{"title":"Mathematical modelling Books","description":"","products":[{"product_id":"the-primacy-of-doubt-9780192843609","title":"The Primacy of Doubt","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eA bold, visionary, and mind-bending exploration of how the geometry of chaos can explain our uncertain worldfrom weather and pandemics to quantum physics and free willCovering a breathtaking range of topicsfrom climate change to the foundations of quantum physics, from economic modelling to conflict prediction, from free will to consciousness and spiritualityThe Primacy of Doubt takes us on a unique journey through the science of uncertainty. A key theme that unifies these seemingly unconnected topics is the geometry of chaos: the beautiful and profound fractal structures that lie at the heart of much of modern mathematics. Royal Society Research Professor Tim Palmer shows us how the geometry of chaos not only provides the means to predict the world around us, it suggests new insights into some of the most astonishing aspects of our universe and ourselves. This important and timely book helps the reader makes sense of uncertainty in a rapidly changing world.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eThe Primacy of Doubt provides a remarkably broad-ranging account of uncertainty in physics, in all its various aspects. I strongly recommend this highly thought-provoking book. * Roger Penrose, OM, FRS, winner of the 2020 Nobel Prize in Physics *\u003cbr\u003eTim Palmer is a scientific polymath. It's hard to think of anyone else who could have written so authoritatively—and so accessibly—on themes extending from quantum gravity to climate modelling. This fascinating and important book offers some profoundly original speculations on conceptual linkages across different sciences. * Lord Martin Rees, Astronomer Royal of the United Kingdom *\u003cbr\u003eIn a whirlwind of a book that's partly scientific autobiography and partly the manifest of a visionary, Tim Palmer masterfillly weaves together climate change and quantum mechanics into one coherent whole. Using uncertainty as a unifying principle, Palmer puts forward new perspectives on old problems. A revolutionary thinker way ahead of his time. * Sabine Hossenfelder, author of Lost in Math *\u003cbr\u003eThe Primacy of Doubt is an important book by one of the pioneers of dynamical weather prediction, indispensable for daily life. * Suki Manabe, winner of the 2021 Nobel Prize in Physics *\u003cbr\u003eQuite possibly the best popular science book I've ever read... The Primacy of Doubt is like getting off one of those exciting roller coaster rides, when your immediate inclination is to think 'I want to do that again, but I'll have a bit of a break first.' I will be reading this book again, without doubt. Remarkable. * Brian Clegg, Popular Science *\u003cbr\u003eimportant book * Andrew Robinson, Nature *\u003cbr\u003ePhysicist Palmer delivers a challenging but rewarding look at how uncertainty helps scientists make sense of the world ... Despite the complexity of his arguments, the author succeeds at bringing complicated theories within reach of those who have a basic familiarity with physics. Science-minded readers, take note. * Publishers Weekly *\u003cbr\u003eThe Primacy of Doubt also contains very informative explanations as to the application of chaos theory in climate and meteorological models, and why meteorologists failed to predict southern Britain's 1987 hurricane. To my mind this were probably the book's strongest areas and are 'must reads' for those with an interest in climate forecasting. * Jonathan Cowie, SF2 Concatenation *\u003cbr\u003edelightful and substantive * William Hooke, Living on the Real World *\u003cbr\u003eAn exploration of the amorphous concept of uncertainty... [an] informative, ingenious book. * Kirkus Reviews *\u003cbr\u003eProvocative... useful for scientists and non-scientists alike * Jessica Flack, Physics World *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction Part I: The Science of Uncertainty 1: Chaos, Chaos Everywhere 2: The Geometry of Chaos 3: Noisy, Million-Dollar Butterflies 4: Quantum Uncertainty: Reality Lost? Part II: Predicting our Chaotic World 5: The Two Roads to Monte Carlo 6: Climate Change: Catastrophe or Just Lukewarm? 7: Pandemics 8: Financial Crashes 9: Deadly Conflict and the Digital Ensemble of Spaceship Earth 10: Decisions! Decisions! Part III: Understanding the Chaotic Universe and our Place in it 11: Quantum Uncertainty: Reality Regained? 12: Our Noisy Brains 13: Free Will, Consciousness, and God","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732592537943,"sku":"9780192843609","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192843609.jpg?v=1719997566"},{"product_id":"the-primacy-of-doubt-from-climate-change-to-quantum-physics-how-the-science-of-uncertainty-can-help-predict-and-understand-our-chaotic-world-9780192843593","title":"The Primacy of Doubt From climate change to","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eA bold, visionary, and mind-bending exploration of how the geometry of chaos can explain our uncertain world - from weather and pandemics to quantum physics and free willCovering a breathtaking range of topics - from climate change to the foundations of quantum physics, from economic modelling to conflict prediction, from free will to consciousness and spirituality - The Primacy of Doubt takes us on a unique journey through the science of uncertainty. A key theme that unifies these seemingly unconnected topics is the geometry of chaos: the beautiful and profound fractal structures that lie at the heart of much of modern mathematics. Royal Society Research Professor Tim Palmer shows us how the geometry of chaos not only provides the means to predict the world around us, it suggests new insights into some of the most astonishing aspects of our universe and ourselves. This important and timely book helps the reader makes sense of uncertainty in a rapidly changing world.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eimportant book * Andrew Robinson, Nature *\u003cbr\u003eThe Primacy of Doubt also contains very informative explanations as to the application of chaos theory in climate and meteorological models, and why meteorologists failed to predict southern Britain's 1987 hurricane. To my mind this were probably the book's strongest areas and are 'must reads' for those with an interest in climate forecasting. * Jonathan Cowie, SF2 Concatenation *\u003cbr\u003eQuite possibly the best popular science book I've ever read... The Primacy of Doubt is like getting off one of those exciting roller coaster rides, when your immediate inclination is to think 'I want to do that again, but I'll have a bit of a break first.' I will be reading this book again, without doubt. Remarkable. * Brian Clegg, Popular Science *\u003cbr\u003edelightful and substantive * William Hooke, Living on the Real World *\u003cbr\u003eThe Primacy of Doubt provides a remarkably broad-ranging account of uncertainty in physics, in all its various aspects. I strongly recommend this highly thought-provoking book. * Roger Penrose, OM, FRS, winner of the 2020 Nobel Prize in Physics *\u003cbr\u003eTim Palmer is a scientific polymath. It's hard to think of anyone else who could have written so authoritatively—and so accessibly—on themes extending from quantum gravity to climate modelling. This fascinating and important book offers some profoundly original