Architecture of Mathematics describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as such provides unique reading for professional mathematicians and nonmathematicians alike. This book can be a very important resource both for the teaching of mathematics and as a means to outline the research links between different subjects within and beyond the subject. Features All notions and properties are introduced logically and sequentially, to help the reader gradually build understanding. Focusses on illustrative examples that explain the meaning of mathematical objects and their properties. Suitable as a supplementary resource for teaching undergraduate mathematics, and as an aid to interdisciplinary research. Forming the reader's understanding of Mathematics as a unified science, the book helps to increase his general mathematical culture.

It is well-known that modern stochastic calculus has been exhaustively developed under usual conditions. Despite such a well-developed theory, there is evidence to suggest that these very convenient technical conditions cannot necessarily be fulfilled in real-world applications. Optional Processes: Theory and Applications seeks to delve into the existing theory, new developments and applications of optional processes on "unusual" probability spaces. The development of stochastic calculus of optional processes marks the beginning of a new and more general form of stochastic analysis. This book aims to provide an accessible, comprehensive and up-to-date exposition of optional processes and their numerous properties. Furthermore, the book presents not only current theory of optional processes, but it also contains a spectrum of applications to stochastic differential equations, filtering theory and mathematical finance. Features Suitable for graduate students and researchers in mathematical finance, actuarial science, applied mathematics and related areas Compiles almost all essential results on the calculus of optional processes in unusual probability spaces Contains many advanced analytical results for stochastic differential equations and statistics pertaining to the calculus of optional processes Develops new methods in finance based on optional processes such as a new portfolio theory, defaultable claim pricing mechanism, etc.

There are thousands of books relating to poker, blackjack, roulette and baccarat, including strategy guides, statistical analysis, psychological studies, and much more. However, there are no books on Pell, Rouleno, Street Dice, and many other games that have had a short life in casinos! While this is understandable - most casino gamblers have not heard of these games, and no one is currently playing them - their absence from published works means that some interesting mathematics and gaming history are at risk of being lost forever. Table games other than baccarat, blackjack, craps, and roulette are called carnival games, as a nod to their origin in actual traveling or seasonal carnivals. Mathematics of Casino Carnival Games is a focused look at these games and the mathematics at their foundation. Features * Exercises, with solutions, are included for readers who wish to practice the ideas presented * Suitable for a general audience with an interest in the mathematics of gambling and games * Goes beyond providing practical 'tips' for gamblers, and explores the mathematical principles that underpin gambling games

Today econometrics has been widely applied in the empirical study of economics. As an empirical science, econometrics uses rigorous mathematical and statistical methods for economic problems. Understanding the methodologies of both econometrics and statistics is a crucial departure for econometrics. The primary focus of this book is to provide an understanding of statistical properties behind econometric methods. Following the introduction in Chapter 1, Chapter 2 provides the methodological review of both econometrics and statistics in different periods since the 1930s. Chapters 3 and 4 explain the underlying theoretical methodologies for estimated equations in the simple regression and multiple regression models and discuss the debates about p-values in particular. This part of the book offers the reader a richer understanding of the methods of statistics behind the methodology of econometrics. Chapters 5-9 of the book are focused on the discussion of regression models using time series data, traditional causal econometric models, and the latest statistical techniques. By concentrating on dynamic structural linear models like state-space models and the Bayesian approach, the book alludes to the fact that this methodological study is not only a science but also an art. This work serves as a handy reference book for anyone interested in econometrics, particularly in relevance to students and academic and business researchers in all quantitative analysis fields.

The theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the subject to dynamical systems, ergodic theory, mathematical physics and probability. It is based on the author's own graduate course and is reasonably self-contained with an extensive set of exercises provided at the end of each chapter. This book makes a welcome addition to the literature, serving as a graduate text and a valuable reference for researchers in the field.

