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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

    • Mechanism Design, Behavioral Science and Artificial Intelligence in International Relations

      • 1st Edition
      • Tshilidzi Marwala
      • English
      Recent advances in AI and Mechanism Design provide a vital tool for solving collective action problems, common in international relations. By using AI to optimize mechanisms for cooperation and coordination, we can better address issues such as climate change, trade, and security. Mechanism Design, Behavioral Science and Artificial Intelligence in International Relations shows readers how the intersection of Mechanism Design and Artificial Intelligence is revolutionizing the way we approach international relations. By using AI to optimize mechanisms, we can design better institutions, policies, and agreements that are more effective and efficient. Dr. Tshilidzi Marwala, United Nations University Rector and UN Under-Secretary General, presents the essential technologies used in Game Theory, Mechanism Design and AI and applies these to significant global issues such as interstate conflict, cybersecurity, and energy. International relations are a complex field, with many different actors and interests in play. By incorporating AI into our analysis and decision-making processes, we can better understand and predict the behavior of multiple actors and design mechanisms that take these behaviors into account, thereby producing more desirable and creative interdisciplinary approaches. The book presents real-world applications of these rapidly evolving technologies in crucial research fields such as Interstate Conflict, International Trade, Climate Change, Water management, Energy, cybersecurity, and global finance.

    • Information Modeling and Relational Databases

      • 3rd Edition
      • Terry Halpin + 1 more
      • English
      Information Modeling and Relational Databases, Third Edition, provides thorough coverage of information modeling approaches, including object-role modeling (ORM), entity-relationship (ER) modeling, and the unified modeling language (UML). It shows how to map models developed with those approaches to a variety of relational and nonrelational database systems, including document databases, column-oriented databases, graph databases, and deductive databases. Process and state modeling, ontological modeling, and metamodeling are also covered. For this new edition, the coverage of ORM, ER, UML, SQL, OWL, and BPMN has been thoroughly updated to include their latest versions. A significant amount of new material has been added. Various data file formats such as CSV, XML, JSON, YAML, and some other markup languages are now covered, and a more thorough treatment is provided for nonrelational databases, especially NoSQL. One of the major features of the book is its large number of exercises, which have been thoroughly class-tested. This book is intended for anyone with a stake in the accuracy and efficacy of databases such as systems analysts, information modelers, database designers and administrators, and programmers.

    • Visualizing More Quaternions

      • 1st Edition
      • Andrew J. Hanson
      • English
      Visualizing More Quaternions is a sequel to Dr. Andrew J. Hanson’s first book, Visualizing Quaternions, which appeared in 2006. This new volume develops and extends concepts that have attracted the author’s attention in the intervening 18 years, providing new insights into existing scholarship, and detailing results from Dr. Hanson’s own published and unpublished investigations relating to quaternion applications. Among the topics covered are the introduction of new approaches to depicting quaternions and their properties, applications of quaternion methods to cloud matching, including both orthographic and perspective projection problems, and orientation feature analysis for proteomics and bioinformatics. The quaternion adjugate variables are introduced to embody the nontrivial quaternion topology on the three-sphere and incorporate it into machine learning tasks. Other subjects include quaternion applications to a wide variety of problems in physics, including quantum computing, complexified quaternions in special relativity, and a detailed study of the Kleinian “ADE”discrete groups of the ordinary two-sphere. Quaternion geometry is also incorporated into the isometric embedding of the Eguchi–Hanson gravitational instanton corresponding to the k = 1 Kleinian cyclic group. Visualizing More Quaternions endeavors to explore novel ways of thinking about challenging problems that are relevant to a broad audience involved in a wide variety of scientific disciplines.

    • Fractional Calculus

      Bridging Theory with Computational and Contemporary Advances
      • 1st Edition
      • Behzad Ghanbari
      • English
      Fractional Calculus: Bridging Theory with Computational and Contemporary Advances is an authoritative and comprehensive guide that delves into the world of fractional calculus, offering a unique blend of theoretical foundations, numerical algorithms, practical applications, and innovative perspectives. This book explores the mathematical framework of fractional calculus and its relevance across various disciplines, providing readers with a deep understanding of this rapidly growing field. The author presents a rigorous yet accessible approach to fractional calculus, making it suitable for mathematicians, researchers, academics, graduate students, and professionals in engineering and applied sciences. The book covers a wide range of topics, including numerical methods for fractional calculus equations, fractional differential equations, fractal dynamics, and fractional control systems. It also explores applications in areas such as physics, engineering, signal processing, and data analysis. Fractional Calculus: Bridging Theory with Computational and Contemporary Advances equips readers with the necessary tools to tackle challenging problems involving fractional calculus, empowering them to apply these techniques in their research, professional work, or academic pursuits. The book provides a comprehensive introduction to the fundamentals of fractional calculus, explaining the theoretical concepts and key definitions in a clear and accessible manner. This helps readers build a strong foundation in the subject. The book then covers a range of numerical algorithms specifically designed for fractional calculus problems, explaining the underlying principles, step-by-step implementation, and computational aspects of these algorithms. This enables readers to apply numerical techniques to solve fractional calculus problems effectively. The book also provides examples that illustrate how fractional calculus is applied to solve real-world problems, providing readers with insights into the wide-ranging applications of the subject.