speculations on conceptual linkages across different sciences. * Lord Martin Rees, Astronomer Royal of the United Kingdom *\u003cbr\u003eThe Primacy of Doubt is an important book by one of the pioneers of dynamical weather prediction, indispensable for daily life. * Suki Manabe, winner of the 2021 Nobel Prize in Physics *\u003cbr\u003eIn a whirlwind of a book that's partly scientific autobiography and partly the manifest of a visionary, Tim Palmer masterfillly weaves together climate change and quantum mechanics into one coherent whole. Using uncertainty as a unifring principle, Palmer puts forward new perspectives on old problems. A revolutionary thinker way ahead of his time. * Sabine Hossenfelder, author of Lost in Math *\u003cbr\u003eAn exploration of the amorphous concept of uncertainty... [an] informative, ingenious book. * Kirkus Reviews *\u003cbr\u003ePhysicist Palmer delivers a challenging but rewarding look at how uncertainty helps scientists make sense of the world... Despite the complexity of his arguments, the author succeeds at bringing complicated theories within reach of those who have a basic familiarity with physics. Science-minded readers, take note. * Publishers Weekly *\u003cbr\u003eProvocative... useful for scientists and non-scientists alike * Jessica Flack, Physics World *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface 1: The Primacy of Doubt DS From Two Perspectives Part I: The Science of Uncertainty and the Geometry of Chaos 2: Chaos, Chaos Everywhere 3: The Geometry of Chaos 4: Noisy, Million-Dollar Butterflies 5: Quantum Uncertainty DS Determinism Lost? Part II: The Science of Uncertainty to Predict Our Chaotic World 6: The Two Roads to Monte Carlo 7: Climate Change: Catastrophe or Just Lukewarm? 8: Pandemics 9: Financial Crashes 10: Deadly Conflict and the Digital Ensemble of Spaceship Earth 11: Decisions! Decisions! Part III: The Science of Uncertainty to Understand Our Chaotic World 12: Quantum Uncertainty: Determinism Regained? 13: Noisy Billion-Dollar Brains 14: Free Will, Consciousness and Theology Acknowledgements Bibliography","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732592570711,"sku":"9780192843593","price":23.84,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192843593.jpg?v=1719997566"},{"product_id":"statistical-modeling-with-r-a-dual-frequentist-and-bayesian-approach-for-life-scientists-9780192859020","title":"Statistical Modeling With R a dual frequentist","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eAn accessible textbook that explains, discusses, and applies both the frequentist and Bayesian theoretical frameworks to fit the different types of statistical models that allow an analysis of the types of data most commonly gathered by life scientists.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePart 1: The Conceptual Basis For Fitting Statistical Models 1: General introduction 2: Statistical modeling: a short historical background 3: Estimating parameters: the main purpose of statistical inference Part II: Applying The Generalized Linear Model to Varied Data Types 4: The General Linear Model I: numerical explanatory variables 5: The General Linear Model II: categorical explanatory variables 6: The General Linear Model III: interactions between explanatory variables 7: Model selection: one, two, and more models fitted to the data 8: The Generalized Linear Model 9: When the response variable is binary 10: When the response variables are counts, often with many zeros 11: Further issues involved in the modeling of counts 12: Models for positive real-valued response variables: proportions and others Part III: Incorporating Experimental and Survey Design Using Mixed Models 13: Accounting for structure in mixed\/hierachical structures 14: Experimental design in the life sciences - the basics 15: Mixed-hierachical models and experimental design data Afterword R packages used in the book Appendix 1: Using R and RStudio: the basics (only available online at www.oup.com\/companion\/InchaustiSMWR) Appendix 2: Exploring and describing the evidence in graphics (only available online at www.oup.com\/companion\/InchaustiSMWR)","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732602204503,"sku":"9780192859020","price":42.74,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192859020.jpg?v=1791454083"},{"product_id":"evolutionary-quantitative-genetics-9780192859396","title":"Evolutionary Quantitative Genetics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eA concise, accessible introduction to the principal ideas, methods, and underlying statistical concepts for understanding and applying evolutionary quantitative genetics. It includes a broad taxonomic range of examples - human, animal, and plant; both model organisms and wild populations.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction 1: Selection on a Single Trait 2: Selection on Multiple Traits 3: The Selection Surface and Adaptive Landscape for a Single Trait 4: The Selection Surface and Adaptive Landscape for Multiple Traits 5: Inheritance of a Single Trait 6: Inheritance of Multiple Traits 7: Modularity, Performance, and Functional Complexes 8: Drift of a Single, Neutral Trait 9: Drift of Multiple, Neutral Traits 10: Response of a Single Trait to Selection 11: Response of Multiple Traits to Selection 12: Evolution of a Single Trait on a Stationary Adaptive Landscape 13: Evolution of Multiple Traits on a Stationary Adaptive Landscape 14: Trait Evolution on Dynamic Adaptive Landscapes 15: Evolution of Genetic Variance 16: Evolution of the G-Matrix on a Stationary Adaptive Landscape 17: Evolution of the G-Matrix on Dynamic Adaptive Landscapes 18: Evolution Along Selective Lines of Least Resistance 19: Speciation and Extinction of Lineages 20: Coevolution of Species with Trait-Based Interactions 21: Coevolution of Species with Density-Dependent Interactions 22: From Evolutionary Process to Pattern: A Synthesis","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732602335575,"sku":"9780192859396","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192859396.jpg?v=1791454084"},{"product_id":"competition-theory-in-ecology-oxford-series-in-ecology-and-evolution-9780192895530","title":"Competition Theory in Ecology Oxford Series in","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis novel textbook addresses the shortcomings of current competition theory and suggests a more useful approach that can provide a basis for future models that have far greater predictive ability in both ecology and evolution.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eThis book offers readers a compelling introduction to these complexities. * Mark A. McPeek, Biological Sciences, Dartmouth College, Hanover, New Hampshire, The Quarterly Review of Biology *","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732612854103,"sku":"9780192895530","price":41.