The author has shown that practically all our laws, principles, and theories are not physically realizable, since they were derived from an empty space paradigm. From which this book is started with the origin of our temporal (t > 0) universe, it shows that temporal subspace is a physically realizable space within our universe. As in contrasted with generally accepted paradigm where time is an independent variable. From which the author has shown that it is not how rigorous mathematics is, but it is the temporal (t > 0) space paradigm determines the physically realizable solution. Although Einstein's relativity and Schroedinger's principle had revolutionized the modern science, this book has shown that both theory and principle are physically non-realizable since they were developed from an empty space paradigm. One of the most important contribution of this book must be the revolutionary idea of our temporal (t > 0) space, for which the author has shown that absolute certainty exists only at the present (t = 0) moment. Where past-time information has no physical substance and future-time represents a physically realizable yet uncertainty. From which the author has shown that all the existent laws, principles, and theories were based on past-time certainties to predict the future, but science is supposed to be approximated. The author has also shown that this is precisely our theoretical science was developed. But time independent laws and principles are not existed within our temporal universe, in view of the author's temporal exclusive principle. By which the author has noted that timeless science has already created a worldwide conspiracy for examples such as superposition principle, qubit information, relativity theory, wormhole travelling and many others. This book has also shown that Heisenberg's uncertainty is an observational principle independent with time, yet within our universe everything changes with time. In this book the author has also noted that micro space behaviors the same as macro space regardless of the particle size. Finally, one of interesting feature is that, that big bang creation was ignited by a self-induced gravitational force instead by time as commonly believed. Nevertheless, everything has a price to pay; a section of time t and an amount of energy E and it is not free. The author has also shown that time is the only variable that cannot be changed. Although we can squeeze a section of time t as small as we wish but we can never able to squeeze t to zero even we have all the needed energy. Nevertheless, this revolutionary book closer to the truth is highly recommended to every scientist and engineer, otherwise we will forever be trapped within the timeless fantasyland of science. This book is intended for cosmologists, particle physicists, astrophysicists, quantum physicists, computer scientists, optical scientists, communication engineers, professors, and students as a reference or a research-oriented book.

Bringing together idiomatic Python programming, foundational numerical methods, and physics applications, this is an ideal standalone textbook for courses on computational physics. All the frequently used numerical methods in physics are explained, including foundational techniques and hidden gems on topics such as linear algebra, differential equations, root-finding, interpolation, and integration. The second edition of this introductory book features several new codes and 140 new problems (many on physics applications), as well as new sections on the singular-value decomposition, derivative-free optimization, Bayesian linear regression, neural networks, and partial differential equations. The last section in each chapter is an in-depth project, tackling physics problems that cannot be solved without the use of a computer. Written primarily for students studying computational physics, this textbook brings the non-specialist quickly up to speed with Python before looking in detail at the numerical methods often used in the subject.

Earthen levees are extensively used to protect the population and infrastructure from periodic floods and high water due to storm surges. The causes of failure of levees include overtopping, surface erosion, internal erosion, and slope instability. Overtopping may occur during periods of flooding due to insufficient freeboard. The most problematic situation involves the levee being overtopped by both surge and waves when the surge level exceeds the levee crest elevation with accompanying wave overtopping. Overtopping of levees produces fast-flowing, turbulent water velocities on the landward-side slope that can potentially damage the protective grass covering and expose the underlying soil to erosion. If overtopping continues long enough, the erosion may eventually result in loss of levee crest elevation and possibly breaching of the protective structure. Hence, protecting levees from erosion by surge overflow and wave overtopping is necessary to assure a viable and safe levee system. This book presents a cutting-edge approach to understanding overtopping hydraulics under negative free board of earthen levees, and to the study of levee reinforcing methods. Combining soil erosion test, full-scale laboratory overtopping hydraulics test, and numerical modeling for the turbulent overtopping hydraulics. It provides an analysis that integrates the mechanical and hydraulic processes governing levee overtopping occurrences and engineering approaches to reinforce overtopped levees. Topics covered: surge overflow, wave overtopping and their combination, full-scale hydraulic tests, erosion tests, overtopping hydraulics, overtopping discharge, and turbulent analysis. This is an invaluable resource for graduate students and researchers working on levee design, water resource engineering, hydraulic engineering, and coastal engineering, and for professionals in the field of civil and environmental engineering, and natural hazard analysis.

