Mathematics Books

Book SynopsisUncertainty is everywhere. It lurks in every consideration of the future - the weather, the economy, the sex of an unborn child - even quantities we think that we know such as populations or the transit of the planets contain the possibility of error. It's no wonder that, throughout that history, we have attempted to produce rigidly defined areas of uncertainty - we prefer the surprise party to the surprise asteroid. We began our quest to make certain an uncertain world by reading omens in livers, tea leaves, and the stars. However, over the centuries, driven by curiosity, competition, and a desire be better gamblers, pioneering mathematicians and scientists began to reduce wild uncertainties to tame distributions of probability and statistical inferences. But, even as unknown unknowns became known unknowns, our pessimism made us believe that some problems were unsolvable and our intuition misled us. Worse, as we realized how omnipresent and varied uncertainty is, we encountered chaos, quantum mechanics, and the limitations of our predictive power. Bestselling author Professor Ian Stewart explores the history and mathematics of uncertainty. Touching on gambling, probability, statistics, financial and weather forecasts, censuses, medical studies, chaos, quantum physics, and climate, he makes one thing clear: a reasonable probability is the only certainty.Trade ReviewIntriguing ... a challenging but rewarding trip through a quantum world of uncertainties. * Publisher's Weekly *Praise for Ian Stewart: Stewart is Britain's most brilliant and prolific populariser of maths -- Alex BelosThis is not pure maths. It is maths contaminated with wit, wisdom, and wonder ... He guides us on a mind-boggling journey from the ultra trivial to the profound. Thoroughly entertaining * New Scientist *Humbling and inspiring. Stewart shows with his typical clarity how the power of pure thought has shaped our world for over two millennia. -- Jim Al-Khalili, FRSThis is a superb Cabinet of Mathematical Curiosities that deserves a place with the classics of the genre * Mathematics Today *'With captivating stories and his signature clarity, Ian Stewart shows us how math makes the world - and the rest of the universe - go round. -- Steven Strogatz, Professor of Mathematics, Cornell University, and author of The Joy of XStewart has served up the instructive equivalent of a Michelin-starred tasting menu, or perhaps a smorgasbord of appetisers. And of course, appetisers are designed to give you an appetite for more. -- Tim Radford * Guardian *

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Book SynopsisThe world's best negotiators have moved beyond the conventional wisdom by utilising cutting-edge studies and real-world results. It's time you did too. For over twenty years, David Sally has been teaching the art of negotiation at leading business schools and to executives at top companies. Now, using insights from social psychology and game theory, he delivers the proven, clear, actionable advice you need to stay one step ahead. By studying great examples, from Machiavelli to Wall Street, Xi Jinping and Barack Obama, he explores how the game’s masters navigate the field strategically, craftily, even emotionally. The best know every negotiation is different and that your tactics are, in part, determined by your opponent. One Step Ahead will make sure that you have what it takes to come out on top, no matter who you are facing across the table.Trade Review‘Entertaining and conversational, [One Step Ahead] is an important tool for getting to yes, as well as understanding exactly what will prompt an opponent to say it.’ -- Publishers Weekly‘[A]ppealing, well-written ... a deep, thoughtful master class on the 'negotiation game.' * Kirkus *'A beautifully written book which is wise, funny, scientific, and practical.' -- Colin F. Camerer, Professor of Behavioral Economics at Caltech'I might write, ‘Words matter.’ But David Sally writes, ‘Words present facts, question assumptions, express emotions, issue orders, declare war, elevate cardinals to Pope, sentence offenders to prison, create contracts and promises, and so on.’ That’s why his books are so much more fun to read than mine. This is the wisest, most readable book on negotiation I’ve seen. Destined to become a classic.' -- Robert H. Frank, author of Under the Influence: Putting Peer Pressure to Work'From defusing ultimatums to the art of persuasion, Dave Sally delivers master lessons on negotiation. This book offers brilliant, practical, and engaging advice gleaned from business titans, world leaders, and scholars.' -- Maurice Schweitzer, Professor at the Wharton School and coauthor of Friend & Foe

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Book SynopsisHugh Barker is a non-fiction author and editor; as the latter he has edited several successful popular maths books, including A Slice of Pi. Hugh is a keen amateur mathematician and was accepted to study maths at Cambridge University aged 16.

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Book SynopsisGame Theory isn't just for poker players or economists. You don't have to be a microeconomics or political science expert to understand it _ discover the theory of decision making and optimize your strategic thinking with the help of Gladiators, Pirates and Games of Trust.Have you ever struggled to make a decision? Tried to figure out the winning bidding strategy at an auction? Wondered how best to split the bill in a restaurant? Divide an inheritance? Wished you were better at negotiating? Thought about how to discourage a spouse from cheating?Then Haim Shapira's fascinating exploration of Game Theory and how it affects our everyday life will delight and captivate you. Topics include how to respond to ultimatums, playing chicken, the diner's dilemma, the blackmailer's paradox and matchmaking strategies.Make buying this book your first winning decision.Trade Review"One of the best Decision Making and Game Theory books of all time." —Reid Hoffman (LinkedIn founder) and Nassim Nicholas Taleb (author of Black Swan), BookAuthority

