Название: Seduced by Mathematics: The enduring fascination of mathematics
Автор: James D. Stein
Издательство: World Scientific Publishing
Год: 2023
Страниц: 225
Язык: английский
Формат: pdf (true), epub
Размер: 13.9 MB

Seduction is not just an end result, but a process — and in mathematics, both the end results and the process by which those end results are achieved are often charming and elegant. This helps to explain why so many people — not just those for whom math plays a key role in their day-to-day lives — have found mathematics so seductive. Math is unique among all subjects in that it contains end results of amazing insight and power, and lines of reasoning that are clever, charming, and elegant. This book is a collection of those results and lines of reasoning that make us say, "OMG, that's just amazing," — because that's what mathematics is to those who love it. In addition, some of the stories about mathematical discoveries and the people who discovered them are every bit as fascinating as the discoveries themselves. This book contains material capable of being appreciated by students in elementary school — as well as some material that will probably be new to even the more mathematically sophisticated. Most of the book can be easily understood by those whose only math courses are algebra and geometry, and who may have missed the magic, enchantment, and wonder that is the special province of mathematics.

Название: Elementary Statistical Methods
Автор: Sahana Prasad
Издательство: Springer
Год: 2023
Страниц: 318
Язык: английский
Формат: pdf
Размер: 10.2 MB

Statistics is basically a mathematical science wherein data is first collected, then analysed by using suitable tools, explanation/interpretation given, and then finally converted into a valid conclusion. Statistical techniques are used right from data collection to final measurement. Different experimental designs and survey sampling techniques help in obtaining the data while data quality is improvised by statisticians by using data cleaning techniques. Various forecasting and prediction tools are available for providing inferences. Statistical knowledge is a relevant discipline in various academic organizations—in social and natural sciences and in business set-ups and governmental organizations. This is the first book of two volumes covering the basics of statistical methods and analysis. Significant topics include concepts of research and data analysis, descriptive statistics, probability and distributions, correlation and regression, and statistical inference. The book includes useful examples and exercises as well as relevant case studies for proper implementation of the discussed tools. This book will be a valuable text for undergraduate students of statistics, management, economics, and psychology, wanting to gain basic understanding of statistics and the usage of its various concepts.

Название: Ten Projects in Applied Statistics
Автор: Peter McCullagh
Издательство: Springer
Серия: Springer Series in Statistics
Год: 2023
Страниц: 415
Язык: английский
Формат: pdf (true), epub
Размер: 25.9 MB

The first half of the book is aimed at quantitative research workers in biology, medicine, ecology and genetics. The book as a whole is aimed at graduate students in statistics, biostatistics, and other quantitative disciplines. Ten detailed examples show how the author approaches real-world statistical problems in a principled way that allows for adequate compromise and flexibility. The need to accommodate correlations associated with space, time and other relationships is a recurring theme, so variance-components models feature prominently. Statistical pitfalls are illustrated via examples taken from the recent scientific literature. The aim of the book is not so much to illustrate algorithms or techniques of computation, but to illustrate the role of statistical thinking and stochastic modelling in scientific research. The R package is used throughout the book for all plots and computations.

Название: Qualitative Theory of ODEs: An Introduction to Dynamical Systems Theory
Автор: Henryk Żoladek, Raul Murillo
Издательство: World Scientific Publishing
Год: 2023
Страниц: 283
Язык: английский
Формат: pdf (true)
Размер: 16.4 MB

The Qualitative Theory of Ordinary Differential Equations (ODEs) occupies a rather special position both in Applied and Theoretical Mathematics. On the one hand, it is a continuation of the standard course on ODEs. On the other hand, it is an introduction to Dynamical Systems, one of the main mathematical disciplines in recent decades. Moreover, it turns out to be very useful for graduates when they encounter differential equations in their work; usually those equations are very complicated and cannot be solved by standard methods.

Название: Spatiotemporal Analytics
Автор: Jay Lee
Издательство: CRC Press
Год: 2023
Страниц: 267
Язык: английский
Формат: pdf (true)
Размер: 20.0 MB

This book introduces readers to spatiotemporal analytics that are extended from spatial statistics. Spatiotemporal analytics help analysts to quantitatively recognize and evaluate the spatial patterns and their temporal trends of a set of geographic events or objects. Spatiotemporal analyses are very important in geography, environmental sciences, economy, and many other domains. Spatiotemporal Analytics explains in very simple terms the concepts of spatiotemporal data and statistics, theories, and methods used. Each chapter introduces a case study as an example application for an in-depth learning process. The software used and the codes provided enable readers not only to learn statistics but also to use them effectively in their projects.