This book investigates statistical observables for anomalous and nonergodic dynamics, focusing on the dynamical behaviors of particles modelled by non-Brownian stochastic processes in the complex real-world environment. Statistical observables are widely used for anomalous and nonergodic stochastic systems, thus serving as a key to uncover their dynamics. This study explores the cutting edge of anomalous and nonergodic diffusion from the perspectives of mathematics, computer science, statistical and biological physics, and chemistry. With this interdisciplinary approach, multiple physical applications and mathematical issues are discussed, including stochastic and deterministic modelling, analyses of (stochastic) partial differential equations (PDEs), scientific computations and stochastic analyses, etc. Through regularity analysis, numerical scheme design and numerical experiments, the book also derives the governing equations for the probability density function of statistical observables, linking stochastic processes with PDEs. The book will appeal to both researchers of electrical engineering expert in the niche area of statistical observables and stochastic systems and scientists in a broad range of fields interested in anomalous diffusion, especially applied mathematicians and statistical physicists.

This book is the very first one in the English language entirely dedicated to the Lambert W function, its generalizations, and its applications. One goal is to promote future research on the topic. The book contains all the information one needs when trying to find a result. The most important formulas and results are framed. The Lambert W function is a multi-valued inverse function with plenty of applications in areas like molecular physics, relativity theory, fuel consumption models, plasma physics, analysis of epidemics, bacterial growth models, delay differential equations, fluid mechanics, game theory, statistics, study of magnetic materials, and so on. The first part of the book gives a full treatise of the W function from theoretical point of view. The second part presents generalizations of this function which have been introduced by the need of applications where the classical W function is insufficient. The third part presents a large number of applications from physics, biology, game theory, bacterial cell growth models, and so on. The second part presents the generalized Lambert functions based on the tools we had developed in the first part. In the third part familiarity with Newtonian physics will be useful. The text is written to be accessible for everyone with only basic knowledge on calculus and complex numbers. Additional features include the Further Notes sections offering interesting research problems and information for further studies. Mathematica codes are included. The Lambert function is arguably the simplest non-elementary transcendental function out of the standard set of sin, cos, log, etc., therefore students who would like to deepen their understanding of real and complex analysis can see a new "almost elementary" function on which they can practice their knowledge.

Providing a pedagogical introduction to the essential principles of path integrals and Hamiltonians, this book describes cutting-edge quantum mathematical techniques applicable to a vast range of fields, from quantum mechanics, solid state physics, statistical mechanics, quantum field theory, and superstring theory to financial modeling, polymers, biology, chemistry, and quantum finance. Eschewing use of the Schroedinger equation, the powerful and flexible combination of Hamiltonian operators and path integrals is used to study a range of different quantum and classical random systems, succinctly demonstrating the interplay between a system's path integral, state space, and Hamiltonian. With a practical emphasis on the methodological and mathematical aspects of each derivation, this is a perfect introduction to these versatile mathematical methods, suitable for researchers and graduate students in physics and engineering.

- It provides a rigorous mathematical and physical basis to techniques that are often introduced on empirical basis - While the book covers a broad range of techniques, it starts at a basic theoretical level. This gives the book a strong foundation and makes it accessible to students from various backgrounds. - Has a computational focus unlike many competing titles

We live in a world that's more interconnected than ever before. Our lives are shaped by outbreaks - of disease, of misinformation, even of violence - that appear, spread and fade away with bewildering speed. To understand them, we need to learn the hidden laws that govern them. From 'superspreaders' who might spark a pandemic or bring down a financial system to the social dynamics that make loneliness catch on, The Rules of Contagion offers compelling insights into human behaviour and explains how we can get better at predicting what happens next.

Along the way, Adam Kucharski explores how innovations spread through friendship networks, what links computer viruses with folk stories - and why the most useful predictions aren't necessarily the ones that come true.

Now revised and updated with content on Covid-19.