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Book SynopsisAn Observer Book of the Year A Times Science Book of the Year A New Statesman Book of the Year A Financial Times Science Book of the Year 'Astonishingly bold' Daily Mail 'It is hard to imagine a more timely book ... much of the modern world will make more sense having read it.' The Times 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.Trade ReviewAstonishingly bold * Daily Mail *Perfect timing * Financial Times *Popular science at its best ... sparkling and clear. The subject is deeply fascinating and highly relevant ... Once you have read it, you will want to make sure others read it too. -- Alex Bellos, author * Alex's Adventures in Numberland *An impressively fluent, fascinating and accessible introduction to how epidemics, trends, behaviours and ideas start, spread - and end ... a work of contemporary relevance that Malcolm Gladwell devotees would enjoy. * New Statesman *It is hard to imagine a more timely book ... much of the modern world will make more sense having read it. * The Times *Adam Kucharski [is] fast becoming a key voice of reason in the media circus surrounding the virus ... Here he gives a clear, calm, historical overview of the mathematical ideas at the forefront of our pandemic response, where they came from and how well they stand up when you put them to the test. -- Hannah Fry * Guardian *This is a hell of a moment for a book like this to come out ... the principles of contagion, which, Kucharski argues, can be applied to everything from folk stories and financial crises to itching and loneliness, are suddenly of pressing interest to all of us. * Sunday Times *Rich in stories, The Rules of Contagion is a down-to-earth account of how mathematical approaches can help us better understand and, in turn, better respond to contagion in all its dynamic forms. Tackling issues from pandemics and gun violence, to financial crises and misinformation, Adam Kucharski inspires us all to think like mathematicians. A must read for anybody interested in epidemics and other crises. -- Peter Piot, Director of the London School of Hygiene & Tropical MedicineFor anyone wanting to know how diseases spread, Adam Kucharski's book, The Rules of Contagion is a timely introduction. * Irish Independent *For now Adam Kucharski's The Rules of Contagion is the book you want to reach for ... interesting and topical -- Laura Spinney * Guardian *Illuminating ... Coronavirus has prompted hot-headed public and media reaction; this book offers comfort in the form of cold, hard facts. * Prospect Magazine *One of the Economist's 'five books of science and history that cast light on covid-19': This book charts the history of this now-pivotal science, from its origins in understanding the spread of malaria at the turn of the 20th century, to its central role in predicting the dissemination of everything from diseases to fake news in the 21st. * Economist *The Rules of Contagion is a timely reminder of the importance of disease modelling. Without such models, we would be in far greater trouble battling COVID-19. * Lancet *Lively, intriguing and elegant * Spectator *A geeky but fascinating exploration of the mathematics of things that go viral-not least of them viruses ... Kucharski takes his readers down provocative detours, such as the use of public-health models of disease transmission to examine how social networks figure in urban gun violence, with algorithms that take into account such things as 'age, gang affiliations, and prior arrests.'... Utterly timely and readable. * Kirkus *Essential reading to truly process the pandemic -- Anjana Ahuja * New Statesman *Perhaps no commentator has been in greater demand this year than Adam Kucharski ... The Rules of Contagion is an accessible guide to the mathematical rules that govern the spread of infectious diseases in populations ... [which] makes a convincing case that just as mathematics can predict the arc of an epidemic, so it can also help us understand how social contagions, from financial panics to vaccine conspiracy theories, "go viral". -- Gaia Vince, winner of the Royal Society Prize and author of Adventures in the Anthropocene * Observer *

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Book SynopsisAchieve the best grades in 2025 or 2026 with this unbeatable course book from CGP!This book covers all the content needed for AS and Year 1 of the Edexcel Statistics and Mechanics A-Level course and is fully up to date for the latest specifications. It has the clearest notes on all the theory for every topic, including annotated worked examples and explanations; hundreds of challenging questions for every chapter, including problem-solving and modelling; a realistic Practice Paper with a complete mark scheme; and a free Online Edition to read on PC, Mac or tablet (use the unique code printed inside the cover to gain full access).For full A-Level Maths coverage don't miss the Year 1 Pure Maths Student Textbook (9781789088397), and our Year 2 Student Textbooks for Pure Maths (9781789088410) and Statistics and Mechanics (9781789088427).

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Book SynopsisA Mezze of Mathematical Methods is Volume 1 of Science by Simulation. It is a recipe book of mathematical models that can be enlivened by the transmutation of equations into computer code. In this volume, the examples chosen are an eclectic mix of systems and stories rooted in common experience, rather than those normally associated with constrained courses on Physics, Chemistry or Biology which are taught in isolation and susceptible to going out of date in a few years. Rather than a 'what' of Science, this book is aimed at the 'how', readily applied to projects by students and professionals. Written in a friendly style based upon the author's expertise in teaching and pedagogy, this mathematically rigorous book is designed for readers to follow arguments step-by-step with stand-alone chapters which can be read independently. This approach will provide a tangible and readily accessible context for the development of a wide range of interconnected mathematical ideas and computing methods that underpin the practice of Science.

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Book SynopsisThe book provides the reader with an overview of the actual state of research in ordinary and partial differential equations in the complex domain. Topics include summability and asymptotic study of both ordinary and partial differential equations, and also q-difference and differential-difference equations. This book will be of interest to researchers and students who wish to expand their knowledge of these fields.With the latest results and research developments and contributions from experts in their field, Formal and Analytic Solutions of Differential Equations provides a valuable contribution to methods, techniques, different mathematical tools, and study calculations.

