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RHIT Mathematics - Faculty Authors

Current Faculty

broughton

Allen Broughton

The Science of Nanotechnology: An Introductory Text

Nanotechnology is a rapidly advancing field that studies and utilizes molecular structures that are at the nanometer scale -- just few atoms thick. Fullerenes, carbon nanotubes and non-carbon nanoparticles are just a few of these structures. Nanoscience analyzes the properties, structure, and methods of synthesis of nanostructures. Nanotechnology exploits the structures and properties of nanostructures to produce useful products and applications. The text, written by multidisciplinary team of chemists, physicists, and a mathematician, explores the basic science of nanoparticles, discussing the chemical, mechanical, magnetic, optical, and geometric properties of nanoparticles and nanotubes. The text is written for a sophomore audience in order to bring introductory notions of nanotechnology as early as possible in the undergraduate curriculum. Only a background of freshman mathematics, chemistry and physics is needed. The text was written through an NSF grant (Award DMR-0304487) as part of the NSF Nanotechnology in Undergraduate Education program.

Luanne Tilstra, S. Allen Broughton, Robin S. Tanke, DanJelski, Guo Ping Zhang, Valentina French, Alexander Popov et al., The Science of Nanotechnology: An Introductory Text, Nova Publishers, Hauppauge, NY , 2007

Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing A text co-authored by S. Allen Broughton and Kurt Bryan based on teaching an applied mathematics course on image processing. The course has been taught from the authors' notes as well as Professors Roger Lautzenheiser and Ed Doering for more than 10 years. The course is part of the Imaging Systems Certificate.

Key items of the text are:

  • Focuses on the underlying mathematics, especially the concepts of finite-dimensional vector spaces and matrix methods, and provides a rigorous model for signals and images based on vector spaces and linear algebra methods.
  • Emphasizes discrete and digital methods and utilizes MATLAB(r) to illustrate these concepts
  • Combines traditional methods such as discrete Fourier transforms and discrete cosine transforms with more recent techniques such as filter banks and wavelets
  • Strikes an even balance in emphasis between the mathematics and the applications with the emphasis on linear algebra as a unifying theme

     

S. Allen Broughton, Kurt M. Bryan Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing, Wiley Hoboken, NJ.

Kurt Bryan

Kurt Bryan

Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing

A text co-authored by S. Allen Broughton and Kurt Bryan based on teaching an applied mathematics course on image processing. The course has been taught from the authors' notes as well as Professors Roger Lautzenheiser and Ed Doering for more than 10 years. The course is part of the Imaging Systems Certificate.

Key items of the text are:

  • Focuses on the underlying mathematics, especially the concepts of finite-dimensional vector spaces and matrix methods, and provides a rigorous model for signals and images based on vector spaces and linear algebra methods.
  • Emphasizes discrete and digital methods and utilizes MATLAB(r) to illustrate these concepts
  • Combines traditional methods such as discrete Fourier transforms and discrete cosine transforms with more recent techniques such as filter banks and wavelets
  • Strikes an even balance in emphasis between the mathematics and the applications with the emphasis on linear algebra as a unifying theme

     

S. Allen Broughton, Kurt M. Bryan Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing, Wiley Hoboken, NJ.

Steve Carlson

Stephan Carlson

Topology of Surfaces, Knots, and Manifolds

This book offers an intuition-based and example-driven approach to the basic ideas and problems involving manifolds. A blend of examples and exercises leads the reader to anticipate general definitions and theorems concerning curves, surfaces, knots, and links-the objects of interest in the appealing set of mathematical ideas known as ""rubber sheet geometry."" The result is a text that is accessible to a broad range of undergraduate students, yet still provides solid coverage of the mathematics underlying these topics.