The majority of all knowledge concerning atoms, molecules, and solids has been derived from applications of group theory. Taking a unique, applications-oriented approach, this book gives readers the tools needed to analyze any atomic, molecular, or crystalline solid system. Using a clearly defined, eight-step program, this book helps readers to understand the power of group theory, what information can be obtained from it, and how to obtain it. The book takes in modern topics, such as graphene, carbon nanotubes and isotopic frequencies of molecules, as well as more traditional subjects: the vibrational and electronic states of molecules and solids, crystal field and ligand field theory, transition metal complexes, space groups, time reversal symmetry, and magnetic groups. With over 100 end-of-chapter exercises, this book is invaluable for graduate students and researchers in physics, chemistry, electrical engineering and materials science.

There have been some exciting developments in choice modeling, but much of this work is only accessible to those attending conferences like the International Choice Modeling Conference where researchers from many different fields can share their work. This Handbook brings the best of this new work to a wider audience. The editors have convinced many of the top researchers in choice modeling to contribute essays, and the resulting Handbook is the only reference I know that comes close to covering the current state of the art in choice modeling.' - David Brownstone, University of California, Irvine, US'Choice modelling has been the focus of intensive research activities during the last decades. This book proposes a fantastic consolidation of these recent developments, written by the major actors in the field, including Daniel McFadden, Nobel Laureate. The good balance between fundamental topics and applied considerations, as well as the coverage of area-specific aspects, make it an exceptional reference for researchers and practitioners interested in human choices.' - Michel Bierlaire, EPFL Lausanne, Switzerland 'Decision-making underpins daily life, from the simple to the complex. Neurophysiologists, psychologists and economists have all spent decades studying decision-making from very different perspectives. Theoretical advances in the different fields have complementary strengths, creating the need for an integrated approach. This book represents a milestone in bringing together different theoretical perspectives on decision-making, setting the foundations for exciting new multi-disciplinary approaches.' - Scott Brown, The University of Newcastle, Australia This Handbook provides an authoritative and in-depth overview of the essential topics related to the increasingly important field of choice modeling: a key tool for the understanding of behavior and used to support decision-making across many areas such as transportation, health economics, environmental analysis and marketing. The Handbook of Choice Modelling, composed of contributions from senior figures in the field, summarizes the essential analytical techniques and discusses the key current research issues. The book opens with Nobel Laureate Daniel McFadden calling for deeper engagement with more behavioural and psychological fields, and this is followed by supporting chapters on behavioural economics and mathematical psychology. Further chapters explore the elicitation of data and the context of observation; inter-personal variation; the modeling of complex choice processes taking account of heterogeneity; extending the models to deal with more complex choices; statistical processes for the understanding of data; and finally the practical application of these methods. A final group of chapters discusses the research needs of specific application areas. Offering a unique collection of contributions from many of the top researchers in choice modeling, this Handbook provides essential reading for academics, students and practitioners in a wide range of areas. Contributors: M. Abou Zeid, W.L. Adamowicz, K.W. Axhausen, M. Ben-Akiva, C. Bhat, S. Blackburn, M.C.J. Bliemer, D.S. Bunch, P. Burge, J.R.Busemeyer, R.T. Carson, E. Cherchi, C.G. Chorus, M. Czajkowski, A. Daly, A. de Palma, C. Eckert, F. Feinberg, T.N. Flynn, M. Fosgerau, B. Frischknecht, K. Glenk, K.G. Goulias, W. Greene, G.W. Harrison, D. Hensher, S. Hess, I. Inoa, A. Karlstroem, E. Lancsar, P. Lenk, G. Loomes, J. Louviere, A.A.J. Marley, J. Martinez-Correa, D. McFadden, J. Meyerhoff, J. de Dios Ortuzar, R.M.Pendyala, N. Picard, A. Pinjari, T. Ribeiro, N. Rieser-Schussler, J. Rieskamp, L.I. Rizzi, J.M. Rose, J. Swait, A. Vij, J.L. Walker

The goal of this book is to provide a reference for applications of mathematical modelling in social media and related network analysis and offer a theoretically sound background with adequate suggestions for better decision-making. Social Networks: Modelling and Analysis provides the essential knowledge of network analysis applicable to real-world data, with examples from today's most popular social networks such as Facebook, Twitter, Instagram, YouTube, etc. The book provides basic notation and terminology used in social media and its network science. It covers the analysis of statistics for social network analysis such as degree distribution, centrality, clustering coefficient, diameter, and path length. The ranking of the pages using rank algorithms such as Page Rank and HITS are also discussed. Written as a reference this book is for engineering and management students, research scientists, as well as academicians involved in complex networks, mathematical sciences, and marketing research.