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Book SynopsisAs the speed of globalization accelerates, world cultures are more closely connected to each other than ever before. But what exactly is culture? It seems to be involved in all psychological processes, but can its psychological consequences be studied scientifically? How can cultural differences be described without reifying culture and reinforcing cultural stereotypes? Culture and mind constitute each other, but how? Why do humans need culture? How did the evolution of the mind enable the development of human culture? How does participation in culture transform the mind, and how does the mind process and apply culture? How may culture become a resource for pursuing valued goals, and how does culture become part of the self? How do culture travelers navigate cultures and negotiate multiple cultural identities? The authors of this volume offer a refreshing theoretical perspective and organize seemingly disparate research evidence into a coherent body of psychological knowledge. With its accessible language and lively narrative, this volume engages its readers in an intellectual journey through the fascinating research literatures in psychology, anthropology, and the cognate disciplines. This book will make an ideal textbook for senior undergraduate and graduate courses on psychology and culture, cultural studies, cognitive anthropology, and intercultural communication. Trade Review “This superb account of the way culture and social psychology are interrelated uses a broad set of theoretical and applied perspectives. It is very much up-to-date, describing more recent experiments than even professional cultural psychologists are likely to know. Cultural psychology is a collaborative enterprise, and the inclusion of the biographies of the major researchers allows the reader to become, in a small way, a member of the team of researchers exploring the culture and social psychology link. Both professional psychologists and students will learn a great deal from it.” - Harry C. Triandis, Professor Emeritus, University of Illinois at Urbana-Champaign“This is truly a unique book. Written in a manner that is engaging and accessible to a broad audience, Social Psychology of Culture effectively weaves together theory and concrete illustrations of cultural influences on thought and behavior. The result is a comprehensive review that simultaneously advances our understanding of culture, and of social psychology. Kudos to the authors for a remarkable piece of scholarship.” - Marilynn B. Brewer, Ohio State University“Though the basic orientation of this book is social psychological, the perspective fromwhich the authors view cultural phenomena is unusually broad and integrative. I recommend this book to any psychologist who seeks entrée to this fascinating and burgeoning area of theory and research.” - Robert M. Krauss, Columbia University“This volume provides comprehensive coverage of fundamental issues and applicationsin a balanced and extremely readable manner. A definite must for any course on the social psychology of culture.” - Gün R. Semin, Free University Amsterdam'This superb account of the way culture and social psychology are interrelated uses a broad set of theoretical and applied perspectives. It is very much up-to-date, describing more recent experiments than even professional cultural psychologists are likely to know. Cultural psychology is a collaborative enterprise, and the inclusion of the biographies of the major researchers allows the reader to become, in a small way, a member of the team of researchers exploring the culture and social psychology link. Both professional psychologists and students will learn a great deal from it.'- Harry C. Triandis, Professor Emeritus, University of Illinois at Urbana-Champaign, USA'This is truly a unique book. Written in a manner that is engaging and accessible to a broad audience, Social Psychology of Culture effectively weaves together theory and concrete illustrations of cultural influences on thought and behavior. The result is a comprehensive review that simultaneously advances our understanding of culture, and of social psychology. Kudos to the authors for a remarkable piece of scholarship.'- Marilynn B. Brewer, Ohio State University, USA'Though the basic orientation of this book is social psychological, the perspective from which the authors view cultural phenomena is unusually broad and integrative. I recommend this book to any psychologist who seeks entrée to this fascinating and burgeoning area of theory and research.'- Robert M. Krauss, Columbia University, USA'This volume provides comprehensive coverage of fundamental issues and applications in a balanced and extremely readable manner. A definite must for any course on the social psychology of culture.'- Gün R. Semin, Free University Amsterdam, The NetherlandsTable of ContentsAbout the Authors. Preface. Chapter 1 What Is Culture? Culture in the News. The Concept of Culture in Historical Context. Categories of Culture. Definition of Culture. Organization of the Book. What is Social about Social Psychology of Culture? Chapter 2 Strategies for Describing Culture. Culture in the News … and Fairy Tales. Describing Cultural Variations. The Global Approach. The Focal Approach. Summary and Conclusion. Chapter 3 Psychological Foundation of Human Culture. Culture in the News. Ape Cultures. Human Cultures. Cognitive Foundation of Human Cultures. Social Psychological Foundation of Human Culture. Nature, Culture, and Mind. Chapter 4 What is Culture For? Fact or Hoax? Biological and Cultural Evolution. What Does Culture Do for the Survival of the Species? What Does Culture Do for a Society? What Does Culture Do for the Individual? Conclusion . Chapter 5 Culture as Mental Habits: Shared Unintended Thoughts. Culture Travelers’ Journal. Taxonomy of Knowledge. Interpretive Cautions. Mental Habits as Procedural Knowledge. The Linguistic Relativity Hypothesis. Conclusion. Chapter 6 Culture, Self, and Others: Who Am I and Who Are They? Culture and Architecture. Person Representations. Representations of Other People. Representations of the Self . Representations of Groups. Conclusion. Chapter 7 Events and Norms: How Events Unfold and What We Should Do. Cultural Psychology in Public Bathrooms. Event Representations. Norm Representations. Conclusion. Chapter 8 Organization and Application of Cultural Knowledge. Cultural Icons. Organization of Cultural Knowledge: Is Culture a Coherent Meaning System? Multiple Determinants of Cultural Behavior. Relative Influence of Different Determinants. The Context of Cultural Knowledge. Conclusion. Chapter 9 Reproduction of Culture and Cultural Change. Cultural Change across the Globe. Media of Cultural Transmission. How are Shared Representations Constructed and Reproduced? Cultural Change. Conclusion. Chapter 10 Intercultural Contacts: Implications for Cultural Competence. The Rice Storm and the Butterfly Effect. Nature of Cultural Competence. Psychological Benefits of Intercultural Contacts. Psychological Costs of Intercultural Contacts. Conclusion. Chapter 11 Globalization and Multicultural Identities. Tsunami and Globalization. Migration and Globalization. Will Globalization Lead to Homogenization of Cultures? Globalization and Cultural Diversity. Migration and Management of Multicultural. Identities. Colonization and Identity Negotiation. Conclusion. Chapter 12 Scientific Study of Cultural Processes. Studying Culture in Coffee Shops. Beyond Description of Cultural Differences. Explaining Cultures. Psychic Unity and Cultural Relativity. What is Social about Social Psychology of Culture? References. Author Index . Subject Index

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Book SynopsisWhat is mathematics, and why is it such a mystery to so many people?Mathematics is the greatest creation of human intelligence. It affects us all. We depend on it in our daily lives, and yet many of the tools of mathematics, such as geometry, algebra and trigonometry, are descended from ancient or non-Western civilizations. Introducing Mathematics traces the story of mathematics from the ancient world to modern times, describing the great discoveries and providing an accessible introduction to such topics as number-systems, geometry and algebra, the calculus, the theory of the infinite, statistical reasoning and chaos theory. It shows how the history of mathematics has seen progress and paradox go hand in hand - and how this is still happening today.

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Book SynopsisMathematician Matthew Watkins and illustrator Matt Tweed have compressed almost every familiar equation from mathematics and physics into one tiny book. A quick, fun, stylish reference book with appeal to anyone interested in the sciences.