    • Advanced Calculus for Mathematical Modeling in Engineering and Physics

      With Discrete and Numerical Analogies
      • 1st Edition
      • David Stapleton
      • English
      Advanced Calculus for Mathematical Modeling in Engineering and Physics: With Discrete and Numerical Analogies introduces the principles and methods of advanced calculus for mathematical modeling through a balance of theory and application using a state space approach with elementary functional analysis. This framework facilitates a deeper understanding of the nature of mathematical models, and of the behavior of their solutions. The work provides a variety of advanced calculus models for mathematical, physical science, and engineering audiences, with discussions on how calculus-based models and their discrete analogies are generated. This valuable textbook offers scientific computations driven by Octave/MATLAB script.

    • Numerical Analysis meets Machine Learning

      • 1st Edition
      • Volume 25
      • English
      Numerical Analysis Meets Machine Learning series, highlights new advances in the field, with this new volume presenting interesting chapters. Each chapter is written by an international board of authors.

    • API Design for C++

      • 2nd Edition
      • Martin Reddy
      • English
      API Design for C++, Second Edition provides a comprehensive discussion of Application Programming Interface (API) development, from initial design through implementation, testing, documentation, release, versioning, maintenance, and deprecation. It is the only book that teaches the strategies of C++ API development, including interface design, versioning, scripting, and plug-in extensibility. Drawing from the author's experience on large scale, collaborative software projects, the text offers practical techniques of API design that produce robust code for the long-term. It presents patterns and practices that provide real value to individual developers as well as organizations.The Second Edition includes all new material fully updated for the latest versions of C++, including a new chapter on concurrency and multithreading, as well as a new chapter discussing how Objective C++ and C++ code can co-exist and how a C++ API can be accessed from Swift programs. In addition, it explores often overlooked issues, both technical and non-technical, contributing to successful design decisions that produce high quality, robust, and long-lived APIs. It focuses on various API styles and patterns that will allow you to produce elegant and durable libraries. A discussion on testing strategies concentrates on automated API testing techniques rather than attempting to include end-user application testing techniques such as GUI testing, system testing, or manual testing.

    • An Introduction to Probability and Statistical Inference

      • 3rd Edition
      • George G. Roussas
      • English
      An Introduction to Probability and Statistical Inference, Third Edition guides the reader through probability models and statistical methods to develop critical-thinking skills. Written by award-winning author George Roussas, this valuable text introduces a thinking process to help users obtain the best solution to a posed question or situation and provides a plethora of examples and exercises to illustrate applying statistical methods to different situations.

    • Fractional Differential Equations

      Theoretical Aspects and Applications
      • 1st Edition
      • Praveen Agarwal + 2 more
      • English
      Fractional Differential Equations: Theoretical Aspects and Applications presents the latest mathematical and conceptual developments in the field of Fractional Calculus and explores the scope of applications in research science and computational modeling. The book delves into these methods and applied computational modelling techniques, including analysis of equations involving fractional derivatives, fractional derivatives and the wave equation, analysis of FDE on groups, direct and inverse problems, functional inequalities, and computational methods for FDEs in physics and engineering. Other modeling techniques and applications explored include general fractional derivatives involving the special functions in analysis and fractional derivatives with respect to other functions. Fractional Calculus, the field of mathematics dealing with operators of differentiation and integration of arbitrary real or even complex order, extends many of the modelling capabilities of conventional calculus and integer-order differential equations and finds its application in various scientific areas, such as physics, mechanics, engineering, economics, finance, biology, and chemistry, among others.

    • An Introductory Handbook of Bayesian Thinking

      • 1st Edition
      • Stephen C. Loftus
      • English
      An Introductory Handbook of Bayesian Thinking brings Bayesian thinking and methods to a wide audience beyond the mathematical sciences. Appropriate for students with some background in calculus and introductory statistics, particularly for nonstatisticians with a sufficient mathematical background, the text provides a gentle introduction to Bayesian ideas with a wide array of supporting examples from a variety of fields.

Related subjects

Mathematics and applied mathematics

Statistics and probability