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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

  • Synthetic Media, Deepfakes, and Cyber Deception

    Attacks, Analysis, and Defenses
    • 1st Edition
    • Cameron H. Malin
    • English
    Synthetic Media, Deepfakes, and Cyber Deception: Attacks, Analysis, and Defenses introduces the only analytical Synthetic Media Analysis Framework (SMAF) to help describe cyber threats and help security professionals anticipate and analyze attacks. This framework encompasses seven dimensions: Credibility, Control, Medium, Interactivity, Familiarity, Intended Target, and Evocation. Synthetic media is a broad term that encompasses the artificial manipulation, modification, and production of information, covering a spectrum from audio-video deepfakes to text-based chatbots. Synthetic media provides cyber attackers and scammers with a game-changing advantage over traditional ROSE attacks because they have the potential to convincingly impersonate close associates through text, imagery, voice, and video. This burgeoning threat has yet to be meaningfully addressed through any written treatment on the topic. The book is co-authored by three cyber influence and deception experts who have gained deep knowledge and experience on the topic through diverse, true operational pathways and backgrounds. The diversity and perspectives of the author team makes the content in the book the broadest and deepest treatment of synthetic media attacks available to readers.

  • Introductory Statistics

    • 5th Edition
    • Sheldon M. Ross
    • English
    Introductory Statistics, Fifth Edition, reviews statistical concepts and techniques in a manner that will teach students not only how and when to utilize the statistical procedures developed, but also how to understand why these procedures should be used. The text's main merits are the clarity of presentation, contemporary examples and applications from diverse areas, an explanation of intuition, and the ideas behind the statistical methods.Concepts are motivated, illustrated, and explained in a way that attempts to increase one's intuition. To quote from the preface, it is only when a student develops a feel or intuition for statistics that they are really on the path toward making sense of data. Ross achieves this goal through a coherent mix of mathematical analysis, intuitive discussions, and examples.Application... and examples refer to real-world issues, such as gun control, stock price models, vaccines and other health issues, driving age limits, school admission ages, use of helmets, sports, scientific fraud, and many others.

  • Neural Networks

    • 1st Edition
    • Volume 55
    • English
    Neural Networks, Volume 55 delves into the world of deep learning machines, defining neural networks and covering their central role in the development of modern language models, machine‑learning‑bas... decision‑making systems, and many other advances in artificial intelligence. Chapters in this new release include Neural networks with random weights, Bayesian Neural Networks for Official Statistics: Modeling High-Dimensional Structure in Complex Surveys and Administrative Records, Weakly supervised learning for neural networks, How to test a neural network as a null hypothesis, Test-Time Adaptation with Neural Networks: Approaches and Advances in Image Classification, and much more.Additional sections cover Semantics and Verification of Neural Network Components in Robotic Control Software, Artificial Neural Network Procedures for the Nonlinear Dynamical Plankton System, Neural Networks from Statistical Perspective, Neural Network applications in Assistive and Collaborative Robotics, Neural Network applications in Assistive and Collaborative Robotics, and Neural Networks using SPDEs.

  • Functional Analysis

    Theory and Applications
    • 1st Edition
    • Anita Tomar + 2 more
    • English
    An applied understanding of functional analysis is essential for students pursuing research or careers in pure mathematics, applied mathematics, mathematical physics, and engineering, among other disciplines.Function... Analysis: Theory and Applications offers a comprehensive exploration of functional analysis. Authored by esteemed mathematicians with extensive expertise in the field, this book thoroughly introduces fundamental concepts in functional analysis, including Banach spaces, Hilbert spaces, operator theory, nonlinear analysis, linear operators, and normed spaces, and implements these in real-world problems across various scientific and engineering disciplines.The book's rigorous mathematical treatment is combined with worked examples, exercises and solutions, visual aids, application case studies, and future directions across all chapters to reinforce learning, while appendices offer supplementary materials, proofs of theorems, and tables of important results, among other resources.

  • Essential Statistics, Regression, and Econometrics

    • 3rd Edition
    • Gary Smith
    • English
    Essential Statistics, Regression, and Econometrics, Third Edition will helps students in introductory statistics courses develop statistical reasoning and critical thinking skills. The book demonstrates the power, elegance, and beauty of statistical reasoning, providing hundreds of new and updated examples and discussing the uses and potential abuses of statistics. Examples are drawn from real, contemporary areas to showcase that statistical reasoning is not an irrelevant abstraction, but instead an important part of everyday life. This updated resource highlights recent, exciting discoveries and provides a thorough foundation for students, instructors, and researchers alike, all of which are approaching the field from different backgrounds.Innovati... in its extended emphasis on statistical reasoning, real data, pitfalls in statistical analysis, the perils of p-hacking and data mining, and modeling issues, including functional forms and causality, the book includes extensive word problems that emphasize intuition, understanding, and practical applications.

