Название: The Invisible Power of Mathematics: The Pervasive Impact of Mathematical Engineering in Everyday Life
Автор: Giovanni Samaey, Joos P. L. Vandewalle
Издательство: Springer
Год: 2023
Страниц: 176
Язык: английский
Формат: pdf (true), epub
Размер: 19.8 MB

How does homebanking work? How are board games developed? How reliable can wind energy get? How do we discover forged paintings? Do smart girls stay single? How dangerous can a bioterrorist get? In all these questions (and many others), mathematics plays a crucial role in the search for an answer.​ This book tells the story behind twenty of these questions. This is explicitly not a mathematics book, but a book about the crucial role that mathematics plays in devising the creative solutions the world needs. The questions are divided into three categories: home, garden and kitchen mathematics; mathematics for the workplace; and mathematics for tomorrow's society. The themes illustrate not only the incredibly broad applicability of mathematics in the world around us, but also the great diversity of useful mathematical techniques.

Название: Fluorescent Dye Labels and Stains : A Database of Photophysical Properties
Автор: Tarso B. Ledur Kist
Издательство: Wiley
Год: 2023
Страниц: 498
Язык: английский
Формат: pdf (true)
Размер: 21.8 MB

Fluorescent Dye Labels and Stains The only comprehensive database of fluorophores and their physical and photochemical properties. Fluorophores are chemical compounds that strongly absorb in the ultraviolet, visible, and/or near-infrared and with bright emission in these ranges. As a result, they are exceptionally valuable as dyes for various analytical processes, capable of labelling and staining particular targets for purposes of fluorescent imaging, sensitive detection, and quantification (exhibiting linear responses over very wide concentration ranges). These compounds are many and varied, and panoramic views of their options, physical properties and their reactions to light excitations can be critical to their successful integration into chemical analysis, pharmaceutical analysis, clinical analysis, microscopies, optical bioimaging, cancer imaging, real-time PCR, flow cytometry, multiplexing in proteomics, life sciences in general, and many other high-tech fields (material sciences, traceability, photovoltaics, quantum computing).

Название: STEM Education with Robotics: Lessons from Research and Practice
Автор: Purvee Chauhan, Vikram Kapila
Издательство: Routledge
Год: 2023
Страниц: 288
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

This book offers a synthesis of research, curriculum examples, pedagogy models, and classroom recommendations for the effective use of robotics in STEM teaching and learning. Authors Chauhan and Kapila demonstrate how the use of educational robotics can improve and enhance student learning and understanding within the STEM disciplines. The science and technology of robotics design, manufacturing, and application has grown by leaps and bounds over the past decades. This revolution has been fueled by developments both in software (particularly Machine Learning and Artificial Intelligence) as well as better understanding of the mechanics of movement and object manipulation. In that sense, robotics is almost a perfect encapsulation and convergence of ideas in the STEM (science, technology engineering, and mathematics) disciplines.

Название: Математическое программирование в примерах и задачах: Учебное пособие для вузов. 4-е изд.
Автор: Акулич И.Л.
Издательство: Лань
Год: 2022
Страниц: 348
Язык: русский
Формат: pdf
Размер: 15,6 MB

В учебном пособии рассматриваются задачи линейного, нелинейного и динамического программирования. Приведены определения, формулы, а также методические указания, необходимые для решения задач; даны решения типовых задач, показаны возможности использования в этих целях различных пакетов прикладных программ. В конце каждого параграфа приведены задачи для самостоятельного решения. Учебное пособие предназначено для студентов, аспирантов и преподавателей вузов, изучающих экономико-математические методы и модели и их использование при решении практических задач.

Название: Neural Machines_A Defense of Non-Representationalism in Cognitive Neuroscience
Автор: Matej Kohar
Издательство: Springer
Год: 2023
Страниц: 199
Язык: английский
Формат: pdf (true), epub
Размер: 10.2 MB

In this book, Matej Kohar demonstrates how the new mechanistic account of explanation can be used to support a non-representationalist view of explanations in cognitive neuroscience, and therefore can bring new conceptual tools to the non-representationalist arsenal. Kohar focuses on the explanatory relevance of representational content in constitutive mechanistic explanations typical in cognitive neuroscience. The work significantly contributes to two areas of literature: 1) the debate between representationalism and non-representationalism, and 2) the literature on mechanistic explanation. The goal of cognitive neuroscience is to uncover neural mechanisms responsible for intelligent behaviour in humans and animals. Intelligent behaviour has traditionally been taken to include decision-making, use of language and other high-level cognitive phenomena. Over time, however, the scope of what is meant by intelligent behaviour for the purposes of determining the proper subject matter of cognitive sciences (including cognitive neuroscience) has expanded to include any context-dependent responses to stimuli. Cognitive neuroscience therefore engages in search for neural mechanisms underlying sensory perception, memory, navigation, object-recognition, tracking, avoidance, etc. That is, the scope of cognitive neuroscience covers the search for neural mechanisms all the way from sensory processing, through response selection to motor control.