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780192895530.jpg?v=1719997650"},{"product_id":"predicting-our-climate-future-9780198812937","title":"Predicting Our Climate Future","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis book is about how climate science works and why you should absolutely trust some of its conclusions and absolutely distrust others. Climate change raises new, foundational challenges in science. It requires us to question what we know and how we know it. The subject is important for society but the science is young and history tells us that scientists can get things wrong before they get them right. How, then, can we judge what information is reliable and what is open to question? Stainforth goes to the heart of the climate change problem to answer this question. He describes the fundamental characteristics of climate change and shows how they undermine the application of traditional research methods, demanding new approaches to both scientific and societal questions. He argues for a rethinking of how we go about the study of climate change in the physical sciences, the social sciences, economics, and policy. The subject requires nothing less than a restructuring of academic resea\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eClimate is, in some respects, highly predictable; yet, in other respects, highly unpredictable. But there is no contradiction. The resolution of this seeming paradox in Predicting Our Climate Future leads in turn to a vision for how humankind must respond to this most important problem of all time. * George Akerlof, Nobel Laureate in Economics, 2001 *\u003cbr\u003eA profound yet very accessible guide to climate science, highlighting the significant uncertainties without apology. This book explains clearly why doubt creates a greater and more urgent need to act now to build a better future. * Trevor Maynard, Executive Director of Systemic Risks, Cambridge Centre for Risk Studies *\u003cbr\u003eThe immense complexity of the climate system raises deep questions about what science can usefully say about the future. David Stainforth navigates philosophical and mathematical questions that could hardly be of greater practical importance. He questions what it is reasonable to ask of climate scientists and his conclusions challenge the way in which science should be conducted in the future. * Jim Hall, Professor of Climate and Environmental Risk, University of Oxford *\u003cbr\u003eIs the science settled? Are climate models rubbish? Stainforth's book serves up nuanced answers to big questions in climate science, in an easy conversational style. * Cameron Hepburn, Professor of Environmental Economics, University of Oxford *\u003cbr\u003eA thoughtful exploration of the foundations and limitations of climate prediction that explains how its chaotic and probabilistic nature lead to deep uncertainty when assessing climate risk. * Ramalingam Saravanan, Professor of Atmospheric Sciences, Texas A\u0026amp;M University *\u003cbr\u003ePredicting Our Climate Future is an erudite and very personal reflection on climate change, the state of climate science, and their implications for the decisions society needs to take. It should be top of the reading list for scientists, practitioners and anyone who wants to truly comprehend the challenge of climate prediction. * Simon Dietz, Professor of Environmental Policy, London School of Economics and Political Science *\u003cbr\u003eA provocative contribution to the literature of climate change. * Kirkus *\u003cbr\u003ePredicting Our Climate Future is an ambitious exploration of a critical topic. It is a recommended read for climate scientists, especially those trying to model the future, for the researchers-in many disciplines-that are focused on understanding and forecasting the physical and human impacts of the coming climate changes, and for policy makers engaged in climate issues. * Steven Earle, New York Journal of Books *\u003cbr\u003eIntelligent, accessible, well reasoned and working very hard to get it's teeth into a complex but vitally important issue. * Irish Tech News *\u003cbr\u003eFascinating...[there is a] a refreshing honesty [in Stainforth's writing] about the limitations we have with certain kinds of prediction. * Brian Clegg, Popular Science *\u003cbr\u003eStainforth is good at explaining the complexities [of climate modelling], leavening the highly technical bits with ... lots of relatable real-world analogies. * Geordie Torr, The Geographical *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eSection 1 Chapter 1: The obvious and the obscure Chapter 2: A problem of prediction Chapter 3: Going beyond what we've seen Chapter 4: The one-shot bet. Chapter 5: From chaos to pandemonium Chapter 6: The curse of bigger and better computers Chapter 7: Talking at cross purposes Chapter 8: Not just of academic interest Section 2 Challenge 1: How to balance justified arrogance with essential humility. Chapter 9 - Stepping up to the task of prediction Chapter 10 The Times They Are A Changin' Chapter 11 Starting from scratch Chapter 12 Are scientists being asked to answer impossible questions? Challenge 2: Tying down what we mean by climate and climate change.  Chapter 13 The essence of climate Chapter 14 A Walk in Three Dimensions Chapter 15 A walk in three dimensions over a two dimensional sea Challenge 3: When is a study with a climate model a study of climate change? Chapter 16 Climate change in climate models Challenge 4: How can we measure what climate is now and how it has changed? Chapter 17 Measuring climate change Challenge 5: How can we relate what happens in a model to what will happen in reality? Chapter 18 - Can climate models be realistic? Chapter 19 More models, better information? Chapter 20 How bad is too bad? Challenge 6: How can we use today's climate science well? Chapter 21 - What we do with what we've got Challenge 7: Getting a grip on the scale of future changes in climate? Chapter 22 - Stuff of the Genesis myth Chapter 23 Things ... can only get hotter Challenge 8: How can we use the information we have, or could have, to design a future that is better than it would otherwise be? Chapter 24 - Making it personal Chapter 25 - Where physics and economics meet. Challenge 9: How can we build physical and social science that is up to the task of informing society about what matters for society? Chapter 26 - Controlling factors. Chapter 27 - Beyond comprehension? No, just new challenges for human intellect.","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732792881495,"sku":"9780198812937","price":18.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198812937.jpg?v=1719998423"},{"product_id":"introduction-to-the-theory-of-complex-systems-9780198821939","title":"Introduction to the Theory of Complex Systems","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis book is a comprehensive introduction to quantitative approaches to complex adaptive systems. Practically all areas of life on this planet are constantly confronted with complex systems, be it ecosystems, societies, traffic, financial markets, opinion formation and spreading, or the internet and social media. Complex systems are systems composed of many elements that interact strongly with each other, which makes them extremely rich dynamical systems showing a huge range of phenomena. Properties of complex systems that are of particular importance are their efficiency, robustness, resilience, and proneness to collapse.The quantitative tools and concepts needed to understand the co-evolutionary nature of networked systems and their properties are challenging. The book gives a self-contained introduction to these concepts, so that the reader will be equipped with a toolset that allows them to engage in the science of complex systems. Topics covered include random processes of path-de\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eWell written and structured * Ejay Nsugbe, Mathematics Today *\u003cbr\u003eThe authors make an excellent job in describing their introduction to Complex