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Elsevier

Books in Mathematics and applied mathematics

This portfolio offers comprehensive coverage of pure and applied mathematics, including algebra, calculus, differential equations, and computational techniques. It supports researchers, educators, and students in advancing theoretical understanding and practical problem-solving across engineering, physics, and data science. Featuring innovative methodologies, real-world case studies, and emerging trends, these resources enable breakthroughs in modelling, simulation, and analytical skills critical for technological progress and scientific discovery.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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, Interactive Visualizations, and Generative AI Tools for the Analysis of Qualitative, Mixed-Methods, and Multimodal Evidence

    • 1st Edition
    • Manuel González Canché
    • English
    Data Science, Interactive Visualization, and Generative AI 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.

  • Lebesgue Measure and Integration Theory

    Foundations and Solved Exercises
    • 1st Edition
    • Alberto Cabada + 1 more
    • English
    Lebesgue Measure and Integration Theory: Foundations and Solved Exercises offers a thorough, engaging introduction to Lebesgue measure and the theory of integration for students of mathematics and physics. This book provides the complete theoretical underpinnings of this theory, with the corresponding proofs, adapted to the level of advanced undergraduate and graduate students in these disciplines. Beginning with a fundamental discussion of measure spaces, the book moves onto measurable and non-measurable sets, approximation of measurable sets, measurable functions, the Lebesgue integral, the relationship between differentiation and integration on R, and product measures, among other topics. Examples and solved exercises are included across chapters to reinforce understanding and application.

  • 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.

  • Trigonometry

    From Theory to Application
    • 1st Edition
    • João Ricardo Branco + 1 more
    • English
    Trigonometry: From Theory to Application introduces the basics of trigonometry and key areas of practice, fully considering in straightforward, pragmatic terms the characterization of triangles, coordinate transport, and coordinate systems, with emphasis on interpreting key concepts and applying them. The book begins with a review of basic trigonometric functions and their properties, and then moves on to trigonometric identities, equations, and practical applications. Special sections dedicated to real-world and technological problems demonstrate how trigonometry is applied in everyday situations, inspiring and motivating students to see the relevance of trigonometry beyond the classroom, across fields ranging from engineering to physics and beyond.Each chapter is interconnected, ensuring that students build a solid and cumulative understanding of concepts, with detailed examples, varied exercises, and full-color illustrations.

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