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.

Books Journals

31-40 of 3351 results in All results

Statistical Modeling and Robust Inference for One-shot Devices

1st Edition
April 1, 2025
Narayanaswamy Balakrishnan + 1 more
English

The study of one-shot devices such as automobile airbags, fire extinguishers or antigen tests, is rapidly becoming an important problem in the area of reliability engineering. These devices, which get destroyed or must be rebuilt after use, are a particular case of extreme censoring, which makes the problem of estimating their reliability and lifetime challenging. However, classical statistical and inferential methods do not consider the issue of robustness. Statistical Modeling and Robust Interference for One-shot Devices offers a comprehensive investigation of robust techniques of one-shot devices under accelerated life tests. With numerous examples and case studies in which the proposed methods are applied, this book includes detailed R codes in each chapter to help readers implement their own codes and use them in the proposed examples and in their own research on one-shot device testing data. Researchers, mathematicians, engineers, and students working on accelerated life testing data analysis and robust methodologies will surely find this to be a welcomed resource.

Data Science and Interactive Visualization Tools for the Analysis of Qualitative Evidence

1st Edition
April 1, 2025
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.

Approximation Theory and Applications

1st Edition
March 1, 2025
Sergei Aliukov
English

Approximation Theory and Applications: Piecewise Linear and Generalized Functions presents the main provisions of approximation theory, and considers existing and new methods for approximating piecewise linear and generalized functions, widely used to solve problems related to mathematical modeling of systems, processes, and phenomena in fields ranging from engineering to economics. The widespread use of piecewise linear and generalized functions is explained by the simplicity of their structure. However, challenges often arise when constructing solutions over the entire domain of these functions, requiring the use special mathematical methods to put theory into practice. This book first offers a first full foundation in approximation theory as it relates to piecewise linear and generalized functions, followed by staged methods to resolve common problems in practice, with applications examined across structural mechanics, medicine, quantum theory, signal theory, semiconductor theory, mechanical engineering, heat engineering, and other fields. Later chapters consider numerical verification of approximation methods, and approximation theory as the basis for new macroeconomic theory with impulse and jump characteristics. Each chapter includes questions for review and sample problems, accompanied by a separate Solutions Manual hosted for instructor access.

Generalized Quantum Calculus with Applications

1st Edition
March 1, 2025
English

Generalized Quantum Calculus with Applications is devoted to the qualitative theory of general quantum calculus and its applications to general quantum differential equations and inequalities. The book is aimed at upper-level undergraduate students and beginning graduate students in a range of interdisciplinary courses including physical sciences and engineering, from quantum mechanics to differential equations, with pedagogically-organized chapters that each conclude with a section of practical problems. Generalized quantum calculus includes a generalization of the q-quantum calculus and the time scale calculus. There are many open problems and difficulties in q-quantum calculus and time-scale calculus, and this book explores how to use the generalized quantum operators to solve difficulties arising in q-quantum calculus and time scale calculus including but not limited to: generalized quantum integration, generalized quantum chain rules, and generalized quantum Taylor formula.Since generalized quantum calculus includes the q-quantum calculus and time-scale calculus, this book can be utilized by a wide audience of researchers and students. This text exists as one of the few foundational books on generalized quantum calculus and can be used for future discoveries in the area of integral transforms, variational calculus, integral equations, and inequalities in the language of generalized quantum calculus. This book also offers detailed proofs, exercises, and examples to aid instructors, researchers, and users in their studies.

Recent Developments in Theory and Applications of Fractional Order Systems

1st Edition
February 1, 2025
Mehmet Yavuz + 2 more
English

Recent Developments in Theory and Applications of Fractional Order Systems presents a rigorous and thorough analysis of various aspects of Fractional Calculus. The book provides readers with a thorough understanding of fundamental concepts and methods of applied mathematics utilized in a variety of scientific and engineering disciplines. The authors present each computational modelling concept with a definition, methods, theorems, and observations followed by typical application problems along with the step-by-step solutions. Each topic is covered in detail, followed typically by several meticulously worked out examples, and a problem set containing many additional related problems. The authors discuss recent development in and the latest research on Fractional Calculus and its applications, demonstrating important applications in Engineering, Computer Science, Management, Social Science, and the Humanities.

