COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics

Recent Faculty Authored Books

Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences

- by David J. Wollkind and Bonni J. Dichone

This text demonstrates the process of comprehensive applied mathematical modeling through the introduction of various case studies. The case studies are arranged in increasing order of complexity based on the mathematical methods required to analyze the models. The development of these methods is also included, providing a self-contained presentation. To reinforce and supplement the material introduced, original problem sets are offered involving case studies closely related to the ones presented. With this style, the text’s perspective, scope, and completeness of the subject matter are considered unique. Having grown out of four self-contained courses taught by the authors, this text will be of use in a two-semester sequence for advanced undergraduate and beginning graduate students, requiring rudimentary knowledge of advanced calculus and differential equations, along with a basic understanding of some simple physical and biological scientific principles.

Mobile point sensors and actuators in the controllability theory of partial differential equations

- by Alex Khapalov

This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time. Based on the author’s extensive research in the area of controllability theory, this monograph specifically focuses on the issues of controllability, observability, and stabilizability for parabolic and hyperbolic partial differential equations. The topics in this book also cover related applied questions such as the problem of localization of unknown pollution sources based on information obtained from point sensors that arise in environmental monitoring. Researchers and graduate students interested in controllability theory of partial differential equations and its applications will find this book to be an invaluable resource to their studies.

Linear Algebra and Its Applications, 5th Edition
- by David C. Lay, Steven R. Lay, and Judi J. McDonald

With traditional linear algebra texts, the course is relatively easy for students during the early stages as material is presented in a familiar, concrete setting. However, when abstract concepts are introduced, students often hit a wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations) are not easily understood and require time to assimilate. These concepts are fundamental to the study of linear algebra, so students' understanding of them is vital to mastering the subject. This text makes these concepts more accessible by introducing them early in a familiar, concrete Rn setting, developing them gradually, and returning to them throughout the text so that when they are discussed in the abstract, students are readily able to understand.
Also available with MyMathLab
MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. MyMathLab includes assignable algorithmic exercises, the complete eBook, interactive figures, tools to personalize learning, and more.

Combinatorial Reasoning: An Introduction to the Art of Counting
- by Duane W. DeTemple and William Webb

Combinatorial Reasoning: An Introduction to the Art of Counting presents a clear and comprehensive introduction to the concepts and methodology of beginning combinatorics. Focusing on modern techniques and applications, the book develops a variety of effective approaches to solving counting problems.

Balancing abstract ideas with specific topical coverage, the book utilizes real world examples with problems ranging from basic calculations that are designed to develop fundamental concepts to more challenging exercises that allow for a deeper exploration of complex combinatorial situations. Simple cases are treated first before moving on to general and more advanced cases. Additional features of the book include:

  • Approximately 700 carefully structured problems designed for readers at multiple levels, many with hints and/or short answers
  • Numerous examples that illustrate problem solving using both combinatorial reasoning and sophisticated algorithmic methods
  • A novel approach to the study of recurrence sequences, which simplifies many proofs and calculations
  • Concrete examples and diagrams interspersed throughout to further aid comprehension of abstract concepts
  • A chapter-by-chapter review to clarify the most crucial concepts covered

Mathematical Reasoning for Elementary School Teachers, 7th Edition
- by Calvin T. Long, Duane W. DeTemple, and Richard S. Millman

Mathematical Reasoning for Elementary School Teachers, Seventh Edition presents the mathematical content needed for teaching within the context of the elementary classroom, giving future teachers the motivation they need while also showing them the bigger picture of when they will use and teach the concepts. The program endeavors to answer the frequently-asked question “Why are we learning this?” by going beyond skill explanations and showing the ways that these concepts are implemented in the future classroom and what types of questions children may ask. Now updated to include the Common Core State Standards for Mathematics, the text imparts mathematical reasoning skills, a deep conceptual understanding, and a positive attitude to those who aspire to be elementary or middle school teachers.

Fundamentals of Matrix Computations, 3rd Edition

- by David S. Watkins

Fundamentals of Matrix Computations, Third Edition thoroughly details matrix computations and the accompanying theory alongside the author’s useful insights. Featuring many new and updated examples and exercises that use the MATLAB® language, this revision presents the most important algorithms of numerical linear algebra and helps readers to understand how the algorithms are developed and why they work. It also includes modern coverage of Singular Value Decomposition, a streamlined discussion of the Gram-Schmidt process, and a discussion on balancing the eigenvalue problem. Practicing scientists and graduate and advanced undergraduate students will find this popular book more than meets their needs.