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Book SynopsisOptimal filtering applied to stationary and non-stationary signals provides the most efficient means of dealing with problems arising from the extraction of noise signals. Moreover, it is a fundamental feature in a range of applications, such as in navigation in aerospace and aeronautics, filter processing in the telecommunications industry, etc. This book provides a comprehensive overview of this area, discussing random and Gaussian vectors, outlining the results necessary for the creation of Wiener and adaptive filters used for stationary signals, as well as examining Kalman filters which are used in relation to non-stationary signals. Exercises with solutions feature in each chapter to demonstrate the practical application of these ideas using Matlab.Table of ContentsPreface xi Introduction xiii Chapter 1. Random Vectors 1 1.1. Definitions and general properties 1 1.2. Spaces L1(dP) and L2(dP) 20 1.2.1. Definitions 20 1.2.2. Properties 22 1.3. Mathematical expectation and applications 23 1.3.1. Definitions 23 1.3.2. Characteristic functions of a random vector 34 1.4. Second order random variables and vectors 39 1.5. Linear independence of vectors of L2(dP) 47 1.6. Conditional expectation (concerning random vectors with density function) 51 1.7. Exercises for Chapter 1 57 Chapter 2. Gaussian Vectors 63 2.1. Some reminders regarding random Gaussian vectors 63 2.2. Definition and characterization of Gaussian vectors 66 2.3. Results relative to independence 68 2.4. Affine transformation of a Gaussian vector 72 2.5. The existence of Gaussian vectors 74 2.6. Exercises for Chapter 2 85 Chapter 3. Introduction to Discrete Time Processes 93 3.1. Definition 93 3.2. WSS processes and spectral measure 105 3.2.1. Spectral density 106 3.3. Spectral representation of a WSS process 110 3.3.1. Problem 110 3.3.2. Results 111 3.3.2.1. Process with orthogonal increments and associated measurements 111 3.3.2.2. Wiener stochastic integral 113 3.3.2.3. Spectral representation 114 3.4. Introduction to digital filtering 115 3.5. Important example: autoregressive process 128 3.6. Exercises for Chapter 3 134 Chapter 4. Estimation 141 4.1. Position of the problem 141 4.2. Linear estimation 144 4.3. Best estimate – conditional expectation 156 4.4. Example: prediction of an autoregressive process AR (1) 165 4.5. Multivariate processes 166 4.6. Exercises for Chapter 4 175 Chapter 5. The Wiener Filter 181 5.1. Introduction 181 5.1.1. Problem position 182 5.2. Resolution and calculation of the FIR filter 183 5.3. Evaluation of the least error 185 5.4. Resolution and calculation of the IIR filter 186 5.5. Evaluation of least mean square error 190 5.6. Exercises for Chapter 5 191 Chapter 6. Adaptive Filtering: Algorithm of the Gradient and the LMS 197 6.1. Introduction 197 6.2. Position of problem 199 6.3. Data representation 202 6.4. Minimization of the cost function 204 6.4.1. Calculation of the cost function 208 6.5. Gradient algorithm 211 6.6. Geometric interpretation 214 6.7. Stability and convergence 218 6.8. Estimation of gradient and LMS algorithm 222 6.8.1. Convergence of the algorithm of the LMS 225 6.9. Example of the application of the LMS algorithm 225 6.10. Exercises for Chapter 6 234 Chapter 7. The Kalman Filter 237 7.1. Position of problem 237 7.2. Approach to estimation 241 7.2.1. Scalar case 241 7.2.2. Multivariate case 244 7.3. Kalman filtering 245 7.3.1. State equation 245 7.3.2. Observation equation 246 7.3.3. Innovation process 248 7.3.4. Covariance matrix of the innovation process 248 7.3.5. Estimation 250 7.3.6. Riccati’s equation 258 7.3.7. Algorithm and summary 260 7.4. Exercises for Chapter 7 262 Table of Symbols and Notations 281 Bibliography 283 Index 285

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Book SynopsisWritten by bestselling author Stephen Doyle, this student book will engage and motivate you throughout the course. // Endorsed by WJEC offering high quality support you can trust. // Thorough coverage of all the topics in the A2 Level Applied specification. // Extra support for the problem solving and unstructured questions in the specification. // Plenty of examples with worked answers throughout to enable you to check your understanding as you progress through the course. // Answers to questions are provided in order to check your work.

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Book SynopsisAre you considering studying mathematics at university, having fallen in love with the subject at school? Are you ready to develop a variety of practical skills that employers need? Are you keen to have a wide range of career options after you graduate? Studying any subject at degree level is an investment in the future that involves significant cost. Now more than ever, students and their parents need to weigh up the potential benefits of university courses. That’s where the Why Study series comes in. This book, aimed at students, parents and teachers, explains in practical terms the range and scope of mathematics at university level and where it can lead in terms of careers or further study. It will enthuse the reader about the subject and answer the crucial questions that a college prospectus does not.

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Book SynopsisThis book provides hands-on guidance for researchers and practitioners in criminal justice and criminology to perform statistical analyses and data visualization in the free and open-source software R. It offers a step-by-step guide for beginners to become familiar with the RStudio platform and tidyverse set of packages. This volume will help users master the fundamentals of the R programming language, providing tutorials in each chapter that lay out research questions and hypotheses centering around a real criminal justice dataset, such as data from the National Survey on Drug Use and Health, National Crime Victimization Survey, Youth Risk Behavior Surveillance System, The Monitoring the Future Study, and The National Youth Survey. Users will also learn how to manipulate common sources of agency data, such as calls-for-service (CFS) data. The end of each chapter includes exercises that reinforce the R tutorial examples, designed to help master the software as well as to provide practice on statistical concepts, data analysis, and interpretation of results. The text can be used as a stand-alone guide to learning R or it can be used as a companion guide to an introductory statistics textbook, such as Basic Statistics in Criminal Justice (2020).Table of Contents1. Getting started.2. Managing your data.3. Data visualization.4. Spatiotemporal data visualization and basic crime analysis.5. Descriptive statistics: measures of central tendency.6. Descriptive statistics: measures of dispersion.7. Statistical inference in criminal justice research.8. Defining the observed significance level of a test.9. Hypothesis testing using the binomial distribution.10. Chi-square: a test commonly used for nominal-level measures.11. The normal distribution and its application to tests of statistical significance.12. Comparing means in two samples.13. Analysis of variance.14. Measures of association for nominal and ordinal variables.15. Measuring association for interval data.16. Introduction to regression analysis.

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Book SynopsisThis graduate-level textbook covers modelling, programming and analysis of stochastic computer simulation experiments, including the mathematical and statistical foundations of simulation and why it works. The book is rigorous and complete, but concise and accessible, providing all necessary background material. Object-oriented programming of simulations is illustrated in Python, while the majority of the book is programming language independent. In addition to covering the foundations of simulation and simulation programming for applications, the text prepares readers to use simulation in their research. A solutions manual for end-of-chapter exercises is available for instructors.Table of ContentsChapter 1: Why Do We Simulate.- Chapter 2: Simulation Programming: Quick Start.- Chapter 3: Examples.- Chapter 4: Simulation Programming with PythonSim.- Chapter 5: Three Views of Simulation.- Chapter 6: Simulation Input.- Chapter 7: Simulation Output.- Chapter 8: Experiment Design and Analysis.- Chapter 9: Simulation Optimization and Sensitivity.- Chapter 10: Simulation for Research.- References.- Index.

