.D., Lehigh University
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
Michael Fisher, Ph.D., Lehigh University
Allison Kolpas, Ph.D., University of California, Santa Barbara
Scott McClintock, PhD., University of Kentucky
Rosemary Sullivan, Ph.D., Lehigh University
Peter Zimmer, Ph.D., University of Kansas

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. 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 schedule an interview with the graduate coordinator prior to enrollment. Applicants must have a minimum of 30 semester hours of mathematics, including a full treatment of calculus, at least one advanced undergraduate course in modern algebra, and one in advanced calculus. 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)

  1. One three-credit course in each (12 semester hours):
    MTE 507, 508, 512, 604
  2. One three-credit course in each (15 semester hours):
    MAT 515, 521, 532, 545, and STA 505
  3. 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)

  1. One three-credit course in each (18 semester hours):
    MAT 515, 516, 545, 546, 575, and an approved course in statistics or applied mathematics
  2. 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).

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)

  1. Required (26 semester hours)
    STA 505, 506, 507, 511, 512, 513, 514, and 531
  2. Electives (6 semester hours)
    Two, three-credit electives from a selected area of concentration or STA 601 and one additional three-credit electives from a selected area of concentration

Thesis Option (32 semester hours)

  1. Required (29 semester hours)
    STA 505, 506, 507, 511, 512, 513, 514, 609, and 610
  2. 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)

  1. Required (13 semester hours)
    STA 507, 511, 512, 514
  2. 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.

513 Linear Algebra (3) Vectors, vector spaces, determinants, linear transformations, matrices, and bilinear and quadratic forms.

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.

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.

572 Proseminar (3) Seminar in generating and solving problems in mathematics.

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

593 Topics in the History of Mathematics (3) Specialized topics in the history of mathematics announced at the time of offering. PREREQ: Permission of instructor.

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.

554 Contemporary Methods of Teaching Mathematics in the Elementary School (3) History and development of the modern elementary school mathematics programs. Theories and findings of recent and contemporary learning theorists are investigated. Modern organizational strategies surveyed, including team teaching, individualized instruction, open space, contemporary instruction strategies, such as individualized learning systems, mathematical laboratories, and individually prescribed instruction, are studied. PREREQ: MTE 553.

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.

562 Computer Applications for Elementary and Middle School Mathematics (3) This technology-driven approach to teaching elementary school mathematics will include activities designed to enable teachers to use content-oriented software, spreadsheets, and graphic tools in the development of lessons involving mathematical applications. Emphasis will focus on teacher participation in simulations dealing with student-thinking skills.

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 (3-6) 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