Graduate Studies

MA 525 is a standard introductory course in complex analysis. Topics to be covered include complex numbers and complex-valued functions, differentiation of complex functions, power series, uniform convergence, integration, contour integrals, and conformal mapping.

Text: *Complex Variables and Applications*, 8th edition, by Churchill and Brown.

Prerequisites: A course in advanced calculus or real analysis with a grade of C- or above, or permission of instructor.

Instructor: Yifei Pan, Ph. D.

Yifei Pan received a Ph. D. from the University of Michigan. His thesis was written on a topic in several complex variables and he has published papers on complex functions of one and several variables.

Time and location: Mondays and Wednesdays, 6-7:15 p.m. starting January 11 in Kettler G43.

We review the basics of linear algebra: vector spaces, linear mappings, dimension, matrices, determinants, and systems of linear equations. We then study the theory of Jordan and rational canonical forms for a linear operator.

Text: *Linear Algebra*, 2nd edition, by Kenneth Hoffman and Ray Kunze

Prerequisite: A first course in linear algebra and a first course in abstract algebra, with C- or above.

Instructor: Adam Coffman, Ph. D.

Professor Coffman received a Ph.D. from the University of Chicago, and has taught upper-level courses in algebra, analysis, and geometry at IPFW since 1997. His research interests are in geometry and complex analysis.

Time and location: Mondays and Wednesdays, 4:30-5:45 p.m. starting January 11 in Kettler 216.

This course will present a logical development of plane geometry, both Euclidean and non-Euclidean, from a modern axiomatic perspective. There will be an emphasis on understanding the proofs of the theorems as well as their content. Historical and philosophical aspects of geometry will be included.

Text: *Euclidean and Non-Euclidean Geometries: Development and History* (4th edition) by Marvin Greenberg.

Prerequisites: MA 305 (Foundations of Higher Mathematics) with C- or better. Some experience with proofs and abstract mathematics in a previous or concurrent university course will be helpful.

Instructor: Lowell W. Beineke, Ph. D.

Lowell W. Beineke received a doctorate from the University of Michigan and is the Jack Schrey Professor of Mathematics. He has won several teaching awards (including a listing in Purdue's *Book of Great Teachers *) and research awards, and has published more than 100 papers and several books in graph theory. He served as editor of *The College Mathematics Journal.*

Time and location: Tuesdays and Thursdays, 4:30-5:45 p.m. starting January 11 in Kettler 216.

This course introduces fundamental concepts and some common models for the analysis of time series data. Topics to be covered include the autocovariance function and spectrum of stationary processes, the structure, estimation, interpretation, and identification of AutoRegressive (Iterated) Moving Average (ARIMA) models, forecasting, model diagnostics, seasonal models, and transfer function models. Resources in R, an open-source programming environment, will be used for data analysis and graphics.

Text: *Time Series Analysis with applications in R*, second edition by Cryer and Chan, Springer.

Prerequisite: STAT 512 with C- or above.

Instructor: Yvonne Zubovic, Ph. D.

Yvonne Zubovic received a Ph. D. from The Ohio State University in 1988 and has taught at IPFW since 1991. In 1997, she received the Outstanding Teacher award for IPFW. Her main research interests are in biostatistics.

Time and location: Tuesdays and Thursdays 6-7:15, beginning January 12, in Kettler 216.

This course presents the basic theory of some algebraic structures of importance in modern mathematics: groups, rings, and fields. The theory will be applied to the solution of polynomial equations and other problems from geometry.

Text: *Abstract Algebra*, 3rd edition, by John A. Beachy and William D. Blair.

Prerequisite: A first course in abstract algebra, such as MA 453, or consent of instructor. Some background in linear algebra is also helpful.

Instructor: Adam Coffman, Ph.D.

Professor Coffman received a Ph.D. from the University of Chicago, and has taught upper-level courses in algebra, analysis, and geometry at IPFW since 1997. His research interests are in geometry and complex analysis.

Time and location: Mondays and Wednesdays, 4:30-5:45 p.m., beginning August 24, in Kettler 218. (*update July 2015: MA 553 has been canceled for Fall 2015, it may be offered again in some future Fall semester*.)