 

Carlson, Stephan C., Topology of Surfaces, Knots, and Manifolds, Wiley,New York,2001

evans

Diane Evans

Computational Probability

Computational probability encompasses data structures and algorithms that have emerged over the past decade that allow researchers and students to focus on a new class of stochastic problems. This book examines and presents these computational methods in a systematic manner. The techniques described here address problems that require exact probability calculations, many of which have been considered intractable in the past. The book covers computational probability analysis, APPL, the probability modeling language created by the authors, and three applications-based chapters that emphasize applications in survival analysis and stochastic simulation.The algorithmic material associated with continuous random variables is presented separately from the material for discrete random variables. Four sample algorithms, which are implemented in APPL, are presented in detail: transformations of continuous random variables, products of independent continuous random variables, sums of independent discrete random variables, and order statistics drawn from discrete populations.

 

Drew, J.H., Evans, D.L., Glen, A.G., Leemis, L.M. , Computational Probability, International Series in Operations Research & Management Science, Springer, New York, 2007.

grimaldi

Ralph Grimaldi

Discrete and Combinatorial Mathematics

This book strives to accomplish many goals including 1) Introducing the student to the topics and techniques of discrete methods and combinatorial reasoning 2) Introducing a wide variety of applications 3) Develop the mathematical maturity of the student through the study of an area that is so different from the traditional coverage in calculus and differential equations 4) Present an adequate survey of topics for the computer science student who will be taking more advanced courses in the area.

Grimaldi, Ralph P., Discrete and Combinatorial Mathematics: An Applied Introduction, 5th ed., Addison-Wesley Longman, Reading, MA, 2003. (1st - 4'th eds., 1985-1999)

leader

Josh Holden

Making Mathematics with Needlework: Ten Papers and Ten Projects

  • Chapter 9: The Graph Theory of Blackwork Embroidery

Mathematical craftwork has become extremely popular, and mathematicians and crafters alike are fascinated by the relationship between their crafts. The focus of this book, written for mathematicians, needleworkers, and teachers of mathematics, is on the relationship between mathematics and the fiber arts (including knitting, crocheting, cross-stitch, and quilting). Each chapter starts with an overview of the mathematics and the needlework at a level understandable to both mathematicians and needleworkers, followed by more technical sections discussing the mathematics, how to introduce the mathematics in the classroom through needlework, and how to make the needlework project, including patterns and instructions.

leader

Jeffery Leader

Numerical Analysis and Scientific Computation

This book represents the numerical analysis course I have taught for the past nine years, first as a required course for sophomore engineering majors and currently as an elective course for juniors and seniors in mathematics, computer science, physics, and engineering. It has been strongly influenced by my summertime computational consulting work at the U.S. Army Research Laboratory (Adelphi, MD), Naval Surface Warfare Center (Dahlgren, VA), and Air Force Research Laboratory (Dayton, OR), and other consulting and research experiences. Some of the key features I have incorporated into the text based on these teaching and research experiences are:

 

  • Modern approach to numerical linear algebra
  • Explanation of the numerical techniques used by the major computational programs students are likely to use in practice (especially MATLAB, but also Maple and the Netlib library
  • Appropriate mix of numerical analysis theory and practical scientific computation principles
  • Greater than usual emphasis on optimization
  • Numerical experiments so students can gain experience
  • Efficient and unobtrusive introduction to Matlab

Leader, Jeffery J., Numerical Analysis and Scientific Computation, Pearson Addison Wesley, 2004.

leader

David Rader

Deterministic Operations Research

Thoroughly classroom-tested over the past eight years, this book focuses on the study of linear optimization (both continuous and discrete), and it also emphasizes the modeling of real problems as linear optimization problems and designs algorithms to solve them.

Topics in linear programming, network optimization, and integer programming are discussed, and three aspects of deterministic operations research are emphasized: modeling real-world problems as linear optimization problems; designing algorithms (both heuristic and exact methods) to solve these problems; and using mathematical theory to improve the understanding of the problem, to improve existing algorithms, and to design new algorithms. These three aspects are important for both researchers and practitioners of operations research. Such topics are not always in the forefront of operations research textbooks, and while it is true that many books highlight optimization modeling and algorithms to solve these problems, very few, if any, explicitly discuss the algorithm design process used to solve problems.

