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: Mondays and Wednesdays, 4:30-5:45 p.m. starting January 13 in Kettler 216.
Prerequisite: STAT 512 with C- or above.
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, 6th 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: Matthew Walsh, Ph. D.
Matthew Walsh studied at the University of Waterloo and at Auburn University, receiving his doctorate from the latter in 2002. He has published multiple research papers on diverse topics in graph theory
and related subjects. He is a fellow of the Institute for Combinatorics and its Applications, and was awarded their Kirkman medal for promising young researchers in 2005.
Time and location: MTWR 5:30-7:15 p.m. in Kettler G47, July 1 to August 9.
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 27, in Kettler 119.
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.
Text: 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: Mondays and Wednesdays 6-7:15 p.m., beginning August 26, in Kettler G44.
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 26, 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.
Text: Introduction to Topology (3rd ed) by Bert Mendelson and 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, Ph.D.
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 27, in Kettler 239.
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: To be determined
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: Tuesdays and Thursdays 6-7:15, beginning August 27, in Kettler 218.