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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.

BooksJournals

    • 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.

    • Measure and Integration

      Concepts, Examples, and Applications
      • 1st Edition
      • Rudi Weikard + 2 more
      • English
      Measure and Integration: Examples, Concepts, and Applications offers a comprehensive introduction to the fundamental principles and methods of real analysis, providing readers with a solid foundation through clear explanations, rigorous proofs, and an abundance of thoughtfully constructed exercises. From the very first chapter, students are encouraged to engage actively with concepts, applying them to a range of practical examples that reinforce both understanding and analytical skills. The book’s structured approach ensures that readers not only grasp key theorems and core techniques, but also develop the problem-solving abilities essential for higher-level mathematics and related applications.The text also delves into advanced areas such as integration on product spaces, Radon functionals, functions of bounded variation, Lebesgue-Stieltjes measures, convolutions, probability, and differential equations. Each chapter concludes with advanced exercises, clearly marked for difficulty, allowing both students and instructors to tailor their study or coursework. An appendix with complete solutions supports independent learning, making the book a valuable resource for both classroom use and self-study.

    • 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.

    • Trigonometry

      From Theory to Application
      • 1st Edition
      • João Ricardo Branco + 1 more
      • English
      Trigonometry: From Theory to Application offers a clear and practical introduction to the foundational principles of trigonometry, guiding readers through the subject with an emphasis on real-world relevance. The book thoughtfully explores the characterization of triangles, coordinate transport, and coordinate systems, providing straightforward explanations and practical insights. Beginning with an accessible review of basic trigonometric functions and their properties, the text gradually expands to cover identities, equations, and a broad range of applications. Each chapter builds on the last, ensuring that learners develop a strong, cumulative grasp of the material through detailed examples and engaging exercises.In addition to its comprehensive approach, the book features special sections devoted to real-life and technological problems, illustrating how trigonometry is not just a theoretical subject but a vital tool in solving everyday challenges. Full-color illustrations and a variety of exercises help students connect concepts to applications in fields like engineering and physics, making the subject both inspiring and relevant. This integrated approach motivates learners to appreciate the significance of trigonometry beyond the classroom environment.

    • 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.

    • 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.

    • Multidimensional Signal Processing

      • 1st Edition
      • Volume 54
      • English
      Multidimensional Signal Processing, Volume 54 in the Handbook of Statistics series is dedicated to presenting the latest developments and methodologies in multidimensional signal processing. The book aims to provide a comprehensive overview of the theories, models, and methods that form the foundation of this field. Chapters in this new release include Robust Parameter Estimation of Two Dimensional Chirp Model, Computability Theory for Multidimensional Signal Processing, Tensor signal processing, Spectral compressed sensing by structured matrix optimization methods, Space-time imaging, Hypercomplex Widely Linear Processing, and much more. The book's chapters are meticulously curated to offer detailed, educational content rather than conventional journal-style articles.Other chapters cover Hypercomplex phase retrieval, Hypercomplex widely linear estimation, MIMO radar signal processing, Computational lidar, Signal processing applications of higher-dimensional graphs, Space-Time Radio Signal Processing by Photonic Upconversion, Computational imaging, and Topology identification and learning over graphs using multi-dimensional data.

Related subjects

Mathematics and applied mathematics

Statistics and probability