Graduate Studies

Graduate Courses in Mathematics and Statistics Fall 2018

MA 540 - Analysis I

Motivation for analysis comes from needing to answer questions like “How big?”, “How close?”, and “How smooth?”. Many applications fall within the corresponding techniques. Assigning probabilities comes down to measuring the size of a selected set of outcomes relative to all possible outcomes. Numerical approximations of otherwise unsolvable mathematical models are sought to achieve a required degree of accuracy. Expanding a desired solution in terms of an infinite series, e.g., Taylor or Fourier series, is often done assuming integrability, continuity, or differentiability as needed for the calculations. The question remains as to whether these assumptions are actually satisfied by the resulting series.

Methods based upon the idea of increasing accuracy through iteration, such as “Newton’s method” for approximating roots of a function or the method of “steepest ascent (descent)” for optimizing an energy, cost, or “action” integral, have been seen to also give chaotic results. A quick search of the web will reveal example infinite series formed as sums of very well-behaved functions that nevertheless converge to a discontinuous “square wave” or to a continuous, nowhere differentiable “Weierstrass function”. Considerable care is necessary to understand the occurrence of such phenomena, particularly in light of active research directions focused on chaos, numerical instabilities, and various forms of threshold behaviors resulting from nonlinear models.

We consider how familiar concepts like distance or dot products may be extended to spaces where the “points” are more generally functions. A differential or integral equation, for example, might then be conveniently identified with solving a “functional equation” on that space. Once provided with suitable meanings for closeness, a framework for limits, continuity, integration, etc. is additionally available. While the resulting techniques are general and very powerful, a primary focus will be on building meaning through concrete examples seen to have great utility in both current applications and continuing research directions. A parallel goal will be to identify where gaps in our treatments still remain, providing motivation for further studies.
PDF files for the textbooks will be provided to students for free by the instructor, and may also be available online:
(1) Real Analysis, N.L. Carothers
(2) Analysis for Applied Mathematics, Cheney
Prerequisite: The formal prerequisite is MA 441 (Real Analysis) with C or better, or equivalent, but the material will be accessible with a background including MA 261 (Multivariate Calculus) and MA 351 (Linear Algebra). Contact the instructor if you have a question about your preparation.

Instructor: Jeff Anderson, Ph.D. AndersJR (at) ipfw.edu  260-481-0343

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, 4:30-5:45 p.m., starting August 20, in LT B35 (the Helmke Library TV studio).  This course is also offered online.

MA 598 - 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

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

Instructor: Dr. Peter Boyvalenkov is a Visiting Professor of Mathematics at Purdue University Fort Wayne for Fall 2018, while on sabbatical from the Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences, where he serves as an Associate Director and a Professor. He received his Ph.D. from Sofia University in 1993 and his Doctor of Science degree from the Bulgarian Academy of Science in 2004. He has published over 80 research articles in the field of Coding Theory and Cryptography, as well as 4 secondary education textbooks and over 10 books and 50 articles on Math Olympiads and Competitions for high school students. For the last five years he has been the Head Coach of the Bulgarian International Math Olympiads Team.

Time and location: MW 4:30-5:45 in Kettler 216.  There is also an online section.

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 (4th 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 20, in Kettler 218.  There is also an online section.

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 20, in Kettler 216.  This course is also offered online.

Graduate Course in Mathematics Summer 2018

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

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

Instructor: Betsy Berry, Ph. D.

Betsy Berry received her Ph. D. in mathematics education from Purdue University in 2007. As an undergraduate and master's student, she had the opportunity to study with the inimitable math historian, Dr. Howard Eves at the University of Maine and is looking forward to bringing his enthusiasm and expertise and passion for the history of math into her teaching of this course.

Time and location: MTWR 5:30-7:15 p.m. in Kettler 123, June 25 - August 3.

 

Graduate Courses in Mathematics and Statistics for Spring 2018

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: Mondays and Wednesdays, 6-7:15 p.m. starting January 8 in Kettler 216. Also offered by internet.

MA 560 - Foundations of Geometry

This course will present a logical development of plane geometry, both Euclidean and non-Euclidean, from an axiomatic perspective, following Hilbert, and also a coordinate approach, following Poincaré. There will be an emphasis on understanding the proofs of the theorems as well as their content.

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: Adam Coffman, Ph.D. ( CoffmanA (at) ipfw.edu - (260)-481-6188 )

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 January 8 in Kettler 216. This course is also offered by internet.

STAT 520 - Time Series Analysis & Applications

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: 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, beginning January 9, in Kettler 220.  This course is also offered by internet.

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 (3rd 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 (4th 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.

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