Название: Numbercrunch: A Mathematician's Toolkit for Making Sense of Your World
Автор: Oliver Johnson
Издательство: Heligo Books
Год: 2023
Страниц: 368
Язык: английский
Формат: epub (true)
Размер: 10.2 MB

Our everyday lives are increasingly ruled by data and by algorithms. We can make ourselves understood by talking to Siri, and instantaneously receive almost professional-quality translations of foreign language text using Google Translate. Netflix can match our previous viewing to profiles of similar users, to recommend the next box set that we are most likely to get hooked on. However, it may be less obvious that this kind of ‘Artificial Intelligence’ or ‘Machine Learning’ emerged from mathematics and from statistics. These ideas have had a rebrand for the 21st century and been supercharged by ever-increasing computing power, but it’s always mathematics under the bonnet. These Silicon Valley marvels rely on ideas like the geometry of clouds of points in a world of millions of dimensions, techniques for finding structure and form in randomness and mathematically rigorous ways of dealing with vast amounts of data. Most people don’t know what a professional mathematician does all day. Perhaps they imagine that we are memorising harder and harder times tables (‘one 19,573 is 19,573, two 19,573s are 39,146’) or competing to see who can remember the most digits of pi. Maybe they imagine a dusty old man writing incomprehensible chalk equations full of Greek letters on a blackboard (and to be fair, this isn’t always so far wrong). Some of this is the mathematicians’ fault. We haven’t exactly gone out of our way to explain why what we do matters. This book is an attempt to redress that balance.

Название: Practical Time Series Analysis in Natural Sciences
Автор: Victor Privalsky
Издательство: Springer
Год: 2023
Страниц: 209
Язык: английский
Формат: pdf (true), epub
Размер: 20.08 MB

This book presents an easy-to-use tool for time series analysis and allows the user to concentrate upon studying time series properties rather than upon how to calculate the necessary estimates. The two attached programs provide, in one run of the program, a time and frequency domain description of scalar or multivariate time series approximated with a sequence of autoregressive models of increasing orders. The optimal orders are chosen by five order selection criteria. The results for scalar time series include time domain stochastic difference equations, spectral density estimates, predictability properties, and a forecast of scalar time series based upon the Kolmogorov-Wiener theory. For the bivariate and trivariate time series, the results contain a time domain description with multivariate stochastic difference equations, statistical predictability criterion, and information for calculating feedback and Granger causality properties in the bivariate case. The frequency domain information includes spectral densities, ordinary, multiple, and partial coherence functions, ordinary and multiple coherent spectra, gain, phase, and time lag factors. The programs seem to be unique and using them does not require professional knowledge of theory of random processes. The book contains many examples including three from engineering.

Название: Bornologies and Lipschitz Analysis
Автор: Gerald Beer
Издательство: CRC Press
Год: 2023
Страниц: 243
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

This monograph, for the first time in book form, considers the large structure of metric spaces as captured by bornologies: families of subsets that contain the singletons, that are stable under finite unions, and that are stable under taking subsets of its members. The largest bornology is the power set of the space and the smallest is the bornology of its finite subsets. Between these lie (among others) the metrically bounded subsets, the relatively compact subsets, the totally bounded subsets, and the Bourbaki bounded subsets. Classes of functions are intimately connected to various bornologies; e.g., (1) a function is locally Lipschitz if and only if its restriction to each relatively compact subset is Lipschitz; (2) a subset is Bourbaki bounded if and only if each uniformly continuous function on the space is bounded when restricted to the subset. A great deal of attention is given to the variational notions of strong uniform continuity and strong uniform convergence with respect to the members of a bornology, leading to the bornology of UC-subsets and UC-spaces. Spaces on which its uniformly continuous real-valued functions are stable under pointwise product are characterized in terms of the coincidence of the Bourbaki bounded subsets with a usually larger bornology.

Название: Bayesian Scientific Computing
Автор: Daniela Calvetti, Erkki Somersalo
Издательство: Springer
Серия: Applied Mathematical Sciences
Год: 2023
Страниц: 295
Язык: английский
Формат: pdf (true), epub
Размер: 38.1 MB

The once esoteric idea of embedding scientific computing into a probabilistic framework, mostly along the lines of the Bayesian paradigm, has recently enjoyed wide popularity and found its way into numerous applications. This book provides an insider's view of how to combine two mature fields, scientific computing and Bayesian inference, into a powerful language leveraging the capabilities of both components for computational efficiency, high resolution power and uncertainty quantification ability. The impact of Bayesian scientific computing has been particularly significant in the area of computational inverse problems where the data are often scarce or of low quality, but some characteristics of the unknown solution may be available a priori. The ability to combine the flexibility of the Bayesian probabilistic framework with efficient numerical methods has contributed to the popularity of Bayesian inversion, with the prior distribution being the counterpart of classical regularization. However, the interplay between Bayesian inference and numerical analysis is much richer than providing an alternative way to regularize inverse problems, as demonstrated by the discussion of time dependent problems, iterative methods, and sparsity promoting priors in this book. The quantification of uncertainty in computed solutions and model predictions is another area where Bayesian scientific computing plays a critical role. This book demonstrates that Bayesian inference and scientific computing have much more in common than what one may expect, and gradually builds a natural interface between these two areas.

Название: The Mathematical Representation of Physical Reality
Автор: Shahen Hacyan
Издательство: Springer
Год: 2023
Страниц: 157
Язык: английский
Формат: pdf (true), epub
Размер: 10.1 MB

This book deals with the rise of mathematics in physical sciences, beginning with Galileo and Newton and extending to the present day. The book is divided into two parts. The first part gives a brief history of how mathematics was introduced into physics—despite its "unreasonable effectiveness" as famously pointed out by a distinguished physicist—and the criticisms it received from earlier thinkers. The second part takes a more philosophical approach and is intended to shed some light on that mysterious effectiveness. For this purpose, the author reviews the debate between classical philosophers on the existence of innate ideas that allow us to understand the world and also the philosophically based arguments for and against the use of mathematics in physical sciences. In this context, Schopenhauer’s conceptions of causality and matter are very pertinent, and their validity is revisited in light of modern physics. The final question addressed is whether the effectiveness of mathematics can be explained by its “existence” in an independent platonic realm, as Godel believed. Mathematics has been impressively successful in describing a wide variety of phenomena in Nature.