Graduate Studies

The course will describe the origins of mathematical concepts and their evolution over time, from early number systems to recent results in the foundations of mathematics. In addition to the mathematical ideas themselves, we will consider the role of applications in their development, and connections between society and mathematics through the ages.

Text: *An Episodic History of Mathematics*, by Steven G. Krantz, which may be downloaded free at

http://www.freebookcentre.net/maths-books-download/An-Episodic-History-of-Mathematics.html

Prerequisite: At least a year of calculus. Some background in mathematical proof-writing.

Instructor: Jeff Anderson, Ph.D.

Jeff Anderson earned a Ph.D. from Iowa State University in 1989. His research interests are in analysis of boundary value problems for partial differential equations, nonlinear and degenerate diffusion, nonlocal and memory interactions, applied models of angiogenesis as induced by a cancerous solid tumor, ecological threshold phenomena.

Time and location: **Monday through Thursday, 5:30-7:15 p.m., from June 27 to August 5 in Kettler G20**. (This location is different from a previous announcement.) This course is also offered online.

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.