Название: Quantum-like Networks: An Approach to Neural Behavior through their Mathematics and Logic
Автор: Stephen A Selesnick
Издательство: World Scientific Publishing
Год: 2023
Страниц: 354
Язык: английский
Формат: pdf (true), epub
Размер: 30.1 MB

Do brains compute? If they do, what do they compute and how do they do it? The first part of the book introduces the development of a model that simulates actual biological neurons more closely than do current standard models of neural networks, as well as the deduction of its physics-like and computational properties from first principles. The second part presents a collection of applications of the model to memory formation and loss, a general syntax for memory retrieval, language itself, and certain forms of aphasia. A linear development of the discussion with proofs in situ is employed by the author, making the book essentially self-contained. A pair of helpful appendices are provided to acquaint the reader with necessary fundamentals of topics in logic and mathematics. Quantum-like Networks: An Approach to Neural Behavior through their Mathematics and Logic will show you an entirely new approach to an ancient subject. Readership: Researchers and graduate students in Neuroscience, Biomathematics, Biophysics, Mathematics, Computer Science, and related fields.

Название: Data Science and Human-Environment Systems
Автор: Steven M. Manson
Издательство: Cambridge University Press
Год: 2023
Страниц: 279
Язык: английский
Формат: pdf
Размер: 10.0 MB

Transformation of the Earth's social and ecological systems is occurring at a rate and magnitude unparalleled in human experience. Data Science is a revolutionary new way to understand human-environment relationships at the heart of pressing challenges like climate change and sustainable development. However, data science faces serious shortcomings when it comes to human-environment research. There are challenges with social and environmental data, the methods that manipulate and analyze the information, and the theory underlying the data science itself; as well as significant legal, ethical and policy concerns. This timely book offers a comprehensive, balanced, and accessible account of the promise and problems of this work in terms of data, methods, theory, and policy. It demonstrates the need for data scientists to work with human-environment scholars to tackle pressing real-world problems, making it ideal for researchers and graduate students in Earth and environmental science, data science and the environmental social sciences. Data Science and cognate fields like Big Data and Artificial Intelligence hold great promise for studying human-environment systems.

Название: The Mystery of Time: Asymmetry of Time and Irreversibility in the Natural Processes
Автор: A.L. Kuzemsky
Издательство: World Scientific Publishing
Год: 2023
Страниц: 484
Язык: английский
Формат: pdf (true), epub
Размер: 10.0 MB

The book focuses on the study of the temporal behavior of complex many-particle systems. The phenomenon of time and its role in the temporal evolution of complex systems is a remaining mystery. The book presents the necessity of the interdisciplinary point of view regarding on the phenomenon of time. The aim of the present study is to summarize and formulate in a concise but clear form the trends and approaches to the concept of time from a broad interdisciplinary perspective exposing tersely the complementary approaches and theories of time in the context of thermodynamics, statistical physics, cosmology, theory of information, biology and biophysics, including the problem of time and aging. Various approaches to the problem show that time is an extraordinarily interdisciplinary and multifaceted underlying notion which plays an extremely important role in various natural complex processes.

Название: A Bridge to Advanced Mathematics: From Natural to Complex Numbers
Автор: Sebastian M. Cioaba, Werner Linde
Издательство: American Mathematical Society
Год: 2023
Страниц: 544
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

Most introduction to proofs textbooks focus on the structure of rigorous mathematical language and only use mathematical topics incidentally as illustrations and exercises. In contrast, this book gives students practice in proof writing while simultaneously providing a rigorous introduction to number systems and their properties. Understanding the properties of these systems is necessary throughout higher mathematics. The book is an ideal introduction to mathematical reasoning and proof techniques, building on familiar content to ensure comprehension of more advanced topics in abstract algebra and real analysis with over 700 exercises as well as many examples throughout. Readers will learn and practice writing proofs related to new abstract concepts while learning new mathematical content. The first task is analogous to practicing soccer while the second is akin to playing soccer in a real match. The authors believe that all students should practice and play mathematics. The book is written for students who already have some familiarity with formal proof writing but would like to have some extra preparation before taking higher mathematics courses like abstract algebra and real analysis.

Название: Anisotropy Across Fields and Scales
Автор: Özarslan E., Schultz T., Zhang E., Fuster A.
Издательство:Springer
Год: 2021
Формат: PDF
Страниц:290
Размер: 10,7 МБ
Язык: English

This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain.