# Graduate Course News Archive 2011-12

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- Graduate Course News Archive 2011-12

## Graduate Courses in Mathematical Sciences for Fall 2012

### STAT 519 - Introduction to Probability

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

### MA 540 - Analysis I

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 in the areas of partial differential equations and complex analysis.

### STAT 512 - Applied Regression Analysis

*Applied Linear Statistical Models*, 5th edition, by Kutner, Nachtsheim, Neter, and Li.

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.

### 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: Robert Vandell, Ph.D. (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. **This is a change from a previously announced time.** Starting August 20, in a room to be announced.

### Graduate Courses in Mathematical Sciences for Summer 2012

### 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.

*The History of Mathematics: An Introduction*, by David M. Burton, 7th edition.

mathematical proof-writing.

**Graduate courses in Mathematical Sciences for Spring 2012**

### MA 525 - Complex Analysis

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: Tuesdays and Thursdays, 6-7:15 p.m. starting January 10 in Kettler 123.

### MA 554 - Linear Algebra

We review the basics of linear algebra: vector spaces, linear mappings, dimension, matrices, determinants, and systems of linear equations. We then study modules over a principal ideal domain, which leads to the theory of finitely generated abelian groups and 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: Doug Weakley, Ph. D.

Doug Weakley received a Ph. D. from Northwestern University in 1980. He has published papers in algebra, combinatorics, and graph theory.

Time and location: Tuesdays and Thursdays, 4:30-5:45 p.m. starting January 10, in Kettler G43.

### MA 560 - Fundamental Concepts of Geometry

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.

*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 9 in Kettler 123.

### STAT 520 - Time Series Analysis & Applications

A first course in stationary time series with applications using real and simulated data. Computing projects are assigned, so some computer language (e.g. C, FORTRAN, SPLUS etc.) or statistical package should also be familiar. Topics include stationarity, autocovariance function and spectrum; integral representation of a stationary time series and interpretation; linear filtering, transfer functions; estimation of spectrum; multivariate time series. Use of computer programs for covariance and spectral estimation.

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

Prerequisite: STAT 512 with C- or above.

Instructor: Yihao Deng, Ph. D.

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, generalized linear models, and multivariate data analysis.

## Graduate courses in Mathematical Sciences for Fall 2011

### MA 511 - Linear Algebra with Applications

### MA 553 - Introduction to Abstract Algebra

Doug Weakley received a Ph. D. from Northwestern University. He has published papers in algebra, combinatorics, graph theory, and coding theory.

### MA 523 - Introduction to Partial Differential Equations

### MA 571 - Elementary Topology

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.

### STAT 512 - Applied Regression Analysis

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.

## Graduate course in Mathematical Sciences for Summer 2011

### 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, 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.

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.