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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
      • July 22, 2024
      • Tshilidzi Marwala
      • English
      • Paperback
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      • eBook
        9 7 8 0 4 4 3 2 3 9 8 3 0
      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.

    • Fractional Calculus

      • 1st Edition
      • June 21, 2024
      • Behzad Ghanbari
      • English
      • Paperback
        9 7 8 0 4 4 3 3 1 5 0 0 8
      • eBook
        9 7 8 0 4 4 3 3 1 5 0 1 5
      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.

    • Numerical Analysis meets Machine Learning

      • 1st Edition
      • Volume 25
      • June 13, 2024
      • English
      • Hardback
        9 7 8 0 4 4 3 2 3 9 8 4 7
      • eBook
        9 7 8 0 4 4 3 2 3 9 8 5 4
      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.

    • Modeling and Analysis of Longitudinal Data

      • 1st Edition
      • Volume 50
      • February 7, 2024
      • English
      • Hardback
        9 7 8 0 4 4 3 1 3 6 5 1 1
      • eBook
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      Longitudinal Data Analysis, Volume 50 in the Handbook of Statistics series covers how data consists of a series of repeated observations of the same subjects over an extended time frame and is thus useful for measuring change. Such studies and the data arise in a variety of fields, such as health sciences, genomic studies, experimental physics, sociology, sports and student enrollment in universities. For example, in health studies, intra-subject correlation of responses must be accounted for, covariates vary with time, and bias can arise if patients drop out of the study.

    • Probability Models

      • 1st Edition
      • Volume 51
      • September 27, 2024
      • English
      • Hardback
        9 7 8 0 4 4 3 2 9 3 2 8 3
      • eBook
        9 7 8 0 4 4 3 2 9 3 2 9 0
      Probability Models, Volume 51 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on Stein’s methods, Probabilities and thermodynamics third law, Random Matrix Theory, General tools for understanding fluctuations of random variables, An approximation scheme to compute the Fisher-Rao distance between multivariate normal distributions, Probability Models Applied to Reliability and Availability Engineering, Backward stochastic differential equation– Stochastic optimization theory and viscous solution of HJB equation, and much more.Additional chapters cover Probability Models in Machine Learning, The recursive stochastic algorithm, randomized urn models and response-adaptive randomization in clinical trials, Random matrix theory: local laws and applications, KOO methods and their high-dimensional consistencies in some multivariate models, Fourteen Lectures on Inference for Stochastic Processes, and A multivariate cumulative damage model and some applications.

    • Applying Computational Intelligence for Social Good

      • 1st Edition
      • Volume 132
      • January 14, 2024
      • English
      • Hardback
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      • eBook
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      Applying Computational Intelligence for Social Good: Track, Understand and Build a Better World, Volume 132 presents views on how Computational Intelligent and ICT technologies can be applied to ease or solve social problems by sharing examples of research results from studies of social anxiety, environmental issues, mobility of the disabled, and problems in social safety. Sample chapters in this release include Why is implementing Computational Intelligence for social good so challenging? Principles and its Application, Smart crisis management system for road accidents using Geo-Spacial Machine Learning Techniques, Residential Energy Management System (REMS) Using Machine Learning, Text-Based Personality Prediction using XLNet, and much more.

    • Applications of Nature-Inspired Computing and Optimization Techniques

      • 1st Edition
      • Volume 135
      • April 2, 2024
      • English
      • Hardback
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      • eBook
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      Advances in Computers, Volume 135 highlights advances in the field, with this new volume, Applications of Nature-inspired Computing and Optimization Techniques presenting interesting chapters on a variety of timely topics, including A Brief Introduction to Nature-inspired Computing, Optimization and Applications, Overview of Non-linear Interval Optimization Problems, Solving the Aircraft Landing Problem using the Bee Colony Optimization (BCO) Algorithm, Situation-based Genetic Network Programming to Solve Agent Control Problems, Small Signal Stability Enhancement of Large Interconnected Power System using Grasshopper Optimization Algorithm Tuned Power System Stabilizer, Air Quality Modelling for Smart Cities of India by Nature Inspired AI – A Sustainable Approach, and much more.Other sections cover Genetic Algorithm for the Optimization of Infectiological Parameter Values under Different Nutritional Status, A Novel Influencer Mutation Strategy for Nature-inspired Optimization Algorithms to Solve Electricity Price Forecasting Problem, Recent Trends in Human and Bio Inspired Computing: Use Case Study from Retail Perspective, Domain Knowledge Enriched Summarization of Legal Judgment Documents via Grey Wolf Optimization, and a host of other topics.

    • Discrete Mathematics With Logic

      • 1st Edition
      • July 20, 2023
      • Martin Milanic + 2 more
      • English
      • Paperback
        9 7 8 0 4 4 3 1 8 7 8 2 7
      • eBook
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      Discrete Mathematics provides key concepts and a solid, rigorous foundation in mathematical reasoning. Appropriate for undergraduate as well as a starting point for more advanced class, the resource offers a logical progression through key topics without assuming any background in algebra or computational skills and without duplicating what they will learn in higher level courses. The book is designed as an accessible introduction for students in mathematics or computer science as it explores questions that test the understanding of proof strategies, such as mathematical induction. For students interested to dive into this subject, the text offers a rigorous introduction to mathematical thought through useful examples and exercises.

    • Optical Communications from a Fourier Perspective

      • 1st Edition
      • November 17, 2023
      • Palle Jeppesen + 1 more
      • English
      • Paperback
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      • eBook
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      Optical Communications from a Fourier Perspective: Fourier Theory and Optical Fiber Devices and Systems covers Fourier theory and signal analysis over photonic components, including time lenses in optical communication. Sections cover wave propagation in optical waveguides based on Maxwell equations and the nonlinear Schrödinger equation. Optical Fourier transform in the form of time lens is covered, for example in modulation format conversion and spectrum magnification, and couplers and their use for optical discrete Fourier transformation are also discussed. Other important subjects are discussed such as shot noise, thermal noise and also the basics of four wave mixing in relation to time lenses. Detailed derivations and a deeper background for the chapters are provided in appendices where appropriate. Some of the theory is more generally applicable beyond optical communication and is of relevance also for communications engineering. The Fourier theory dimension of the book presents the relationship between Fourier series and Fourier integrals and also the related Laplace transform.

    • Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law

      • 1st Edition
      • April 21, 2023
      • Ilwoo Cho + 1 more
      • English
      • Paperback
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      • eBook
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      In Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law, the authors consider the so-called free Hilbert spaces, which are the Hilbert spaces induced by the usual l2 Hilbert spaces and operators acting on them. The construction of these operators itself is interesting and provides new types of Hilbert-space operators. Also, by considering spectral-theoretic properties of these operators, the authors illustrate how “free-Hilbert-space” Operator Theory is different from the classical Operator Theory. More interestingly, the authors demonstrate how such operators affect the semicircular law induced by the ONB-vectors of a fixed free Hilbert space. Different from the usual approaches, this book shows how “inside” actions of operator algebra deform the free-probabilistic information—in particular, the semicircular law.

Related subjects

Mathematics and applied mathematics

Statistics and probability