This book successfully fills this gap in the literature and incorporates these components into the study of linear and integer programming, currently the two most-used optimization models in business and industry. Each chapter of the book is designed to be the continuation of the "story" of how to both model and solve optimization problems by using the specific problems (linear and integer programs) as guides. This enables the reader (and instructors) to see how solution methods can be derived instead of just seeing the final product (the algorithms themselves). 

Rader, David J., Deterministic Operations Research: Models and Methods in Linear Optimization, Wiley, 2010.

Former Faculty

Leroy Franklin

Business Statistics

Prepares students to meet the unique challenges of today's business environment. It also presents a solid foundation in traditional inferential statistics, making the concepts of processes, variability, and quality unifying themes throughout the book. The challenges are met through readable and interesting text discussions; inclusion of real business applications, scenarios, and real data; emphasis on the use of statistics for problem solving and decision making; and various learning and motivational features.
Triola, Mario F. and LeRoy A. Franklin, Business Statistics, Addison-Wesley, New York, 1994.

 

Robert Lopez

Advanced Engineering Mathematics

A book of applied and engineering mathematics, written in traditional notation and language, for students of science, engineering, and applied mathematics. It contains examples drawn from a wide spectrum of physical and mathematical disciplines, and provides a fairly complete curriculum in undergraduate applied mathematics.
Lopez, Robert J., Advanced Engineering Mathematics, Addison-Wesley, Reading, MA, 2001.

 

Discovering Calculus with Maple

Contains examples of great detail showing many new Maple features and expanding the use of a computer algebra system in solving different types of problems.
Harris, Kent and Robert J. Lopez, Discovering Calculus with Maple, 2nd ed., John Wiley & Sons, New York, 1995.

Linear Algebra: Ideas and Applications

A student resource manual to accompany Linear Algebra: Ideas and Applications by Richard C. Penney. On Line Maple Translations by Robert Lopez.
Emerson, William and Robert J. Lopez, LINEAR ALGEBRA - Ideas and Applications, John Wiley & Sons, New York, 1998.

Maple V: Mathematics and its Application

This volume contains the contributed papers of the Maple Summer Workshop and Symposium, MSWS '94, which reflects the growing community of Maple users around the world. Also included are brief abstracts of the talks by the invited speakers.
Lopez, Robert J., Maple V: Mathematics and its Application, Birkhäuser, Boston, MA, 1994.

Maple Labs for Linear Algebra

These labs are a transcription into Maple of an equivalent set of MATLAB linear algebra labs keyed to Terry Lawson's text, Linear Algebra. The original set of labs was written by Terry Lawson and is accompanied by a number of additional MATLAB files that generate the LAWSON TOOLBOX.
Lawson, Terry and Robert J. Lopez, Maple Labs for Linear Algebra, John Wiley, New York ,996.

Maple via Calculus: A Tutorial Approach
"Modern software tools like Maple have the potential to alter radically the way mathematics is taught, learned, and done." With this principle firmly in mind one can obtain a fresh look at the standard calculus curriculum, colored by the existence of technology like Maple -- a tool that can be used in class during lectures and exams and at home while working assignments, a tool whose universal access will eventually make a software-based approach to mathematics the norm.
Lopez, Robert J., Maple via Calculus: A Tutorial Approach, Birkhäuser, Boston, MA, 1994.

Numerical Analysis: A Practical Approach

Numerical analysis is a blend of mathematics and computer science that has produced powerful tools for solving otherwise intractable problems in science and engineering. Consequently, this subject can be viewed from the perspective of a mathematician when an algorithm is being created or assessed, a computer scientist when it is implemented in software or modified for optimal performance on a particular device, or a problem solver once a mathematical model is created.
Maron, Melvin J. and Robert J. Lopez, Numerical Analysis: A Practical Approach, 3rd ed., Wadsworth Pub. Co., Belmont, CA, 1991, & Spanish edition, 1995.