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Books in Mathematics and applied mathematics

  • Mathematics and Biomedical Engineering in Medicine, Physiology 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.

  • Functional Analysis

    Theory and Applications
    • 1st Edition
    • Ravi P. Agarwal + 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.

  • 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.

  • 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.

  • 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.

  • Quantitative Biology

    Mathematical Modeling and Computation
    • 1st Edition
    • Alonso Ogueda-Oliva + 1 more
    • English
    Quantitative Biology provides quantitative and data-driven approaches for analyzing biological and bio-inspired systems, covering the foundations of mathematical modeling, analysis, and computation. The book presents a practical mix of both theory and computation for a variety of biological applications, with tied-in, engaging project activities, instruction, programming language, and technological tools. Modeling approaches combine mathematical foundations, statistical reasoning, and computational thinking, with applications in compartmental, agent-based, bio image, biological interaction, and neural network modeling, as well as machine learning, parameter identification, and applications across societal challenges.Each chapter includes exposure to models and modeling, a foundational instructional framework, benchmark applications, and numerical simulations with a literate programming guided style that helps readers go beyond replication models and into prediction and data-driven discovery. A companion website also features interactive code to accompany projects across each chapter.

  • Extended Hypergeometric Functions and Orthogonal Polynomials

    • 1st Edition
    • Praveen Agarwal + 1 more
    • English
    Extended Hypergeometric Functions and Orthogonal Polynomials presents a comprehensive and accessible resource for researchers and graduate students interested in exploring the rich connections between extended hypergeometric functions, orthogonal polynomials, and multivariable polynomials. Integrating all three fields and their applications in Maple, Mathematica, and MATLAB, this book fosters interdisciplinary understanding and inspires new avenues of research in mathematics, engineering, physics, and computer science. It also provides a glimpse into future research directions in these areas, including potential applications in emerging fields of applied mathematics and interdisciplinary collaborations. Each chapter begins with an introduction, includes sections on theory, followed by sections on applications, and ends with exercises, problems, references and suggested readings.

  • 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.

  • An Introduction to Writing Mathematical Proofs

    Shifting Gears from Calculus to Advanced Mathematics
    • 1st Edition
    • Thomas Bieske
    • English
    An Introduction to Writing Mathematical Proofs: Shifting Gears from Calculus to Advanced Mathematics addresses a critical gap in mathematics education, particularly for students transitioning from calculus to more advanced coursework. It provides a structured and supportive approach, guiding students through the intricacies of writing proofs while building a solid foundation in essential mathematical concepts. Sections introduce elementary proof methods, beginning with fundamental topics such as sets and mathematical logic, systematically develop the properties of real numbers and geometry from a proof-writing perspective, and delve into advanced proof methods, introducing quantifiers and techniques such as proof by induction, counterexamples, contraposition, and contradiction. Finally, the book applies these techniques to a variety of mathematical topics, including functions, equivalence relations, countability, and a variety of algebraic activities, allowing students to synthesize their learning in meaningful ways. It not only equips students with essential proof-writing skills but also fosters a deeper understanding of mathematical reasoning. Each chapter features clearly defined objectives, fully worked examples, and a diverse array of exercises designed to encourage exploration and independent learning. Supplemented by an Instructors' Resources guide hosted online, this text is an invaluable companion for undergraduate students eager to master the art of writing mathematical proofs.

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