Includes example in Mathematica and MATLAB. Contains theoretical and applied exercises for each section. Presents various popular methods for analyzing fuzzy data.

Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic.
Infinite Words explores "all" aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Buchi, McNaughton and Schutzenberger.
Serves as both an introduction to the field and as a reference book.
Contains numerous exercises desgined to aid students and readers.
Self-contained chapters provide helpful guidance for lectures.

Complex networks are typically not homogeneous, as they tend to display an array of structures at different scales. A feature that has attracted a lot of research is their modular organisation, i.e., networks may often be considered as being composed of certain building blocks, or modules. In this Element, the authors discuss a number of ways in which this idea of modularity can be conceptualised, focusing specifically on the interplay between modular network structure and dynamics taking place on a network. They discuss, in particular, how modular structure and symmetries may impact on network dynamics and, vice versa, how observations of such dynamics may be used to infer the modular structure. They also revisit several other notions of modularity that have been proposed for complex networks and show how these can be related to and interpreted from the point of view of dynamical processes on networks.

Our lives and the functioning of modern societies are intimately intertwined with electricity consumption. We owe our quality of life to electricity. However, the electricity generation industry is partly responsible for some of the most pressing challenges we currently face, including climate change and the pollution of natural environments, energy inequality, and energy insecurity. Maintaining our standard of living while addressing these problems is the ultimate challenge for the future of humanity. The objective of this book is to equip engineering and science students and professionals to tackle this task. Written by an expert with over 25 years of combined academic and industrial experience in the field, this comprehensive textbook covers both fossil fuels and renewable power generation technologies. For each topic, fundamental principles, historical backgrounds, and state-of-the-art technologies are covered. Conventional power production technologies, steam power plants, gas turbines, and combined cycle power plants are presented. For steam power plants, the historical background, thermodynamic principles, steam generators, combustion systems, emission reduction technologies, steam turbines, condensate-feedwater systems, and cooling systems are covered in separate chapters. Similarly, the historical background and thermodynamic principles of gas turbines, along with comprehensive discussions on compressors, combustors, and turbines, are presented and then followed with combined cycle power plants. The second half of the book deals with renewable energy sources, including solar photovoltaic systems, solar thermal power plants, wind turbines, ocean energy systems, and geothermal power plants. For each energy source, the available energy and its variations, historical background, operational principles, basic calculations, current and future technologies, and environmental impacts are presented. Finally, energy storage systems as required technologies to address the intermittent nature of renewable energy sources are covered. While the book has been written with the needs of undergraduate and graduate college students in mind, professionals interested in widening their understanding of the field can also benefit from it.

Fractional calculus is used to model many real-life situations from science and engineering. The book includes different topics associated with such equations and their relevance and significance in various scientific areas of study and research. In this book readers will find several important and useful methods and techniques for solving various types of fractional-order models in science and engineering. The book should be useful for graduate students, PhD students, researchers and educators interested in mathematical modelling, physical sciences, engineering sciences, applied mathematical sciences, applied sciences, and so on. This Handbook: Provides reliable methods for solving fractional-order models in science and engineering. Contains efficient numerical methods and algorithms for engineering-related equations. Contains comparison of various methods for accuracy and validity. Demonstrates the applicability of fractional calculus in science and engineering. Examines qualitative as well as quantitative properties of solutions of various types of science- and engineering-related equations. Readers will find this book to be useful and valuable in increasing and updating their knowledge in this field and will be it will be helpful for engineers, mathematicians, scientist and researchers working on various real-life problems.