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Book SynopsisThis book convenes a collection of carefully selected problems in mathematical analysis, crafted to achieve maximum synergy between analytic geometry and algebra and favoring mathematical creativity in contrast to mere repetitive techniques. With eight chapters, this work guides the student through the basic principles of the subject, with a level of complexity that requires good use of imagination.In this work, all the fundamental concepts seen in a first-year Calculus course are covered. Problems touch on topics like inequalities, elementary point-set topology, limits of real-valued functions, differentiation, classical theorems of differential calculus (Rolle, Lagrange, Cauchy, and l’Hospital), graphs of functions, and Riemann integrals and antiderivatives. Every chapter starts with a theoretical background, in which relevant definitions and theorems are provided; then, related problems are presented. Formalism is kept at a minimum, and solutions can be found at the end of each chapter.Instructors and students of Mathematical Analysis, Calculus and Advanced Calculus aimed at first-year undergraduates in Mathematics, Physics and Engineering courses can greatly benefit from this book, which can also serve as a rich supplement to any traditional textbook on these subjects as well.Trade Review“This reviewer warmly welcomes the publication of this nice selection of problems and would recommend its use as a complimentary reading for analysis and calculus courses. … The book under review nicely complements existing literature on the subject; it is a stimulating reading requiring, as suggested by the authors, a bit of critical reflection.” (Svitlana P. Rogovchenko, zbMATH 1494.00003, 2022)“A sequence of a traditional textbook for an undergraduate calculus course. From this standpoint, this book can be used as a supplement to any conventional calculus text. … It is well known that students struggle with inducing abstract math concepts to gain insight into behavior in real-world phenomena to understand better those behaviors; including such examples is seen as a potential asset.” (Andrzej Sokolowski, MAA Reviews, August 1, 2022)Table of ContentsSummary of basic theory of inequalities.- Sets, sequences, functions.- Limits of functions, continuity.- Differentiation.- Classical theorems of differential calculus.- Monotonicity, concavity, minima, maxima, inflection points.- Graphs of functions.- Integrals.

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Book SynopsisThis innovative undergraduate textbook approaches number theory through the lens of abstract algebra. Written in an engaging and whimsical style, this text will introduce students to rings, groups, fields, and other algebraic structures as they discover the key concepts of elementary number theory. Inquiry-based learning (IBL) appears throughout the chapters, allowing students to develop insights for upcoming sections while simultaneously strengthening their understanding of previously covered topics. The text is organized around three core themes: the notion of what a “number” is, and the premise that it takes familiarity with a large variety of number systems to fully explore number theory; the use of Diophantine equations as catalysts for introducing and developing structural ideas; and the role of abstract algebra in number theory, in particular the extent to which it provides the Fundamental Theorem of Arithmetic for various new number systems. Other aspects of modern number theory – including the study of elliptic curves, the analogs between integer and polynomial arithmetic, p-adic arithmetic, and relationships between the spectra of primes in various rings – are included in smaller but persistent threads woven through chapters and exercise sets.Each chapter concludes with exercises organized in four categories: Calculations and Informal Proofs, Formal Proofs, Computation and Experimentation, and General Number Theory Awareness. IBL “Exploration” worksheets appear in many sections, some of which involve numerical investigations. To assist students who may not have experience with programming languages, Python worksheets are available on the book’s website. The final chapter provides five additional IBL explorations that reinforce and expand what students have learned, and can be used as starting points for independent projects. The topics covered in these explorations are public key cryptography, Lagrange’s four-square theorem, units and Pell’s Equation, various cases of the solution to Fermat’s Last Theorem, and a peek into other deeper mysteries of algebraic number theory.Students should have a basic familiarity with complex numbers, matrix algebra, vector spaces, and proof techniques, as well as a spirit of adventure to explore the “numberverse.”Table of ContentsPreface.- What is a Number?- A Quick Survey of the Last Two Millenia.- Number Theory in $\mathcal{Z}$ Beginning.- Number Theory in the Mod-n Era.- Gaussian Number Theory: $\mathcal{Z}[i]$ of the Storm.- Number Theory: From Where We $\mathcal{R}$ to across the $mathcal{C}$.- Cyclotomic Number Theory: Roots and Reciprocity. Number Theory Unleashed: Release $\mathcal{Z}_p$!- The Adventure Continues.- Appendix: Number Systems.

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Book SynopsisThis book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach.The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing.The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.Table of ContentsSpace-time approximations for linear acoustic, elastic, and electro-magnetic wave equations.- Local wellposedness and long-time behavior of quasilinear Maxwell equations.- Error analysis of second-order time integration methods for discontinuous Galerkin discretizations of Friedrichs’ systems.- An abstract framework for inverse wave problems with applications.

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Book SynopsisDieses Buch will dem Leser eine Einführung in wichtige Techniken und Methoden der heutigen reellen Algebra und Geometrie vermitteln. An Voraussetzungen werden dabei nur Grundkenntnisse der Algebra erwartet, so daß das Buch für Studenten mittlerer Semester geeignet ist.Das erste Kapitel enthält zunächst grundlegende Fakten über angeordnete Körper und ihre reellen Abschlüsse und behandelt dann verschiedene Methoden zur Bestimmung der Anzahl reeller Nullstellen von Polynomen. Das zweite Kapitel befaßt sich mit reellen Stellen und gipfelt in Artins Lösung des 17. Hilbertschen Problems. Kapitel III schließlich ist dem noch jungen Begriff des reellen Spektrums und seinen Anwendungen gewidmet."Neben dem 1987 erschienenen "Géometrie algébrique réelle" von J. Bochnak-M. Coste- M. Roy stellt die vorliegende Monographie das erste Lehrbuch auf diesem Gebiet dar... Damit liegt eine sehr empfehlenswerte Einführung...vor..." (H. Mitsch, Monatshefte für Mathematik 3/111, 1991)Trade Review“More than 30 years after its initial publication, the present textbook is still a very valuable source for results in real algebra. It can serve as a textbook for a university course, but also experts will benefit from the nice account of concepts and results. It’s great that the book is available again, in particular in an English translation for an international audience.” (Tim Netzer, zbMATH 1505.13001, 2023)Table of Contents1 Ordered fields and their real closures.- 2 Convex valuation rings and real places.- 3 The real spectrum.- 4 Recent developments.

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Book SynopsisThis volume, originally published in China and translated into four other languages, presents a fascinating and unique account of the history of mathematics, divided into eight chronologically organized chapters. Tracing the development of mathematics across disparate regions and peoples, with particular emphasis on the relationship between mathematics and civilization, it examines mathematical sources and inspirations leading from Egypt, Babylon and ancient Greece and expanding to include Chinese, Indian and Arabic mathematics, the European Renaissance and the French revolution up through the Nineteenth and Twentieth Centuries. Each chapter explores connections among mathematics and cultural elements of the time and place treated, accompanying the reader in a varied and exciting journey through human civilizations. The book contemplates the intersections of mathematics with other disciplines, including the relationship between modern mathematics and modern art, and the resulting applications, with the aid of images and photographs, often taken by the author, which further enhance the enjoyment for the reader. Written for a general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities. Table of Contents1. The Middle East, or the Beginning.- 2. The Sages of Ancient Greece.- 3. The Chinese Middle Ages.- 4. India and Persia.- 5. From the Renaissance to the Birth of Calculus.- 6. The Age of Analysis and the French Revolution.- 7. Modern Mathematics, Modern Art.- 8. Abstraction: Mathematics Since the Twentieth Century.