In this course, we discuss 1st and 2nd order PDEs, including transport equations, heat equations, wave equations and Laplace equations. We will mainly focus on solutions and the corresponding properties (uniqueness, maximum principle etc) of solutions. Since PDEs are derived directly from models in physics and engineering, the understanding of solutions can be used to explain various physical phenomena.

Texts:

*Partial Differential Equations for Scientists and Engineers.*Author: Stanley Farlow. ISBN-13: 978-0486676203*Partial Differential Equations: An introduction***(optional)**Author: Walter Strauss. ISBN-13: 978-0-470-05456-7

Prerequisite: a first course in differential equations, such as MA 363. See the instructor if you have a question about your background.

Instructor: Yuan Zhang, Ph. D.

Yuan Zhang received a Ph. D. from Rutgers University. Her current research interest is several complex variables and the corresponding PDEs.

Time and location: Tuesdays and Thursdays 6-7:15 p.m., beginning August 25, in Kettler G40.

This is a second course in linear algebra, with applications. The course starts with a quick review of matrix algebra, then covers vector spaces, linear transformations, and a variety of topics related to eigenvalues and eigenvectors.

Text: *Linear Algebra*, 4th edition, by Friedberg, Insel, and Spence.

Prerequisite: An undergraduate course in linear algebra, such as MA 351.

Instructor: Safwan Akkari, Ph. D.

Safwan Akkari joined the IPFW faculty in 1988. He has a B.S. from the Lebanese University and an M.S. from the University of Tennessee Space Institute. He received a Ph.D. from Louisiana State University in 1988. His research interests are in matroid theory and graph theory.

Time and location: Tuesdays and Thursdays 4:30-5:45 p.m., beginning August 25, in Kettler 218.

MA 571 is an introductory graduate course in point-set topology, covering the ideas of metric and topological spaces, continuity, connectedness, and compactness. The course will emphasize both proofs and examples, and it will relate topology to the foundations of analysis.

Texts:

*Introduction to Topology*(3^{rd}ed) by Bert Mendelson*Counterexamples in Topology*by Lynn Arthur Steen and J. Arthur Seebach, Jr. These are both Dover paperbacks.

Prerequisite: A grade of C or better in MA 441 (Real Analysis) or its equivalent. See the instructor if you have a question about your background.

Instructor: Cecilia A. Weakley

Cecilia Weakley received a Ph.D. from the University of North Carolina at Chapel Hill and has taught at IPFW since 1989. She has published papers in measure theory and functional analysis.

Time and location: Tuesdays and Thursdays 4:30-5:45, beginning August 25, in Kettler 216.

Topics covered include inference in simple and multiple linear regression, polynomial regression, model building with real data; one-way and two-way analysis of variance, analysis of covariance; use of existing statistical computer programs.

Text: Selected chapters from *Applied Linear Statistical Models* (5^{th} ed) by Kutner, Nachtsheim, Neter, and Li (McGraw Hill). The IPFW bookstore will have a custom edition with those chapters.

Prerequisite: A statistics course similar to STAT 511, 517, or 528. See the instructor if you have a question about your background.

Instructor: Yvonne Zubovic, Ph. D.

Yvonne Zubovic received a Ph. D. from The Ohio State University in 1988 and has taught at IPFW since 1991. In 1997, she received the Outstanding Teacher award for IPFW. Her main research interests are in biostatistics.

Time and location: Mondays and Wednesdays 6-7:15, beginning August 24, in Kettler 218.

Major topics include divisibility theory, Euclidean Algorithm, prime numbers, congruences, Fermat's little theorem, number theoretic functions, and quadratic reciprocity. Other topics include cryptography and perfect numbers, as time permits.

Text: *Elementary Number Theory*, 7th edition, by David M. Burton.

Prerequisite: Any mathematics course where proofs were given in class or expected of the students. See the instructor if you have a question about your background.

Instructor: Robert Vandell, Ph. D.

Robert Vandell received a Ph. D. from Western Michigan University in 1996.

