Rose-Hulman Mathematics

RHIT Mathematics - Faculty Authors

Current Faculty

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

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

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.

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)

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.

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.