Systems theory . . . The book is certainly an excellent start for students (who can find also a series of exercises in every chapter and for practioners). For scientists it is a useful handbook to find whatever needed to start their journey in Complexity Science. * Guido Caldarelli, IMT Alti Studi Lucca, Mathematics Magazine *\u003cbr\u003eIt seems to me that the authors have succeeded admirably in their aims and that, by helping to train and enthuse the next generation of researchers on complex systems, their book will contribute substantially towards overcoming any possible bottleneck that is impeding further progress. * Peter V. E. McClintock, Department of Physics, Lancaster University, Contemporary Physics *\u003cbr\u003eThis book is a comprehensive introduction to quantitative approaches to complex adaptive systems, starting from basic principles. It also equips the reader with a basic self-contained toolkit for engaging in complex systems science. It extends earlier classical literature in the field to summarize in a clear, structured, and comprehensive way the methodological progress made in complex systems science over the past 20 years. * Mathematical Reviews Clippings *\u003cbr\u003eThis book will surely become a standard text for anyone who wants to seriously understand complexity no matter what their background or stage of career. It is written from a physicists perspective, stressing mechanism, underlying principles and mathematical rigour, yet is eminently readable and pedagogical. * Geoffrey West, Santa Fe Institute *\u003cbr\u003eComplexity until now has been lacking a strong theoretical underpinning. Now it has one. This book is a tour de force. Excellent! * W. Brian Arthur, Santa Fe Institute *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1: Introduction to complex systems 2: Probability and random processes 3: Scaling 4: Networks 5: Evolutionary processes 6: Statistical mechanics \u0026amp; information theory for complex systems 7: The future of the science of complex systems? 8: Special functions and approximations","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732797010263,"sku":"9780198821939","price":65.55,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198821939.jpg?v=1719998438"},{"product_id":"when-things-grow-many-complexity-universality-and-emergence-in-nature-oxford-graduate-texts-9780198861881","title":"When Things Grow Many Complexity Universality and","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eAn accessible and interdisciplinary introduction to the applications of statistical mechanics across the sciences. The book contains a discussion of the methods of statistical physics and includes mathematical explanations alongside guidance to enable the reader to translate theory into practice.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eThis book has a good mix of interesting topics and shows the breadth of application of the statistical mechanics concepts. * Robert M. Ziff, University of Michigan *\u003cbr\u003eThe book's subject is one which is of great interest and impacts many areas both within and outside physics. I am not aware of any other textbook which includes engaging mathematical content alongside a wide range of accessible applications, so this text has the potential to appeal to both the lay person and the technical expert. * Peter Richmond, Trinity College Dublin *\u003cbr\u003eExplores statistical mechanics at its glorious best, in the form of practical applications of collective behaviors found in the real world. Schulman is refreshingly honest in his approach, helping to stake out the frontiers of the field, posing problems that will inspire and direct future generations of scientists. * Daniel Sheehan, University of San Diego *\u003cbr\u003eI think that the book's collection of topics and its unique style make it a useful addition to the more standard textbook offering. Moreover, given the more colloquial style of the book, I imagine that it may be suitable for an audience that is interested in the physics of emergence and complexity that goes beyond the popular science literature. * Stefan Kirchner, Zhejiang University *\u003cbr\u003eI expect that anyone interested in complex systems and who has the requisite knowledge of elementary calculus and linear algebra will find When Things Grow Many to be a rewarding read. * Robert Deegan, University of Michigan, Physics Today *\u003cbr\u003eI enjoyed reading When Things Grow Many and learned something new from each chapter. Schulman writes in a conversational style, and he peppers the book with jokes and opinions. Even though he intimates that he doesn't have all the answers, his fun, inviting tone will make readers want to find out if he does. * Robert Deegan, Physics Today *\u003cbr\u003eThis book ensures that all readers can grasp the fundamental principles and applications of physics, making it an excellent educational tool for a wide range of students. * Miguel A. F. Sanjuán, Contemporary Physics *\u003cbr\u003eThis book ensures that all readers can grasp the fundamental principles and applications of physics, making it an excellent educational tool for a wide range of students. * Miguel A. F. Sanjuán, Contemporary Physics *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1: Introduction 2: Ideal Gas 3: Rubber Bands 4: Percolitis 5: Ferromagnetism 6: Maximum Entropy Methods 7: Power Laws 8: Universality, Renormalization and Critical Phenomena 9: Social Sciences 10: Biological Sciences 11: Physical Sciences Free","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732818637143,"sku":"9780198861881","price":50.35,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198861881.jpg?v=1791454542"},{"product_id":"materials-modelling-using-density-functional-theory-properties-and-predictions-9780199662449","title":"Materials Modelling using Density Functional","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis book is an introduction to the quantum theory of materials and first-principles computational materials modelling. It explains how to use density functional theory as a practical tool for calculating the properties of materials without using any empirical parameters. The structural, mechanical, optical, electrical, and magnetic properties of materials are described within a single unified conceptual framework, rooted in the Schrödinger equation of quantum mechanics, and powered by density functional theory. This book is intended for senior undergraduate and first-year graduate students in materials science, physics, chemistry, and engineering who are approaching for the first time the study of materials at the atomic scale. The inspiring principle of the book is borrowed from one of the slogans of the Perl programming language, ''Easy things should be easy and hard things should be possible''. Following this philosophy, emphasis is placed on the unifying concepts, and on the frequent use of simple heuristic arguments to build on one''s own intuition. The presentation style is somewhat cross disciplinary; an attempt is made to seamlessly combine materials science, quantum mechanics, electrodynamics, and numerical analysis, without using a compartmentalized approach. Each chapter is accompanied by an extensive set of references to the original scientific literature and by exercises where all key steps and final results are indicated in order to facilitate learning. This book can be used either as a complement to the quantum theory of materials, or as a primer in modern techniques of computational materials modelling using density functional theory.