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Book SynopsisThis second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centered about curvature. Topics covered include spectral theory of elliptic differential operators, the theory of scattering of waves by obstacles, index theory for Dirac operators, and Brownian motion and diffusion. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. It includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds.Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC.Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.”(Peter Lax, SIAM review, June 1998)Table of ContentsPreface.- 7 Pseudodifferential Operators.- 8 Spectral Theory.- 9 Scattering by Obstacles.- 10 Dirac Operators and Index Theory.- 11 Brownian Motion and Potential Theory.- 12 The ∂-Neumann Problem.- C Connections and Curvature.- Index.

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Book SynopsisThis textbook provides an introduction to the mathematical methods used to analyse deterministic models in life sciences, including population dynamics, epidemiology and ecology.

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Book SynopsisThis textbook proposes an informal access to the most important issues of multidimensional differential and integral calculus. To situate the contents within a historical perspective, the book is accompanied by a number of links to the biographies of all scientists mentioned as leading actors in the development of the theory.

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Book SynopsisIntroduction to Statistics.- Types of Data.- Data Collection Methods (Sampling Theory).- Measures of Central Tendency.- Measures of Dispersion.- Measures of Positions.- Outliers.- Introduction to Distributions.- Skewness, Kurtosis and Modality.- Data Visualisation.- Confidence Intervals.- Hypothesis Testing.- Correlation and Linear Regression.- Statistical Project - Steps and Process.- Appendix A - Partioning of the Ordinary Least Square Variance.- Appendix B - Big-O and Little-o Notation.

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Book SynopsisPart 1.How is Music Born?.- Chapter 1.Introduction.- Chapter 2.Intervals, Scales, Tuning and Harmonics.- Chapter 3.Acoustic Basis and Generation of Sound.- Chapter 4.Complexity and Dynamics in Phase Space.- Part 2.Journey across the World.- Chapter 5.Physical and Mathematical Aspects in European Music.- Chapter 6.Music in Other Cultures.- Part 3.Moving beyond.- Chapter 7.Why Do we Know that it is Mozart?.- Chapter 8.Ending without End.

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Book SynopsisThis book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black–Scholes–Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena. The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoretical concepts. Stochastic Analysis for Finance with Simulations is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical study. It will particularly appeal to advanced undergraduate and graduate students in mathematics and business, but not excluding practitioners in finance industry. Trade Review“This book gives an introduction to financial mathematics. It presents also some background of mathematical facts necessary for understanding modern finance. … For the reader convenience, the book contains a detailed contents, a list of figures, a list of tables, a list of simulations, a list of acronyms and a list of used symbols.” (Jacek Jakubowski, zbMATH 1409.91002, 2019)“This excellent textbook is addressed to undergraduate and graduate students in mathematics and finance who want to study the main tools of stochastic calculus and its application to quantitative finance. Also, it can be used as a reference book for practitioners and professionals from the financial industry who want a better understanding of the theoretical aspects of stochastic calculus, and how it can be used in the pricing of financial derivatives.” (Carlos Vázquez Cendón, Mathematical Reviews, August, 2017)Table of Contents

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Book SynopsisThis book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter.Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments.Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.Trade Review“‘The aim of this book is to provide a rigorous introduction to the theory of stochastic calculus for continuous semi-martingales putting a special emphasis on Brownian motion.’ … If the reader has the background and needs a rigorous treatment of the subject this book would be a good choice. Le Gall writes clearly and gets to the point quickly … .” (Richard Durrett, MAA Reviews, March, 2017) “The purpose of this book is to provide concise but rigorous introduction to the theory of stochastic calculus for continuous semimartingales, putting a special emphasis on Brownian motion. … The book is written very clearly, it is interesting both for its construction and maintenance, mostly it is self-contained. It can be recommended to everybody who wants to study stochastic calculus, including those who is interested to its applications in other fields.” (Yuliya S. Mishura, zbMATH, 2017)Table of ContentsGaussian variables and Gaussian processes.- Brownian motion.- Filtrations and martingales.- Continuous semimartingales.- Stochastic integration.- General theory of Markov processes.- Brownian motion and partial differential equations.- Stochastic differential equations.- Local times.- The monotone class lemma.- Discrete martingales.- References.

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Book SynopsisThis textbook is designed with the needs of today’s student in mind. It is the ideal textbook for a first course in elementary differential equations for future engineers and scientists, including mathematicians. This book is accessible to anyone who has a basic knowledge of precalculus algebra and differential and integral calculus. Its carefully crafted text adopts a concise, simple, no-frills approach to differential equations, which helps students acquire a solid experience in many classical solution techniques. With a lighter accent on the physical interpretation of the results, a more manageable page count than comparable texts, a highly readable style, and over 1000 exercises designed to be solved without a calculating device, this book emphasizes the understanding and practice of essential topics in a succinct yet fully rigorous fashion. Apart from several other enhancements, the second edition contains one new chapter on numerical methods of solution.The book formally splits the "pure" and "applied" parts of the contents by placing the discussion of selected mathematical models in separate chapters. At the end of most of the 246 worked examples, the author provides the commands in Mathematica® for verifying the results. The book can be used independently by the average student to learn the fundamentals of the subject, while those interested in pursuing more advanced material can regard it as an easily taken first step on the way to the next level. Additionally, practitioners who encounter differential equations in their professional work will find this text to be a convenient source of reference.Table of Contents1. Introduction.- 2. First Order Equations.- 3. Mathematical Models with First-Order Equations.- 4. Linear Second-Order Equations.- 4. Higher-Order Equations.- 5. Mathematical Models with Second-Order Equations.- 6. Higher-Order Linear Equations.- 7. Systems of Differential Equations.- 8. The Laplace Transformation.- 9. Series Solutions.- 10. Numerical Methods.- A. Algebra Techniques.- B. Calculus Techniques.- C. Table of Laplace Transforms.- D. The Greek Alphabet.- Further Reading.- Answers to Odd-Numbered Exercises.- Index.

