MATHEMATICS

Recent Faculty Authored Books



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

Combinatorial Reasoning: An Introduction to the Art of Counting is an excellent textbook for upper-undergraduate and beginning graduate-level courses on introductory combinatorics and discrete mathematics.



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.