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eAt last an undergraduate\/graduate textbook that demonstrates the power of density functional theory not only to help interpret experimental data but also to predict the properties of new materials. Each chapter is lucidly presented with heuristic, intuitive arguments leading to the main ideas before numerous examples illustrate the often remarkable accuracy of density functional theory over a wide range of electronic, structural, mechanical, optical and magnetic properties. A book that should be on the shelves of every library in Materials Science and Engineering, Physics and Chemistry departments. * David Pettifor, University of Oxford *\u003cbr\u003eThe density functional theory has finally brought quantum mechanics into materials science. Its proven ability to produce correct predictions of properties of real materials means that it has taken over as the premier method in solid state materials, ultimately because of its suitability as a numerical method. While traditional books still build from analytically tractable models, this book reflects more accurately current practice. The book will be ideal for a graduate-level student with a grounding in quantum mechanics, and could be tackled in an undergraduate course. * Graeme Ackland, University of Edinburgh *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1. Computational materials modelling from first principles ; 2. Many-body Schrodinger equation ; 3. Density-functional theory ; 4. Equilibrium structures of materials: fundamentals ; 5. Equilobrium structures of materials: calculation vs. experiment ; 6. Elastic properties of materials ; 7. Vibrations of molecules and solids ; 8. Phonons, vibrational spectroscopy, and thermodynamics ; 9. Band structures and photoelectron spectroscopy ; 10. Dielectric function and optical spectra ; 11. Density-functional theory and magnetic materials ; Appendix A: Derivation of the Hartree-Fock equations ; Appendix B: Derivation of the Kohn-Sham equations ; Appendix C: Numerical solution of the Kohn-Sham equations ; Appendix D: Reciprocal lattice and Brillouin zone ; Appendix E: Pseudopotentials","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48732877652311,"sku":"9780199662449","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780199662449.jpg?v=1719998781"},{"product_id":"inference-and-representation-9780226830049","title":"Inference and Representation","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe first comprehensive defense of an inferential conception of scientific representation with applications to art and epistemology.     Mauricio Suárez develops a conception of representation that delivers a compelling account of modeling practice. He begins by discussing the history and methodology of model building, charting the emergence of what he calls the modeling attitude, a nineteenth-century and fin de siècle development. Prominent cases of models, both historical and contemporary, are used as benchmarks for the accounts of representation considered throughout the book. After arguing against reductive naturalist theories of scientific representation, Suárez sets out his own account: a case for pluralism regarding the means of representation and minimalism regarding its constituents. He shows that scientists employ a variety of modeling relations in their representational practicewhich helps them to assess the accuracy of their representationswhile demonstrating that there is\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“Beautifully bringing together historical and contemporary research on representations in science with themes from aesthetics and the philosophy of art, Suárez’s book is an outstanding interdisciplinary contribution to the philosophy of science. It is essential reading for anyone interested in modeling practices, their connections with the arts, and what this insightful combination of science, art, and practice might bring to the epistemology of science.” -- Chiara Ambrosio, University College London\u003cbr\u003e“Suárez has been a leading voice in the philosophy of modeling for the last two decades. This book is a wonderfully clear and compelling presentation of his ‘inferentialist theory of representation.’ The book will be a central resource for advanced undergraduate and graduate students, and required reading for every philosopher of science.” -- Martin Kusch, University of Vienna\u003cbr\u003e“Suárez has written a brilliant account of the inferential conception of scientific representation, its historical roots, and its application to contemporary scientific modeling. What stands out is his deflationist approach toward metaphysics, the streamlined account in terms of representational force and inferential capacity, and the connection to the phenomenology of artistic perception. A magnificent work.”  -- Bas C. van Fraassen, Princeton University\u003cbr\u003e“\u003ci\u003eInference and Representation\u003c\/i\u003e makes a strong case for an inferential conception of scientific modeling. It argues that the effectiveness of a model lies in its providing an orientation that facilitates fruitful scientific reasoning. It is a valuable contribution to the literature on modeling.” -- Catherine Z. Elgin, Harvard University\u003cbr\u003e“This much-anticipated book is the culmination of over twenty years of pioneering work by Suárez. It is a must-read for anyone wishing to think carefully about models and representations in science. Suárez gives a careful, insightful, and comprehensive exposition and defence of his inferential conception of representation, and he now develops it in an expressly pragmatist direction with a helpful focus on the uses of models. What emerges is a compelling deflationary account of ‘representation without metaphysics,’ engaging fully with the complex realities of inferential practices. Suárez argues that common notions of representation based on similarity or isomorphism are ill-fitting and inadequate, and shows how the activity of representation pervades all sorts of scientific practices. His discussion is clear and systematic throughout, and successfully combines philosophical acuity and historical awareness. In the course of presenting his own position he also gives a fair, critical summing-up and evaluation of the considerable existing literature on models and representation. This landmark work should appeal to philosophers, historians of science and practicing scientists alike.” -- Hasok Chang, University of Cambridge\u003cbr\u003e“During the past quarter-century, philosophers of science have come to appreciate the importance of models and modeling practices in the sciences. Suárez has been one of the pioneers in this work, specifically in investigating how models represent aspects of the world. The present book is the culmination of insights accumulated over more than two decades. It provides a convincing account of representation, one emphasizing the uses to which models are put and the inferences they allow. Suárez develops his views with welcome precision, focuses on an admirably wide range of types of models, and offers numerous insights about the historical development of modeling. His final two chapters explore the notion of representation more broadly, with a lucid and well-informed discussion of representation in visual art, and draw out