# Graduate Course News

## Graduate Courses in Mathematics and Statistics for Fall 2017

### MA 511 - Linear Algebra with Applications

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: **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 21, in Kettler 216. The lectures will be video archived for students.

### MA 523 - Introduction to Partial Differential Equations

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: **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: Tuesdays and Thursdays 6-7:15 p.m., beginning August 21, in Kettler G40.

### MA 553 - Introduction to Abstract Algebra

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: Doug Weakley, Ph.D.

Professor Weakley received a Ph.D. from Northwestern University, and has taught at IPFW since 1986. His research interests are in coding theory and algebraic combinatorics.

Time and location: Tuesdays and Thursdays, 6-7:15 p.m., beginning August 21, in Kettler G29.

### MA 571 - Elementary Topology

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**, 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 21, in Kettler G47.

### STAT 512 - Applied Regression Analysis

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: *Introduction to Linear Regression Analysis* (4^{th} ed) by Montgomery, Peck, and Vining (Wiley).

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 21, in Kettler 218.

## Graduate Courses in Mathematics and Statistics for Summer 2017

#### MA 556 - Introduction to the Theory of Numbers

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 26 to August 4. This course is also offered online.

#### STAT 514 - Design of Experiments

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. 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: MTWR 3-4:45 in Kettler 220, from May 15 to June 23. This course is also offered online.

## Graduate Courses in Mathematics and Statistics for Fall 2016

### MA 540 - Analysis I

In MA 540 (and 541) we examine some fundamental topics from calculus with closer attention to theory and proof. In the setting of metric spaces we study sequences and continuous functions, using the concepts of completeness, compactness, and connectedness.

Text: *Introduction to Analysis* by Maxwell Rosenlicht.

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 Weakley, Ph.D. (weakley (at) ipfw.edu ; (260)-481-6233)

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 p.m., starting August 23, in Kettler G44.

### MA 598 - Coding Theory and Cryptography

Description: An introduction to the mathematical theories of error-correcting codes and cryptography. Linear codes; cyclic codes; the Hamming, Golay, BCH, and Reed-Muller codes; maximum likelihood decoding. History of cryptographic techniques; symmetric-key cryptography (DES, AES); public-key cryptosystems and related techniques; protocols for information security.

Text: *Coding theory and Cryptography: The Essentials*, 2nd edition, Hankerson et al, CRC Press. Material from chapters 1-5 and 10-12 will be covered.

Outline:

●Introduction to error-correcting codes. (1.5 weeks)

●Linear codes. (1.5 weeks)

●Perfect codes, the Hamming and Golay codes. (2 weeks)

●Cyclic linear codes. (1.5 weeks)

●BCH codes over finite fields. (1.5 weeks)

●Introduction to cryptography; historical cryptosystems and cryptanalysis. (1.5 weeks)

●Symmetric key systems, DES and AES. (2 weeks)

●Public-key cryptosystems (RSA, ElGamal) with number-theoretic underpinnings. (3 weeks)

●Cryptographic protocols. (1 week)

Prerequisite: MA 351 or an equivalent linear algebra course with a grade of C or better.

Instructor: Professor **Robert Vandell** (vandellr (at) ipfw.edu; 260-481-6186)

Robert Vandell received a Ph. D. from Western Michigan University in 1996. His research in graph theory has interested him in coding theory.

Time and location: Mondays and Wednesdays, 4:30-5:45 p.m., starting August 22, in Kettler G44.

### STAT 512 - Applied Regression Analysis

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: *Linear Regression Analysis*, Montgomery, Peck, & Vining, **5th edition**, Wiley publ.

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 p.m., starting August 22, in Kettler 220

**STAT 519 - Introduction to Probability**

This course is an introduction to probability as a foundation for statistics. Topics include sample spaces and random variables; joint, conditional, and marginal distributions, special discrete and continuous distributions; moment generating functions, distribution of functions of random variables; limit theorems.

Text: *An Introduction to Probability and Statistical Inference* by George Roussas.

Prerequisite: Multivariable calculus. See the instructor if you have a question about your background.

Instructor: Yihao Deng, Ph.D. (DengY (at) ipfw.edu ; (260)-481-4185)

Yihao Deng joined the faculty in fall 2006, after receiving his Ph.D. in statistics from Old Dominion University. His areas of specialization include longitudinal data analysis, regression analysis, and generalized linear models. He has done consulting work on leadership and organizational change, youth violence prevention, adolescent ADHD, and other topics.

Time and location: Tuesdays and Thursdays, 6-7:15 p.m., starting August 23, in Kettler 218.

# Graduate Course in Mathematics for Summer 2016

### MA 580 History of Mathematics

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.