Einstein's general theory of relativity can be a notoriously difficult subject for students approaching it for the first time, with arcane mathematical concepts such as connection coefficients and tensors adorned with a forest of indices. This book is an elementary introduction to Einstein's theory and the physics of curved space-times that avoids these complications as much as possible. Its first half describes the physics of black holes, gravitational waves and the expanding Universe, without using tensors. Only in the second half are Einstein's field equations derived and used to explain the dynamical evolution of the early Universe and the creation of the first elements. Each chapter concludes with problem sets and technical mathematical details are given in the appendices. This short text is intended for undergraduate physics students who have taken courses in special relativity and advanced mechanics.

To succeed in the lab, it is crucial to be comfortable with the math calculations that are part of everyday work. This accessible introduction to common laboratory techniques focuses on the basics, helping even readers with good math skills to practice the most frequently encountered types of problems. Basic Laboratory Calculations for Biotechnology, Second Edition discusses very common laboratory problems, all applied to real situations. It explores multiple strategies for solving problems for a better understanding of the underlying math. Primarily organized around laboratory applications, the book begins with more general topics and moves into more specific biotechnology laboratory techniques at the end. This book features hundreds of practice problems, all with solutions and many with boxed, complete explanations; plus hundreds of "story problems" relating to real situations in the lab. Additional features include: Discusses common laboratory problems with all material applied to real situations Presents multiple strategies for solving problems help students to better understand the underlying math Provides hundreds of practice problems and their solutions Enables students to complete the material in a self-paced course structure with little teacher assistance Includes hundreds of "story problems"that relate to real situations encountered in the laboratory

Finite Element Analysis of Weld Thermal Cycles Using ANSYS aims at educating a young researcher on the transient analysis of welding thermal cycles using ANSYS. It essentially deals with the methods of calculation of the arc heat in a welded component when the analysis is simplified into either a cross sectional analysis or an in-plane analysis. The book covers five different cases involving different welding processes, component geometry, size of the element and dissimilar material properties. A detailed step by step calculation is presented followed by APDL program listing and output charts from ANSYS. Features: Provides useful background information on welding processes, thermal cycles and finite element method Presents calculation procedure for determining the arc heat input in a cross sectional analysis and an in-plane analysis Enables visualization of the arc heat in a FEM model for various positions of the arc Discusses analysis of advanced cases like dissimilar welding and circumferential welding Includes step by step procedure for running the analysis with typical input APDL program listing and output charts from ANSYS.

In the last decade, both scholars and practitioners have sought novel ways to address the problem of cybersecurity. Innovative outcomes have included applications such as blockchain as well as creative methods for cyber forensics, software development, and intrusion prevention. Accompanying these technological advancements, discussion on cyber matters at national and international levels has focused primarily on the topics of law, policy, and strategy. The objective of these efforts is typically to promote security by establishing agreements among stakeholders on regulatory activities. Varying levels of investment in cyberspace, however, comes with varying levels of risk; in some ways, this can translate directly to the degree of emphasis for pushing substantial change. At the very foundation or root of cyberspace systems and processes are tenets and rules governed by principles in mathematics. Topics such as encrypting or decrypting file transmissions, modeling networks, performing data analysis, quantifying uncertainty, measuring risk, and weighing decisions or adversarial courses of action represent a very small subset of activities highlighted by mathematics. To facilitate education and a greater awareness of the role of mathematics in cyber systems and processes, a description of research in this area is needed. Mathematics in Cyber Research aims to familiarize educators and young researchers with the breadth of mathematics in cyber-related research. Each chapter introduces a mathematical sub-field, describes relevant work in this field associated with the cyber domain, provides methods and tools, as well as details cyber research examples or case studies. Features One of the only books to bring together such a diverse and comprehensive range of topics within mathematics and apply them to cyber research. Suitable for college undergraduate students or educators that are either interested in learning about cyber-related mathematics or intend to perform research within the cyber domain. The book may also appeal to practitioners within the commercial or government industry sectors. Most national and international venues for collaboration and discussion on cyber matters have focused primarily on the topics of law, policy, strategy, and technology. This book is among the first to address the underpinning mathematics.