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Book SynopsisThis textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate students, as well as doctoral students, postdoctoral researchers and academic experts who are engaged in modeling stochastic processes on networks; Providing software that can solve differential equation models or directly simulate epidemics on networks. Replete with numerous diagrams, examples, instructive exercises, and online access to simulation algorithms and readily usable code, this book will appeal to a wide spectrum of readers from different backgrounds and academic levels. Appropriate for students with or without a strong background in mathematics, this textbook can form the basis of an advanced undergraduate or graduate course in both mathematics and other departments alike. Trade Review“The book adds to the knowledge of epidemic modeling on networks by providing a number of rigorous mathematical arguments and confirming the validity and optimal range of applicability of the epidemic models. It serves as a good reference guide for researchers and a comprehensive textbook for graduate students.” (Yilun Shang, Mathematical Reviews, November, 2017)“This is one of the first books to appear on modeling epidemics on networks. … This is a comprehensive and well-written text aimed at students with a serious interest in mathematical epidemiology. It is most appropriate for strong advanced undergraduates or graduate students with some background in differential equations, dynamical systems, probability and stochastic processes.” (William J. Satzer, MAA Reviews, September, 2017)Table of ContentsPreface.- ​Introduction to Networks and Diseases.- Exact Propagation Models: Top Down.- Exact Propagation Models: Bottom-Up.- Mean-Field Approximations for Heterogeneous Networks.- Percolation-Based Approaches for Disease Modelling.- Hierarchies of SIR Models.- Dynamic and Adaptive Networks.- Non-Markovian Epidemics.- PDE Limits for Large Networks.- Disease Spread in Networks with Large-scale structure.- Appendix: Stochastic Simulation.- Index.

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Book SynopsisThis text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, while the study of cluster algebras provides representation theory with new objects of study.The six mini-courses comprising this text were delivered March 7–18, 2016 at a CIMPA (Centre International de Mathématiques Pures et Appliquées) research school held at the Universidad Nacional de Mar del Plata, Argentina. This research school was dedicated to the founder of the Argentinian research group in representation theory, M.I. Platzeck.The courses held were: Advanced homological algebra Introduction to the representation theory of algebras Auslander-Reiten theory for algebras of infinite representation type Cluster algebras arising from surfaces Cluster tilted algebras Cluster characters Introduction to K-theory Brauer graph algebras and applications to cluster algebras Table of ContentsIntroduction to the Representation Theory of Finite-Dimensional Algebras: The Functorial Approach (M. I. Platzeck).- Auslander–Reiten Theory for Finite-Dimensional Algebras (P. Malicki).- Cluster Algebras From Surfaces (R. Schiffler).- Cluster Characters (P.-G. Plamondon).- A Course on Cluster Tilted Algebras (I. Assem).- Brauer Graph Algebras (S. Schroll).

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Book SynopsisThis book celebrates the work of Don Pigozzi on the occasion of his 80th birthday. In addition to articles written by leading specialists and his disciples, it presents Pigozzi’s scientific output and discusses his impact on the development of science. The book both catalogues his works and offers an extensive profile of Pigozzi as a person, sketching the most important events, not only related to his scientific activity, but also from his personal life. It reflects Pigozzi's contribution to the rise and development of areas such as abstract algebraic logic (AAL), universal algebra and computer science, and introduces new scientific results. Some of the papers also present chronologically ordered facts relating to the development of the disciplines he contributed to, especially abstract algebraic logic. The book offers valuable source material for historians of science, especially those interested in history of mathematics and logic.Table of ContentsA Mathematical Life; Pigozzi, Don.- Assertional logics, truth-equational logics, and the hierarchiesof abstract algebraic logic; Albuquerque, Hugo, Font, Josep Maria, Jansana, Ramon, and Moraschini, Tommaso.- Deduction-Detachment Theorem and Gentzen-Style Deductive Systems; Babenyshev, Sergey.- Introducing Boolean Semilattices; Bergman, Clifford.- The Equationally-Defined Commutator in Quasivarieties Generated by Two-Element Algebras; Czelakowski, Janusz.- A short overview of Hidden Logic; Ferreirim, Isabel and Martins, Manuel A.- Absorption and directed J´onsson terms; Kazda, Alexandr, Kozik, Marcin, McKenzie, Ralph and Moore, Matthew.- Relatively congruence modular quasivarieties of modules; Kearnes, Keith A. - The computational complexity of deciding whether a finite algebra generates a minimal variety; McNulty, George F.- Characterization of protoalgebraic k-deductive systems; Palasinska; Katarzyna.- Diagrammatic duality; Romanowska, Anna B. and Smith, Jonathan D.H.- Boolean product representations of algebras via binary polynomials; Salibra, Antonino, Ledda, Antonio, and Paoli, Francesco.- Paraconsistent constructive logic with strong negation as a contraction-free relevant logic; Spinks, Matthew and Veroff, Robert.- Possible classification of finite-dimensional compact Hausdorfftopological algebras; Taylor, Walter.- Categorical Abstract Algebraic Logic: Compatibility Operators and Correspondence Theorems; Voutsadakis; George.

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Book SynopsisThis book is a guide to numerical methods for solving fluid dynamics problems. The most widely used discretization and solution methods, which are also found in most commercial CFD-programs, are described in detail. Some advanced topics, like moving grids, simulation of turbulence, computation of free-surface flows, multigrid methods and parallel computing, are also covered. Since CFD is a very broad field, we provide fundamental methods and ideas, with some illustrative examples, upon which more advanced techniques are built. Numerical accuracy and estimation of errors are important aspects and are discussed in many examples. Computer codes that include many of the methods described in the book can be obtained online. This 4th edition includes major revision of all chapters; some new methods are described and references to more recent publications with new approaches are included. Former Chapter 7 on solution of the Navier-Stokes equations has been split into two Chapters to allow for a more detailed description of several variants of the Fractional Step Method and a comparison with SIMPLE-like approaches. In Chapters 7 to 13, most examples have been replaced or recomputed, and hints regarding practical applications are made. Several new sections have been added, to cover, e.g., immersed-boundary methods, overset grids methods, fluid-structure interaction and conjugate heat transfer.Table of ContentsBasic Concepts of Fluid Flow.- Introduction to Numerical Methods.- Finite Difference Methods.- Finite Volume Methods.- Solution of Linear Equation Systems.-Methods for Unsteady Problems.- Solution of the Navier-Stokes Equations.- Complex Geometries.- Turbulent Flows.- Compressible Flows.- Efficiency, Accuracy and Grid Quality.- Special Topics.

