Mathematics & Statistics Faculty Books

A gallery of books by faculty in the Department of Mathematics and Statistics, College of Sciences, Old Dominion University.

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Pragmatic Mathematics for Scientists and Engineers
2024
Alexander Godunov and John A. Adam

This is a textbook on basic to intermediate mathematics for undergraduate students majoring in the physical sciences and engineering. Many chapters, covering topics like Green's functions, calculus of variations, and functions of a complex variable, are well-suited for graduate classes. Additionally, researchers can benefit from the book as a mathematical refresher for their professional work.The book provides readers with a fundamental understanding of underlying principles, using derivations based more on mathematical intuition rather than exposing them to multiple theorems, proofs, and lemmas. Each chapter includes highly relevant examples with detailed solutions and explanations, promoting a practical application of knowledge to real problems in the physical sciences. For the convenience of both students and instructors, there are end-of-chapter exercises with answers that can be easily utilized for assignments. The book is not a replacement for calculus textbooks, but rather a guide to the mathematics most relevant to the physical sciences and engineering. In conclusion, this book can be readily adapted for upper-level undergraduate and graduate classes, particularly those focusing on mathematical methods for students in physical sciences, applied mathematics, and engineering majors. [From the publisher]
The Mathematics of Patterns, Symmetries, and Beauties in Nature: In Honor of John Adam
2021
Bourama Toni (Editor) and John Adam (Honoree)

This unique book gathers various scientific and mathematical approaches to and descriptions of the natural and physical world stemming from a broad range of mathematical areas – from model systems, differential equations, statistics, and probability – all of which scientifically and mathematically reveal the inherent beauty of natural and physical phenomena. Topics include Archimedean and Non-Archimedean approaches to mathematical modeling; thermography model with application to tungiasis inflammation of the skin; modeling of a tick-Killing Robot; various aspects of the mathematics for Covid-19, from simulation of social distancing scenarios to the evolution dynamics of the coronavirus in some given tropical country to the spatiotemporal modeling of the progression of the pandemic. Given its scope and approach, the book will benefit researchers and students of mathematics, the sciences and engineering, and everyone else with an appreciation for the beauty of nature. The outcome is a mathematical enrichment of nature’s beauty in its various manifestations.

This volume honors Dr. John Adam, a Professor at Old Dominion University, USA, for his lifetime achievements in the fields of mathematical modeling and applied mathematics. Dr. Adam has published over 110 papers and authored several books. [From the publisher]
Function Theory and ℓ^p Spaces
2020
Raymond Cheng

The classical ℓp sequence spaces have been a mainstay in Banach spaces. This book reviews some of the foundational results in this area (the basic inequalities, duality, convexity, geometry) as well as connects them to the function theory (boundary growth conditions, zero sets, extremal functions, multipliers, operator theory) of the associated spaces ℓpA of analytic functions whose Taylor coefficients belong to ℓp. Relations between the Banach space ℓp and its associated function space are uncovered using tools from Banach space geometry, including Birkhoff-James orthogonality and the resulting Pythagorean inequalities. The authors survey the literature on all of this material, including a discussion of the multipliers of ℓpA and a discussion of the Wiener algebra ℓ1A.

Except for some basic measure theory, functional analysis, and complex analysis, which the reader is expected to know, the material in this book is self-contained and detailed proofs of nearly all the results are given. Each chapter concludes with some end notes that give proper references, historical background, and avenues for further exploration.
Linear Algebra: Concepts and Applications
2019
Przemyslaw Bogacki

Linear Algebra: Concepts and Applications is designed to be used in a first linear algebra course taken by mathematics and science majors. It provides a complete coverage of core linear algebra topics, including vectors and matrices, systems of linear equations, general vector spaces, linear transformations, eigenvalues, and eigenvectors. All results are carefully, clearly, and rigorously proven. The exposition is very accessible. The applications of linear algebra are extensive and substantial several of those recur throughout the text in different contexts, including many that elucidate concepts from multivariable calculus. Unusual features of the text include a pervasive emphasis on the geometric interpretation and viewpoint as well as a very complete treatment of the singular value decomposition. The book includes over 800 exercises and numerous references to the author's custom software Linear Algebra Toolkit. [Amazon.com]
Modern Statistical Methods for Spatial and Multivariate Data
2019
Norou Diawara (Editor)