An Introduction to Discrete Mathematics

1st Edition
February 1, 2025
Vidyadhar Kulkarni
English

An Introduction to Discrete Mathematics offers an engaging, accessible introduction to discrete mathematics for beginning undergraduate students across a wide range of application areas, from mathematics to statistics, operations research, business, engineering, and the sciences. It provides solid foundation in precise proof writing methods, with early chapters introducing set theory and logic, followed by deductive and inductive proof techniques, number theory, counting principles, permutations and combinations, probability of events, random variables, graphs, and weighted graphs.In a succinct, one semester format, An Introduction to Discrete Mathematics illustrates fundamental concepts in discrete mathematics with clear and precise definitions. These are paired with examples and counter-examples as applied in combinatorics, discrete probability, and graph theory, with accompany student exercises at the end of each chapter. A Solutions Manual and PollEverywhere example questions are available for instructors on a companion website.

Markov Chains: Theory and Applications

1st Edition
Volume 52
February 1, 2025
C.R. Rao + 1 more
English
eBook
9 7 8 - 0 - 4 4 3 - 2 9 5 7 7 - 5

Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters. Each chapter is written by an international board of authors.

Computer-Aided Diagnosis (CAD) Tools and Applications for 3D Medical Imaging

1st Edition
Volume 136
January 10, 2025
Abhishek Gupta + 2 more
English

Computer-Aided Diagnosis (CAD) Tools and Applications for 3D Medical Imaging, Volume 136 of the Advances in Computers series, presents detailed coverage of innovations in computer hardware, software, theory, design, and applications. Published since 1960, this series provides contributors with a medium to explore their subjects in greater depth and breadth than typical journal articles. This volume discusses various aspects of Computer-Aided Diagnosis.

Agent-Based Models with MATLAB

1st Edition
January 1, 2025
Erik Cuevas + 3 more
English

As the world becomes more complicated and linked, many of our research questions can no longer be answered using straightforward models. Agent-Based Models with MATLAB introduces one of the most important methodologies for complex systems modeling, called Agent-Based Modeling (ABM), using computational implementations and accompanying MATLAB software code as a means of inspiring readers to apply agent-based models to solve a diverse range of problems. Observing the implementation of a particular approach through code can be helpful for readers, even those with strong mathematical abilities, as it eliminates ambiguities and uncertainties, making the material easier to grasp and communicate. The book comes with a large amount of software code accompanying the main text, and the modeling systems described in the book are implemented using MATLAB as the programming language. Despite the heavy mathematical components of Agent-Based Models and complex systems, it is possible to utilize these models without in-depth understanding of their mathematical fundamentals. For many readers, a more feasible goal is to grasp the concepts of these models through programming instead of mathematical formulations. Agent-Based Models with MATLAB enables computer scientists, mathematicians, researchers and engineers to apply ABM in a wide range of research and engineering applications. The book gradually advances from basic to more advanced methods, while reinforcing understanding of complex systems through practical, hands-on applications of various computational models.

Difference Equations and Applications

1st Edition
January 1, 2025
English

Difference Equations and Applications provides unique coverage of high-level topics in the application of difference equations and dynamical systems. The book begins with extensive coverage of the calculus of difference equations, including contemporary topics on l_p stability, exponential stability, and parameters that can be used to qualitatively study solutions to non-linear difference equations, including variations of parameters and equations with constant coefficients, before moving on to the Z-Transform and its various functions, scalings, and applications. It covers systems, Lyapunov functions, and stability, a subject rarely covered in competitor titles, before concluding with a comprehensive section on new variations of parameters.Exercises are provided after each section, ranging from an easy to medium level of difficulty. When finished, students are set up to conduct meaningful research in discrete dynamical systems. In summary, this book is a comprehensive resource that delves into the mathematical theory of difference equations while highlighting their practical applications in various dynamic systems. It is highly likely to be of interest to students, researchers, and professionals in fields where discrete modeling and analysis are essential.