the implications for several large issues in the philosophy of science. This book is an outstanding contribution to the field.” -- Philip Kitcher, Columbia University\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface and Acknowledgments\u003cbr\u003e\u003cbr\u003e 1 Introducing Scientific Representation\u003cbr\u003e\u003cbr\u003e Part I Modeling\u003cbr\u003e 2 The Modeling Attitude: A Genealogy\u003cbr\u003e 3 Models and Their Uses\u003cbr\u003e\u003cbr\u003e Part II Representation\u003cbr\u003e 4 Theories of Representation\u003cbr\u003e 5 Against Substance\u003cbr\u003e 6 Scientific Theories and Deflationary Representation\u003cbr\u003e 7 Representation as Inference\u003cbr\u003e\u003cbr\u003e Part III Implications\u003cbr\u003e 8 Lessons from the Philosophy of Art\u003cbr\u003e 9 Scientific Epistemology Transformed\u003cbr\u003e\u003cbr\u003e Notes\u003cbr\u003e References\u003cbr\u003e Index","brand":"The University of Chicago Press","offers":[{"title":"Default Title","offer_id":48732933456215,"sku":"9780226830049","price":26.6,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780226830049.jpg?v=1719999009"},{"product_id":"macroeconomic-models-and-controversies-9780333585894","title":"Macroeconomic Models and Controversies","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eProviding an introduction to major topics in macroeconomic theory, this book offers the reader three keys for comparing different models. The first key is a mathematical reformulation of Say's Law. The second and third keys deal with the circulation of money and the labour market respectively.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface - Introduction - Keynes and the Classics - Keynesian Macroeconomic Theory - Neoclassical Macroeconomics Reproposed - Macroeconomic Theory of Aggregate Supply. From the Keynesian-Monetarist Debate to the New Classical Macroeconomics - Macroeconomics of Rationing Equilibria - Bibliography - Index","brand":"Palgrave Macmillan","offers":[{"title":"Default Title","offer_id":48733604970839,"sku":"9780333585894","price":116.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780333585894.jpg?v=1791455367"},{"product_id":"contact-mechanics-in-tribology-61-solid-mechanics-and-its-applications-9780792352570","title":"Contact Mechanics in Tribology 61 Solid Mechanics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e1 Introduction.- 2 Mechanics of Discrete Contact.- 3 Friction in Sliding\/Rolling Contact.- 4 Contact of Inhomogeneous Bodies.- 5 Wear Models.- 6 Wear Contact Problems.- 7 Wear of Inhomogeneous Bodies.- 8 Wear of Components.- 9 Conclusion.- 10 References.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1. Introduction. 2. Mechanics of Discrete  Contact. 3. Friction in Sliding\/Rolling Contact. 4.  Contact of Inhomogeneous Bodies. 5. Wear Models. 6. Wear  Contact Problems. 7. Wear of Inhomogeneous Bodies. 8. Wear  of Components. 9. Conclusion. 10. References.","brand":"Springer","offers":[{"title":"Default Title","offer_id":48737281442135,"sku":"9780792352570","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"computational-science-and-engineering-9780961408817","title":"Computational Science and Engineering","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eEncompasses the full range of computational science and engineering from modelling to solution, both analytical and numerical. It develops a framework for the equations and numerical methods of applied mathematics. Gilbert Strang has taught this material to thousands of engineers and scientists (and many more on MIT's OpenCourseWare 18.085-6). His experience is seen in his clear explanations, wide range of examples, and teaching method. The book is solution-based and not formula-based: it integrates analysis and algorithms and MATLAB codes to explain each topic as effectively as possible. The topics include applied linear algebra and fast solvers, differential equations with finite differences and finite elements, Fourier analysis and optimization. This book also serves as a reference for the whole community of computational scientists and engineers. Supporting resources, including MATLAB codes, problem solutions and video lectures from Gilbert Strang's 18.085 courses at MIT, are provi","brand":"Wellesley-Cambridge Press,U.S.","offers":[{"title":"Default Title","offer_id":48737931395415,"sku":"9780961408817","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780961408817.jpg?v=1723811604"},{"product_id":"mathematical-methods-in-the-earth-and-environmental-sciences-9781107117488","title":"Mathematical Methods in the Earth and","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe Earth and environmental sciences are becoming progressively more quantitative due to the increased use of mathematical models and new data analysis techniques. This accessible introduction presents an overview of the mathematical methods essential for understanding Earth processes, providing an invaluable resource for students and early career researchers who may have missed (or forgotten) the mathematics they need to succeed as scientists. Topics build gently from basic methods such as calculus to more advanced techniques including linear algebra and differential equations. The practical applications of the mathematical methods to a variety of topics are discussed, ranging from atmospheric science and oceanography to biogeochemistry and geophysics. Including over 530 exercises and end-of-chapter problems, as well as additional computer codes in Python and MATLAB, this book supports readers in applying appropriate analytical or computational methods to solving real research questio\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface; 1. Estimation and dimensional analysis; 2. Derivatives and integrals; 3. Series and summations; 4. Scalars, vectors, and matrices; 5. Probability; 6. Ordinary differential equations; 7. Vectors and calculus; 8. Special functions; 9. Fourier series and integral transforms; 10. Partial differential equations; 11. Tensors; Appendix A. Units and dimensions; Appendix B. Tables of useful formulae; Appendix C. Complex numbers; Notes; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738239938903,"sku":"9781107117488","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781107117488.jpg?v=1723811850"},{"product_id":"introduction-to-numerical-geodynamic-modelling-9781107143142","title":"Introduction to Numerical Geodynamic Modelling","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis hands-on introduction to numerical geodynamic modelling provides a solid grounding in the necessary mathematical theory and techniques, including continuum mechanics and partial differential equations, before introducing key numerical modelling methods and applications. Fully updated, this second edition includes four completely new chapters covering the most recent advances in modelling inertial processes, seismic cycles and fluid-solid interactions, and the development of adaptive mesh refinement algorithms. Many well-documented, state-of-the-art visco-elasto-plastic 2D models are presented, which allow robust modelling of key geodynamic processes. Requiring only minimal prerequisite mathematical training, and featuring over sixty practical exercises and ninety MATLAB examples, this user-friendly resource encourages experimentation with geodynamic models. It is an ideal introduction for advanced courses and can be used as a self-study aid for graduates seeking to master geodynamic modelling for their own research projects.