Time and location: MTWR 5:30-7:15 p.m., June 29 to August 7.

This course will cover calculus of functions of several variables and vector fields in orthogonal coordinate systems; optimization problems; Green's, Stokes', and Divergence Theorems; and some applications to engineering and physical sciences.

Text: *Introduction to Vector Analysi*s, 7th edition, by Davis and Snider

Prerequisite: MA 261 or 263. If you have a question, call the instructor at 481-6976.

Instructor: Safwan Akkari, Ph.D.

Safwan Akkari joined the IPFW faculty in 1988. He has a B.S. from the Lebanese University and an M.S. from the University of Tennessee Space Institute. He received a Ph.D. from Louisiana State University in 1988. His research interests are in matroid theory and graph theory.

Time and location: TR 6-7:15 p.m. in Kettler G47.

MA 521 is an introduction to optimization and its applications. The course starts with a review of some concepts from linear algebra and multivariate calculus, followed by unconstrained optimization methods, with applications to neural networks and least squares optimization. Constrained optimization is illustrated with linear programming and its nonlinear analogue, convex programming.

Text: *An Introduction to Optimization*, 4th edition, by Edwin K. P. Chong and Stanislaw H. Zak.

Prerequisite: A course in vector calculus or advanced calculus, and a linear algebra course. See the instructor if you have a question about your background.

Instructor: Peter Dragnev, Ph.D.

Peter Dragnev studied at the University of Sofia and the Institute of Mathematics of the Bulgarian Academy of Sciences. He received a Ph.D. from the University of South Florida in 1997. His research interests are in analysis, in particular, approximation theory and potential theory.

Time and location: MW 4:30-5:45 p.m. in Kettler 216

Stat 514 is an introduction to statistical designs that involve planning, conducting experiments, and analyzing the resulting data. The major objective of such designs is to develop a process that is affected minimally by external sources of variability. In this course, the focus is on experiments in engineering and in the chemical sciences. Latin squares, factorial designs, and fractional factorial designs will be discussed. Some background in regression analysis is recommended. Instructor and students will use the statistical software MINITAB.

Text: *Design of Experiments*, 8th edition, by Montgomery.

Prerequisite: STAT 512 or instructor's permission.

Instructor: Chand K. Chauhan, Ph.D.

Chand Chauhan received a Ph.D. from the Ohio State University and has taught at IPFW since 1983. She has conducted seminars and taught short courses in statistics for several area companies. Chauhan has also done consulting work for individuals as well as for companies. She has published and presented papers on the design of experiments.

Time and location: TR 6-7:15 in Kettler 216.

This course is an introduction to mathematical statistics. Topics include distributions of functions of random variables, especially the distributions of statistics when sampling from a normal distribution; the Central Limit Theorem and other limit theorems; point estimation and confidence intervals; properties of estimators; theory of statistical hypothesis tests, including tests based on normal models; and other topics as time permits.

Text: *Introduction to Probability & Statistical Inference* by Roussas.

Prerequisite: STAT 519 (Mathematical Probability)

Instructor: Yvonne Zubovic, Ph. D.

Yvonne Zubovic received a Ph. D. from The Ohio State University in 1988 and has taught at IPFW since 1991. In 1997, she received the Outstanding Teacher award for IPFW. Her main research interests are in biostatistics.

Time and location: MW 6-7:15 in Kettler 218.

This course is an introduction to graphs and networks, with applications. Topics include trees, connectivity, matchings, planarity, chromatic numbers, directed graphs, tournaments, and a variety of applications.

Text: *Graphs and Digraphs*, 5th ed., by G. Chartrand, L. Lesniak, and P. Zhang.

Prerequisite: MA 305 or 351. (A sophomore-level linear algebra course will provide the necessary level of mathematical maturity.) Please ask the instructor if you have a question about your background.

Instructor: Lowell W. Beineke, Ph.D.

Lowell W. Beineke received his Ph.D. from the University of Michigan and is the Schrey Professor of Mathematics. He has won several teaching awards and has published more than 100 papers and several books in graph theory.

Time and location: TR 4:30-5:45 in Kettler 118.