Controllability of Partial Differential Equations Governed by Multiplicative Controls

- by Alex Khapalov

The series Lecture Notes in Mathematics by Springer reports on new developments in mathematical research and teaching.

The goal of this research monograph is to address the issue of global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. Models examined include the linear and nonlinear parabolic and hyperbolic PDE's, the Schrodinger equation, and coupled hybrid nonlinear distributed parameter systems modeling the swimming phenomenon. The book offers a new intrinsically nonlinear methodology to approach these highly nonlinear controllability problems.

Computation of Multivariate Normal and t Probabilities
- by Alan Genz and Frank Bretz

Multivariate normal and t probabilities are needed for statistical inference in many applications. Modern statistical computation packages provide functions for the computation of these probabilities for problems with one or two variables. This book describes recently developed methods for accurate and efficient computation of the required probability values for problems with two or more variables. The book discusses methods for specialized problems as well as methods for general problems. The book includes examples that illustrate the probability computations for a variety of applications.

The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods
- by David S. Watkins

This book presents the first in-depth, complete, and unified theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems: QR-like algorithms for dense problems and Krylov subspace methods for sparse problems. The author discusses the theory of the generic GR algorithm, including special cases (for example, QR, SR, HR), and the development of Krylov subspace methods. Also addressed are a generic Krylov process and the Arnoldi and various Lanczos algorithms, which are obtained as special cases. The chapter on product eigenvalue problems provides further unification, showing that the generalized eigenvalue problem, the singular value decomposition problem, and other product eigenvalue problems can all be viewed as standard eigenvalue problems.

The author provides theoretical and computational exercises in which the student is guided, step by step, to the results. Some of the exercises refer to a collection of MATLAB® programs compiled by the author that are available on a Web site that supplements the book.

Readers of this book are expected to be familiar with the basic ideas of linear algebra and to have had some experience with matrix computations. This book is intended for graduate students in numerical linear algebra. It will also be useful as a reference for researchers in the area and for users of eigenvalue codes who seek a better understanding of the methods they are using.

Perspectives on Supported Collaborative Teacher Inquiry
- by David Slavit, Tamara Holmlund Nelson, Anne Kennedy

Supported collaborative teacher inquiry (SCTI) describes the process of professional development in which teacher teams build collaborative structures for the purpose of inquiring into aspects of their own instructional practice. Professional development performed collaboratively and grounded in "the work teachers do" is a highly effective forum for challenging existing beliefs about content, learners, and teaching and using data and research to reflect on, and possibly change, instructional practice. The contributors to this volume describe supported collaborative inquiry as a framework for teacher professional development and provide specific empirical evidence found in examples of SCTI. The chapters focus on the building of collaborative support structures, nurturing an inquiry stance, progressing through an inquiry process, and the various kinds of support mechanisms necessary to engage in SCTI. This seminal work in teacher research will be of interest to scholars, students, teachers, and administrators seeking insight into teacher education, teacher leadership, and teacher inquiry.

Recent Graduate Student Authored Books

A Friendly Introduction to Differential Equations

- by Mohammed Kaabar

In this book, there are five chapters: The Laplace Transform, Systems of Homogenous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations, and Applications of Differential Equations. In addition, there are exercises at the end of each chapter to let students practice additional sets of problems other than examples, and they can also check their solutions to some of these exercises by looking at the "Answers to Odd-Numbered Exercises" section at the end of the book. The book is useful for college students who studied Calculus II, and other students who want to review some concepts of differential equations before studying courses such as partial differential equations, applied mathematics, and electric circuits II.

A First Course in Linear Algebra: Study Guide for Undergraduate Linear Algebra Course

- by Mohammed Kaabar

In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It also includes exercises at the end of each chapter to let students practice additional sets of problems other than examples, and they can also check their solutions to some of these exercises by looking at the “Answers to Odd-Numbered Exercises” section at the end of the book. The book is useful for college students who studied Calculus I, and other students who want to review some linear algebra concepts before studying a second course in linear algebra.