Teaching and Learning Mathematics Online

Edited with John F. Beyers

The landscape of higher education has been significantly transformed by the advent of online learning, positioning it as a pivotal element of academic offerings in the United States and globally. The flexibility of pursuing entire degree programs or individual courses online caters to a wide array of student needs and schedules, marking a shift towards more accessible and adaptable education models. Furthermore, the integration of online resources into traditional classroom settings has become a common practice among educators, aiming to enhance the learning experience through supplemental materials or innovative approaches like the flipped classroom model. This method reallocates direct instruction to the digital space, allowing for more interactive, hands-on learning during physical class sessions.

However, the transition to online education brings forth a set of challenges, particularly in the realms of student assessment and engagement. These challenges are notably pronounced in the fields of mathematics and statistics, where instructors face the added task of addressing math anxiety, navigating the abstract nature of the subjects, and deciphering complex notations in a virtual environment. This book endeavors to tackle these hurdles head-on, offering a comprehensive guide to navigating the intricacies of online mathematics and statistics education. Through a detailed exploration of innovative teaching methodologies, engagement strategies, and assessment techniques, we provide educators with the tools needed to foster meaningful learning experiences for their students in the digital age.

Accompanying me in this endeavor is John F. Beyers, a respected authority in online mathematics and statistics education, currently serving as the program chair at the University of Maryland Global Campus. Together, we aim to bridge the gap between traditional and online education modalities, presenting practical solutions and insights drawn from our extensive experience in the field. This book is an invaluable resource for educators seeking to adapt to the evolving landscape of higher education, ensuring that students not only learn effectively but also develop a lasting appreciation for the mathematical sciences.

Handbook of Military and Defense Operations Research

Edited with Natalie M. Scala

Operations Research (OR) stands as a foundational pillar in the sphere of military and defense management, marking its significance since its strategic deployment during World War II. Initially, OR played a pivotal role in enhancing the efficiency of supply chains, advancing strategic simulation, and fostering superior management strategies for the Allied forces. The advent of OR during this period was instrumental in leveraging analytical rigor to achieve operational excellence and strategic advantages.

Since its inception, the domain of Operations Research has witnessed exponential growth, branching into a myriad of applications that transcend the confines of military strategy. Today, OR’s influence permeates through the realms of artificial intelligence, cybersecurity, and big data analytics, establishing itself as an integral component of management science across diverse industries including manufacturing, advertising, telecommunications, and beyond.

The Handbook of Military and Defense Operations Research (MDOR) aims to showcase the evolution and current trajectories of OR and analytics within the context of security. By compiling research findings, practical applications, and invaluable insights from field experiences, this book endeavors to illuminate the path for advancing OR and analytics in addressing contemporary security challenges.

This compilation is brought to life through the collaborative efforts of esteemed scholars, including co-editor Natalie M. Scala, an associate professor of business analytics and technology management at Towson University. Scala’s expertise and contributions enrich the discourse within MDOR, making it an essential resource for practitioners, researchers, and policymakers keen on exploring the cutting-edge intersections of OR, analytics, and security strategies.

This book is co-edited with Natalie M. Scala, associate professor of business analytics and technology management at Towson University.

Computational Methods for Numerical Analysis with R

This book offers a comprehensive exploration of numerical analysis, presenting the subject matter through the lens of R, a highly regarded programming language known for its powerful statistical and numerical capabilities. By integrating R into the traditional numerical analysis course framework, this text modernizes and enhances the learning experience, making complex mathematical concepts more accessible and engaging for students.

The structure of the book adheres to the classical curriculum of numerical analysis, beginning with an in-depth discussion on numerical error—a foundational aspect of the field that underscores the importance of accuracy in computational methods. From there, the narrative progresses logically through key topics such as linear algebra, interpolation, numerical integration, optimization techniques, and the numerical solutions of differential equations. This sequence ensures a thorough coverage of the introductory mathematical concepts essential for a robust understanding of numerical analysis.

Designed with advanced undergraduates and first-year graduate students in mind, this text demands a solid grounding in several core mathematical disciplines. Readers are expected to have a strong grasp of linear algebra, differential and integral calculus, and differential equations. The book’s content is tailored to students pursuing mathematics, computer science, physics, engineering, and other disciplines with a significant mathematical component, providing them with the necessary background to fully comprehend the material.

Moreover, the utilization of R as the primary programming language not only facilitates a hands-on learning approach but also prepares students for real-world applications. By the end of this book, readers will have acquired not only a deep theoretical understanding of numerical analysis but also practical skills in implementing numerical methods using R. This dual focus makes the text an invaluable resource for anyone looking to apply mathematical concepts in various scientific and engineering contexts.

Socioeconomic Effects of the National Flood Insurance Program

In this book, I undertake a comprehensive analysis to ascertain the overall social value of the National Flood Insurance Program (NFIP) over the span from 1996 to 2010. The assessment hinges on a detailed estimation of the consumer surplus associated with flood insurance, leveraging historical financial data and survey responses garnered from the NFIP. Through meticulous evaluation, this study generates a pivotal statistic that encapsulates the insurance facet of the NFIP, integrating this finding with additional assessments of the Flood Mitigation Assistance (FMA) program’s advantages to gauge the cumulative social benefits of these intertwined initiatives.

Furthermore, the analysis is enriched by exploring various income weighting scenarios, employing a distributionally weighted benefit-cost approach to assess the programs’ impacts across different socioeconomic strata. This investigation also delves into the fiscal repercussions of the NFIP and FMA on government revenue, providing a nuanced understanding of the economic dynamics at play.

A key feature of this study is the execution of sensitivity analysis on the obtained results, ensuring robustness and reliability in the findings. Each segment of the analysis is meticulously detailed, offering models that can serve as valuable tools for further research. These models offer a framework for future studies aiming to refine, expand upon, or adapt the present analysis to other policy programs, making this book an indispensable resource for policymakers, researchers, and stakeholders interested in the quantitative evaluation of public programs.