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'A great introduction to computational geodynamics with vivid examples, hands-on exercises and step-by-step derivations of formulas. Even better than the first edition.' Sascha Brune, Das Helmholtz-Zentrum Potsdam – Deutsches GeoForschungsZentrum\u003cbr\u003e'This book is so much more than an introduction to geodynamic modelling. Taras Gerya opens the world of geodynamic experiments by taking the reader through a carefully designed set of hands-on programming exercises that will convince you that modelling is not terribly complicated, but a process to logically follow through. Go ahead and get started!' Susanne Buiter, Geological Survey of Norway\u003cbr\u003e'This comprehensive textbook challenges all solid Earth scientists to give geodynamic modelling a try in a hands-on, empowering style. The new edition covers even more ground, including cutting-edge topics. A great achievement, and the community will be the better for it.' Thorsten Becker, University of Texas, Austin\u003cbr\u003ePraise for the first edition: '… the book provides excellent value for those wanting an introduction to the field. Anyone who works carefully through this book and completes all the exercises should be well prepared for further work in geodynamic modelling.' Geoscientist\u003cbr\u003ePraise for the first edition: 'The book is written in a light and engaging style such that it deserves a place on the recommended reading list of any undergraduate or Masters course that includes geodynamics. Additionally, it will be a valuable resource for any geoscientist who wants to include geodynamic modelling within their research activities.' Geological Magazine\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1. The continuity equation; 2. Density and gravity; 3. Numerical solutions of partial differential equations; 4. Stress and strain; 5. The momentum equation; 6. Viscous rheology of rocks; 7. Numerical solutions of the momentum and continuity equations; 8. The advection equation and marker-in-cell method; 9. The heat conservation equation; 10. Numerical solution of the heat conservation equation; 11. 2D thermomechanical code structure; 12. Elasticity and plasticity; 13. 2D implementation of visco-elasto-plasticity; 14. 2D thermomechanical modelling of inertial processes; 15. Seismo-thermomechanical modelling; 16. Hydro-thermomechanical modelling; 17. Adaptive mesh refinement; 18. The multigrid method; 19. Programming of 3D problems; 20. Numerical benchmarks; 21. Design of 2D numerical geodynamic models; Epilogue: outlook; Appendix: MATLAB® program examples; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738241544535,"sku":"9781107143142","price":66.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781107143142.jpg?v=1791469650"},{"product_id":"geomathematics-9781108419444","title":"Geomathematics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eGeomathematics provides a comprehensive summary of the mathematical principles behind key topics in geophysics and geodesy, covering the foundations of gravimetry, geomagnetics and seismology. Theorems and their proofs explain why physical realities in geoscience are the logical mathematical consequences of basic laws. The book also derives and analyzes the theory and numerical aspects of established systems of basis functions; and presents an algorithm for combining different types of trial functions. Topics cover inverse problems and their regularization, the Laplace\/Poisson equation, boundary-value problems, foundations of potential theory, the Poisson integral formula, spherical harmonics, Legendre polynomials and functions, radial basis functions, the Biot-Savart law, decomposition theorems (orthogonal, Helmholtz, and Mie), basics of continuum mechanics, conservation laws, modelling of seismic waves, the Cauchy-Navier equation, seismic rays, and travel-time tomography. Each chapter ends with review questions, with solutions for instructors available online, providing a valuable reference for graduate students and researchers.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1. Introduction; 2. Required Mathematical Basics; 3. Gravitation and Harmonic Functions; 4. Basis Functions; 5. Inverse Problems; 6. The Magnetic Field; 7. Mathematical Models in Seismology; Appendix A. Hints for the Exercises; Appendix B. Questions for Understanding; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738286534999,"sku":"9781108419444","price":85.42,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108419444.jpg?v=1791469696"},{"product_id":"thinking-probabilistically-9781108789981","title":"Thinking Probabilistically","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eProbability theory has diverse applications in a plethora of fields, including physics, engineering, computer science, chemistry, biology and economics. This book will familiarize students with various applications of probability theory, stochastic modeling and random processes, using examples from all these disciplines and more. The reader learns via case studies and begins to recognize the sort of problems that are best tackled probabilistically. The emphasis is on conceptual understanding, the development of intuition and gaining insight, keeping technicalities to a minimum. Nevertheless, a glimpse into the depth of the topics is provided, preparing students for more specialized texts while assuming only an undergraduate-level background in mathematics. The wide range of areas covered - never before discussed together in a unified fashion  includes Markov processes and random walks, Langevin and FokkerPlanck equations, noise, generalized central limit theorem and extreme values stat\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'A remarkable demonstration that advanced topics need not be esoteric. Amir takes us through random walks on networks, extreme value statistics, Kramers theory, anomalous diffusion and other topics generally omitted from introductory texts, always rooting every discussion in applications of terrific current interest. I found the discussion of Lévy-stable distributions especially insightful as a principled approach to the nonstandard walks that abound in contexts from biophysics to finance.' Philip C. Nelson, University of Pennsylvania\u003cbr\u003e'The book is a suitable springboard for self-study because it introduces a wide variety of topics and contains many references to current work. In the classroom, the book can function either as the basis for a course in special topics or as a source of material to spice up more traditional statistical-mechanics courses … the methods for studying random phenomena introduced in Thinking Probabilistically will help readers understand reasoning techniques that may not be terribly familiar to physicists. Moreover, following the author's arguments is a rewarding intellectual exercise in its own right.' Rob de Ruyter, Physics Today\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1. Introduction; 2. Random walks; 3. Langevin and Focker–Planck equations and their applications; 4. Escape over a barrier; 5. Noise; 6. Generalized central limit theorem and extreme value statistics; 7. Anomalous diff usion; 8. Random matrix theory; 9. Percolation theory; Appendix A. Review of basic probability concepts and common distributions; Appendix B. A brief linear algebra reminder, and some Gaussian integrals; Appendix