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Book SynopsisThis book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.Table of ContentsIntroduction.- 1 Prevarieties.- 2 Spectrum of a Ring.- 3 Schemes.- 4 Fiber products.- 5 Schemes over fields.- 6 Local Properties of Schemes.- 7 Quasi-coherent modules.- 8 Representable Functors.- 9 Separated morphisms.- 10 Finiteness Conditions.- 11 Vector bundles.- 12 Affine and proper morphisms.- 13 Projective morphisms.- 14 Flat morphisms and dimension.- 15 One-dimensional schemes.- 16 Examples.

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Book SynopsisThe finite element, an approximation method for solving differential equations of mathematical physics, is a highly effective technique in the analysis and design, or synthesis, of structural dynamic systems. Starting from the system differential equations and its boundary conditions, what is referred to as a weak form of the problem (elaborated in the text) is developed in a variational sense. This variational statement is used to define elemental properties that may be written as matrices and vectors as well as to identify primary and secondary boundaries and all possible boundary conditions. Specific equilibrium problems are also solved. This book clearly reveals the effectiveness and great significance of the finite element method available and the essential role it will play in the future as further development occurs.Table of Contents1. Finite Element Techniques for Nonlinear Postbuckling and Collapse of Elastic Structures 2. Boundary Element Methods in Structural Dynamic System Problems hhhNewton-Raphson Techniques in Finite Ele ment Methods for Nonlinear Structural Problems 3. The Nonlinear Stress Analysis of Metallic and Reinforced Concrete Structures 4. Co-Rational Formulation for Nonlinear Dynamic Analysis of Beam Structures

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Book SynopsisThe book covers a wide range of Artificial Intelligence (AI) and Mathematical Methods issues, research and applications in the area of pavement, geomechanical and few examples on geo-environmental systems: Application of Artificial Neural Networks; Data mining applications; Stochastic Finite Element; Fuzzy Set Theory; Artificial Immune Systems; Probabilistic Reasoning; System Identification Techniques; Image Processing. This collection of papers provides researchers and engineers with a current comprehensive look at available and emerging AI and Mathematical Methods within pavement and geomechanical systems.

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Book SynopsisSports analytics has gathered tremendous momentum as one of the most dynamic fields. Diving deep into the numbers of sports can be game changing or simply a fun exercise for fans. How do you get in the game with numbers? What questions can be explored? What actionable insights can be gleaned?Do you like sports? This book will detail ways to analyze athletics to gain insight that can otherwise be obscured. Like math? You'll find many mathematical topics not involving sports. You'll also see how sports analytics can train you broadly in mathematics.From coaching at the highest levels to national media broadcasts, analytics are becoming increasingly indispensable. Dive into the numbers behind soccer to basketball to baseball to boxing to swimming, dive into the numbers. Learn how to get in the game with sports and mathematics.

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Book SynopsisThe book is the first in the trilogy which will bring you to the fascinating world of numbers and operations with them. Numbers provide information about myriads of things. Together with operations, numbers constitute arithmetic forming in basic intellectual instruments of theoretical and practical activity of people and offering powerful tools for representation, acquisition, transmission, processing, storage, and management of information about the world.The history of numbers and arithmetic is the topic of a variety of books and at the same time, it is extensively presented in many books on the history of mathematics. However, all of them, at best, bring the reader to the end of the 19th century without including the developments in these areas in the 20th century and later. Besides, such books consider and describe only the most popular classes of numbers, such as whole numbers or real numbers. At the same time, a diversity of new classes of numbers and arithmetic were introduced in the 20th century.This book looks into the chronicle of numbers and arithmetic from ancient times all the way to 21st century. It also includes the developments in these areas in the 20th century and later. A unique aspect of this book is its information orientation of the exposition of the history of numbers and arithmetic.

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Book SynopsisThe second edition represents an ongoing effort to make probability accessible to students in a wide range of fields such as mathematics, statistics and data science, engineering, computer science, and business analytics. The book is written for those learning about probability for the first time. Revised and updated, the book is aimed specifically at statistics and data science students who need a solid introduction to the basics of probability.While retaining its focus on basic probability, including Bayesian probability and the interface between probability and computer simulation, this edition's significant revisions are as follows:The approach followed in the book is to develop probabilistic intuition before diving into details. The best way to learn probability is by practising on a lot of problems. Many instructive problems together with problem-solving strategies are given. Answers to all problems and worked-out solutions to selected problems are also provided.Henk Tijms is the author of several textbooks in the area of applied probability. In 2008, he had received the prestigious INFORMS Expository Writing Award for his work. He is active in popularizing probability at Dutch high schools.Table of ContentsCombinatorics and Calculus for Probability; Basics of Probability; Useful Probability Distributions; Real-Life Examples of Poisson Probabilities; Monte Carlo Simulation and Probability; A Primer on Markov Chains; Solutions to Selected Problems;

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Book SynopsisThis volume provides a unified mathematical introduction to stationary time series models and to continuous time stationary stochastic processes. The analysis of these stationary models is carried out in time domain and in frequency domain. It begins with a practical discussion on stationarity, by which practical methods for obtaining stationary data are described. The presented topics are illustrated by numerous examples. Readers will find the following covered in a comprehensive manner:At the end, some selected topics such as stationary random fields, simulation of Gaussian stationary processes, time series for planar directions, large deviations approximations and results of information theory are presented. A detailed appendix containing complementary materials will assist the reader with many technical aspects of the book.

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Book SynopsisThis book presents a concise introduction to differential geometry. It is aimed at advanced undergraduate students and first year graduate students who wish to have a basic solid knowledge of the subject, and it can serve as a starting point for more advanced reading. The book is organized into lectures, so it can easily be used as a textbook for a beginning graduate-level course in differential geometry.

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Book SynopsisThis is a concise book that introduces students to the basics of logical thinking and important mathematical structures that are critical for a solid understanding of logical formalisms themselves as well as for building the necessary background to tackle other fields that are based on these logical principles. Despite its compact and small size, it includes many solved problems and quite a few end-of-section exercises that will help readers consolidate their understanding of the material.This textbook is essential reading for anyone interested in the logical foundations of Informatics, Computer Science, Data Science, Artificial Intelligence, and other related areas. Written with undergraduate students in these disciplines in mind, this book can very well serve the needs of interested and curious readers who wish to get a grasp of the logical principles upon which these fields are built. This book does not require readers to possess math skills beyond those learned in high school.

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