  • Mathematical Foundations of Physiology, Medicine, and Health Sciences

    • 1st Edition
    • Dhanjoo N. Ghista + 3 more
    • English
    Mathematics and Biomedical Engineering in Medicine, Physiology and Health Sciences is a visionary book, whose purpose is to demonstrate how fundamental mathematics and biomedical engineering can be incorporated into physiology, medicine, and health sciences teaching, research,and clinical practice to make these disciplines more quantitative and computational, and hence more explanatory and informative. The book also provides more quantitative formulation of medical procedures, towards supporting the growing field of precision medicine.

  • Data Science and Interactive Visualization Tools for the Analysis of Qualitative Evidence

    • 1st Edition
    • Manuel González Canché
    • English
    Data Science and Interactive Visualization Tools for the Analysis of Qualitative Evidence empowers qualitative and mixed methods researchers in the data science movement by offering no-code, cost-free software access so that they can apply cutting-edge and innovative methods to synthetize qualitative data. The book builds on the idea that qualitative and mixed methods researchers should not have to learn to code to benefit from rigorous open-source, cost-free software that uses artificial intelligence, machine learning, and data visualization tools—just as people do not need to know C++ or TypeScript to benefit from Microsoft Word. The real barrier is the hundreds of R code lines required to apply these concepts to their databases. By removing the coding proficiency hurdle, this book will empower their research endeavors and help them become active members of and contributors to the applied data science community. The book offers a comprehensive explanation of data science and machine learning methodologies, along with access to software application tools to implement these techniques without any coding proficiency. The book addresses the need for innovative tools that enable researchers to tap into the insights that come out of cutting-edge data science tools with absolutely no computer language literacy requirements.

  • Graph Theory

    Fundamentals and Applications
    • 1st Edition
    • Sovan Samanta + 1 more
    • English
    Graph theory is a rapidly evolving and expanding mathematical discipline, with new discoveries, challenges, and techniques emerging every year. Graph Theory: Fundamentals and Applications provides a fully up-to-date and accessible introduction to graph theory, covering both the classical and the modern topics, as well as algorithms and evolving challenges addressed by discipline. Based on the latest syllabi and research trends worldwide, this book includes practical, solved problems that are user friendly to undergraduate, postgraduate, and PhD students, and acts as a key aid in learning the fundamentals and the frontiers of graph theory, as well as developing independent problem-solving and critical thinking skills. This book includes clear instruction in graph representation, basic graph operations, graph connectivity, trees and forests, matching theory, planar graphs and graph drawing, algebraic graph theory, graph traversals, network flows, topological graph theory, and cryptography, among other topics. Each chapter features key term definitions, proofs and algorithms, summary points, and unique exercises to reinforce learning, as well as open problems and research challenges that present unsolved or conjectural problems in graph theory for discussion. Supporting student and instructor sites offer additional exercises, solutions, examples, and case studies in graph theory applications.

  • Introduction to Fuzzy Mathematics

    With Applications to Global Problems
    • 1st Edition
    • John Mordeson + 2 more
    • English
    Delve into the intricate landscape of fuzzy mathematics, where the boundaries of traditional mathematical disciplines— analysis, abstract algebra, geometry, topology, and graph theory—are blurred to address pressing global issues. Through a rigorous examination of fuzzy sets and similarity measures, An Introduction to Fuzzy Mathematics: With Applications to Global Problems lays the groundwork for innovative solutions to complex problems, from medical diagnostics to sustainability, refugee crises, and the fight against human trafficking. Meanwhile, research projects and exercises integrated across chapters reinforce learning and apply fuzzy mathematics to real-world scenarios. Chapters are meticulously organized to guide readers through foundational concepts, including fuzzy sets, evidence theory, and implication operators, before advancing to applications in sustainability and climate change. Further, the book examines refugee dynamics and public health models, culminating in a thorough exploration of fuzzy algebraic structures, geometry, topology, and graph theory. This comprehensive resource not only enhances understanding of fuzzy mathematics but also equips readers—researchers, practitioners, and policymakers alike—with the tools to tackle critical global issues. By integrating mathematical rigor with real-life applications, the book serves as a vital reference for anyone seeking to navigate the complexities of our world through the lens of fuzzy mathematics.

  • Quantum Machine Learning (QML): Platform, Tools and Applications

    • 1st Edition
    • Volume 140
    • English
    Quantum Machine Learning (QML): Platform, Tools and Applications, Volume 140 in the Advances in Computers series, explores the intersection of quantum computing and artificial intelligence, highlighting advances that promise to revolutionize computational science. The book introduces foundational concepts in quantum computing and circuits, building toward the practical implementation of quantum machine learning (QML) algorithms. Chapters address challenges such as the gradient vanishing problem in variational quantum circuits and explore powerful optimization methods enabled by quantum mechanics. The volume also covers advanced applications, including quantum approaches to smart grid management, quantum Monte Carlo simulations, and predictive modeling in numerical solvers using quantum neural networks.Real-world relevance is underscored through discussions of transformative quantum algorithms and their potential to reshape machine learning, enabling unprecedented performance in data analysis, optimization, and beyond.

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