This contributed volume features invited papers on current models and statistical methods for spatial and multivariate data. With a focus on recent advances in statistics, topics include spatio-temporal aspects, classification techniques, the multivariate outcomes with zero and doubly-inflated data, discrete choice modelling, copula distributions, and feasible algorithmic solutions. Special emphasis is placed on applications such as the use of spatial and spatio-temporal models for rainfall in South Carolina and the multivariate sparse areal mixed model for the Census dataset for the state of Iowa. Articles use simulated and aggregated data examples to show the flexibility and wide applications of proposed techniques. Carefully peer-reviewed and pedagogically presented for a broad readership, this volume is suitable for graduate and postdoctoral students interested in interdisciplinary research. Researchers in applied statistics and sciences will find this book an important resource on the latest developments in the field. In keeping with the STEAM-H series, the editors hope to inspire interdisciplinary understanding and collaboration. [Amazon.com]
Rays, Waves, and Scattering: Topics in Classical Mathematical Physics
2017
John A. Adam

This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas.

Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes. ... [Amazon.com
X and the City: Modeling Aspects of Urban Life
2012
John A. Adam

X and the City, a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through tunnels? Can you predict whether a traffic light will stay green long enough for you to cross the intersection? And what is the likelihood that your city will be hit by an asteroid?… [From Amazon.com]
An Introduction to Bootstrap Methods with Applications to R
2011
Michael R. Chernick and Robert A. LaBudde

Bootstrap methods provide a powerful approach to statistical data analysis, as they have more general applications than standard parametric methods. An Introduction to Bootstrap Methods with Applications to R explores the practicality of this approach and successfully utilizes R to illustrate applications for the bootstrap and other resampling methods. This book provides a modern introduction to bootstrap methods for readers who do not have an extensive background in advanced mathematics. Emphasis throughout is on the use of bootstrap methods as an exploratory tool, including its value in variable selection and other modeling environments… [Amazon.com]
New Classes of Multivariate Gamma Survival and Reliability Models
2010
Norou Diawara

Multivariate modeling and analysis based on the multivariate normal distribution is well established and widely used. However, when the marginal distributions have only a positive support, such as time-to-event models, that are positively skewed, often the multivariate normal theory and resulting approximations fail. Accordingly, over the last fifty years, thousands of papers have been published suggesting many ways of generating families of positive support multivariate distributions, such as gamma, Weibull and exponential. As evidenced by recent literature, this quest is still rigorously pursued even today. In this work, we provide a large and flexible class of multivariate gamma distributions that contains both absolutely continuous and discontinuous distributions on the positive hypercube support. All of these models are applicable to the area of reliability and survival modeling. Also, since this theoretical research resulted from a real world application we also provide methods for parameter estimation for a variety of applications. [Amazon.com]
A Mathematical Nature Walk
2009
John A. Adam

How heavy is that cloud? Why can you see farther in rain than in fog? Why are the droplets on that spider web spaced apart so evenly? If you have ever asked questions like these while outdoors, and wondered how you might figure out the answers, this is a book for you. An entertaining and informative collection of fascinating puzzles from the natural world around us, A Mathematical Nature Walk will delight anyone who loves nature or math or both… [From Amazon.com]
Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin
2008
Lawrence Weinstein and John A. Adam

Guesstimation is a book that unlocks the power of approximation--it's popular mathematics rounded to the nearest power of ten! The ability to estimate is an important skill in daily life. More and more leading businesses today use estimation questions in interviews to test applicants' abilities to think on their feet. Guesstimation enables anyone with basic math and science skills to estimate virtually anything--quickly--using plausible assumptions and elementary arithmetic... [From Amazon.com]
Mathematics in Nature: Modeling Patterns in the Natural World
2003
John A. Adam

From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. [From the Publisher]
Survey of Models for Tumor-Immune System Dynamics
1997
John A. Adam and Nicola Bellomo

An enormous amount of human effort and economic resources has been directed in this century to the fight against cancer. The purpose, of course, has been to find strategies to overcome this hard, challenging and seemingly endless struggle. We can readily imagine that even greater efforts will be required in the next century. The hope is that ultimately humanity will be successful; success will have been achieved when it is possible to activate and control the immune system in its competition against neoplastic cells. Dealing with the above-mentioned problem requires the fullest possible cooperation among scientists working in different fields: biology, immunology, medicine, physics and, we believe, mathematics. Certainly, biologists and immunologists will make the greatest contribution to the research. However, it is now increasingly recognized that mathematics and computer science may well able to make major contributions to such problems. We cannot expect mathematicians alone to solve fundamental problems in immunology and (in particular) cancer research, but valuable support, however modest, can be provided by mathematicians to the research aspirations of biologists and immunologists working in this field. [Amazon.com]