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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.

  • An Introduction to Applied Sport Analytics

    • 1st Edition
    • Jon Nachtigal + 1 more
    • English
    An Introduction to Applied Sport Analytics offers a step-by-step path for applying data-driven methods in sport. The book begins with the evolution of sport analytics and foundational concepts like the Pythagorean theorem, correlation, and regression, then moves into hands-on instruction with industry tools such as Excel, SQL, R, Python, and Power BI. Along the way, readers learn how to explore data, evaluate performance, and make informed decisions across team operations, player valuation, and sport business strategy. The book features real-world examples, chapter exercises, and review questions designed to reinforce key concepts through application. A dedicated section on data visualization walks readers through designing reports and dashboards using Power BI and Tableau. It also introduces the growing role of artificial intelligence in sport, showing how tools like machine learning and coding assistants can enhance analysis. A robust ancillary program also provides support to students with additional practice opportunities. With its practical focus and clear structure, An Introduction to Applied Sport Analytics is ideal for undergraduate and graduate courses in sport management, analytics, and business, as well as for professionals seeking to build essential skills in a data-driven sport industry.

  • Foundations of Real Analysis

    • 1st Edition
    • William R. Brian
    • English
    Foundations of Real Analysis offers up a first course in real analysis aimed at advanced undergraduate students or new graduate students. The text covers the central topics of analysis, like continuity, differentiation, and integration, with a particular emphasis on set-theoretic and topological aspects of the real line, such as the Baire Category Theorem and the infinite-length Banach-Mazur games. It is richly illustrated and includes a wealth of interesting examples and counterexamples, such as Hilbert’s space-filling curves and Volterra’s non-integrable derivative. These mathematical spectacles aim to challenge the student’s preconceptions about the real line, while at the same time the main part of the text builds up a more well-founded intuition. Foundations of Real Analysis presents the core ideas of real analysis with intuition-driven arguments and visual appeal. The book connects analysis with other adjacent areas of mathematics, including important arguments and ideas from topology, measure theory, abstract algebra, descriptive set theory, and functional analysis. It aims to give the student a thorough and rigorous introduction to real analysis, leaning on the more intuitive and imaginative aspects of the subject, while also revealing some of the broader context of modern mathematics in which the subject is situated. This introductory course is designed not only for future analysts, but for anyone wanting to understand analysis and to sharpen their mathematical insight. The text is well suited to a two-semester university course, but can also be used for self-study by the curious reader.

  • Mathematical Statistics with Applications in R

    • 4th Edition
    • Kandethody M. Ramachandran + 1 more
    • English
    Mathematical Statistics with Applications in R, Fourth Edition, offers a modern calculus-based theoretical introduction to mathematical statistics and applications that spans numerous foundational and essential concepts in the field. The book covers many modern statistical computational and simulation concepts, including Exploratory Data Analysis, the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. The final chapter of the book provides a step-by-step approach to modelling, analysis, and interpretation data from real-world applications, from the environment and cyber security to health and finance. By combining discussion on the theory of statistics with a wealth of engaging, real-world applications, this book helps students approach statistical problem-solving in a logical manner with accessible, step-by-step procedures on relatable topics. Computational aspects are covered through R and SAS examples.

  • Machine Learning Solutions for Inverse Problems: Part B

    • 1st Edition
    • Volume 27
    • English
    Machine Learning Solutions for Inverse Problems: Part B, Volume 27 in the Handbook of Numerical Analysis, continues the exploration of emerging approaches at the intersection of machine learning and inverse problem theory. This volume presents a collection of chapters addressing a wide range of contemporary topics, including deep image prior methods for computed tomography, data-consistent learning strategies, and unified frameworks for training and inversion in machine learning-based reconstruction methods.Additional chapters examine learned regularization techniques, generative models for inverse problems, and the integration of deep learning with traditional computational frameworks such as full waveform inversion and PDE-based inverse modeling. The volume also discusses advances in self-supervised learning, data selection strategies, plug-and-play denoising methods, and diffusion models for solving imaging inverse problems.Further contributions explore neural network representations, operator learning, and learned iterative schemes, along with theoretical perspectives on stability, approximation hardness, hallucinations, and trustworthiness in AI-driven inverse problem methodologies. Together, these chapters provide a comprehensive overview of current developments in machine learning approaches to inverse problems, offering valuable insights for researchers in numerical analysis, computational mathematics, and scientific computing.

  • 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.

  • 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.

  • 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.

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