C. Contour integration and Fourier transform refresher; Appendix D. Review of Newtonian mechanics, basic statistical mechanics and Hessians; Appendix E. Minimizing functionals, the divergence theorem and saddle point approximations; Appendix F. Notation, notation...; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738330837335,"sku":"9781108789981","price":51.21,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108789981.jpg?v=1791469738"},{"product_id":"computational-statistical-physics-9781108841429","title":"Computational Statistical Physics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eProviding a detailed and pedagogical account of the rapidly-growing field of computational statistical physics, this book covers both the theoretical foundations of equilibrium and non-equilibrium statistical physics, and also modern, computational applications such as percolation, random walks, magnetic systems, machine learning dynamics, and spreading processes on complex networks. A detailed discussion of molecular dynamics simulations is also included, a topic of great importance in biophysics and physical chemistry. The accessible and self-contained approach adopted by the authors makes this book suitable for teaching courses at graduate level, and numerous worked examples and end of chapter problems allow students to test their progress and understanding.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface; Part I. Stochastic Methods: 1. Random Numbers; 2. Random-Geometrical Models; 3. Equilibrium Systems; 4. Monte-Carlo Methods; 5. Phase Transitions; 6. Cluster Algorithms; 7. Histogram Methods; 8. Renormalization Group; 9. Learning and Optimizing; 10. Parallelization; 11. Non-Equilibrium Systems; Part II. Molecular Dynamics: 12. Basic Molecular Dynamics; 13. Optimizing Molecular Dynamics; 14. Dynamics of Composed Particles; 15. Long-Range Potentials; 16. Canonical Ensemble; 17. Inelastic Collisions in Molecular Dynamics; 18. Event-Driven Molecular Dynamics; 19. Non-Spherical Particles; 20. Contact Dynamics; 21. Discrete Fluid Models; 22. Ab-Initio Simulations; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738343321943,"sku":"9781108841429","price":59.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108841429.jpg?v=1791469749"},{"product_id":"numerical-relativity-starting-from-scratch-9781108928250","title":"Numerical Relativity Starting from Scratch","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eNumerical relativity has emerged as the key tool to model gravitational waves - recently detected for the first time - that are emitted when black holes or neutron stars collide. This book provides a pedagogical, accessible, and concise introduction to the subject. Relying heavily on analogies with Newtonian gravity, scalar fields and electromagnetic fields, it introduces key concepts of numerical relativity in a context familiar to readers without prior expertise in general relativity. Readers can explore these concepts by working through numerous exercises, and can see them ''in action'' by experimenting with the accompanying Python sample codes, and so develop familiarity with many techniques commonly employed by publicly available numerical relativity codes. This is an attractive, student-friendly resource for short courses on numerical relativity, as well as providing supplementary reading for courses on general relativity and computational physics.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'Computational general relativity has now become a central tool for the exploration of the astrophysical universe, and gravitational-wave astronomy would not be possible without it. A burgeoning or seasoned astrophysicist who wishes to be up to date must therefore acquire an awareness of the field's methods and main achievements. But where to begin? With this book! Baumgarte and Shapiro are leading experts (indeed, founding experts) of this field, and with their trademark lucid and engaging prose, they take us gently by the hand on a comprehensive guided tour. Mysterious notions (lapse, shift, extrinsic curvature, constraint equations) are introduced seamlessly, and the book features a gallery of the field's most important results to date. A superb achievement for the great benefit of the scientific community.' Eric Poisson, University of Guelph; author of A Relativist's Toolkit\u003cbr\u003e'Numerical relativity well deserves its reputation as a subject of great beauty yet prodigious conceptual difficulty and daunting technical complexity. This outstanding text, by two leading practitioners of the field, is a wonderful Rosetta Stone for those seeking an efficient path toward a working knowledge of the subject. For me it will serve as an essential reference. I'm sorry only that it was not available sooner.' Robert Eisenstein, Massachusetts Institute of Technology\u003cbr\u003e'This is an excellent book explaining the general relativistic two-body problem and its numerical treatment in a highly pedagogical manner to a broad scientific audience. Besides the main topic, readers will also gain some unexpected insight and new viewpoints on numerous wider aspects of Einstein's theory.' Ulrich Sperhake, University of Cambridge\u003cbr\u003e'Black holes and gravitational waves are, thanks to new observations, fast-advancing frontiers of astronomy that attract wide interest. Their implications are best addressed by powerful computers, so this text, by two acknowledged world experts, is especially welcome and timely.' Martin Rees, Astronomer Royal; author of Gravity's Fatal Attraction\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface; 1. Newton's and Einstein's gravity; 2. Foliations of spacetime: constraint and evolution equations; 3. Solving the constraint equations; 4 Solving the evolution equations; 5. Numerical simulations of black-hole binaries; Epilogue; Appendix A. A brief review of tensor properties; Appendix B. A brief introduction to some numerical techniques; Appendix C. A very brief introduction to matter sources; Appendix D. A summary of important results; Appendix E. Answers to selected problems; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738345648471,"sku":"9781108928250","price":51.21,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108928250.jpg?v=1723811955"},{"product_id":"advanced-geodynamics-9781316519622","title":"Advanced Geodynamics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eDavid Sandwell developed this advanced textbook over a period of nearly 30 years for his graduate course at Scripps Institution of Oceanography. The book augments the classic textbook Geodynamics by Don Turcotte and Jerry Schubert, presenting more complex and foundational mathematical methods and approaches to geodynamics. The main new tool developed in the book is the multi-dimensional Fourier transform for solving linear partial differential equations. The book comprises nineteen chapters, including: the latest global data sets; quantitative plate tectonics; plate driving forces associated with lithospheric heat transfer and subduction; the physics of the earthquake cycle; postglacial rebound; and six chapters on gravity field development and interpretation. Each chapter has a set of student exercises that make use of the higher-level mathematical and numerical methods developed in the book. Solutions to the exercises are available online for course instructors, on request.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'Advanced Geodynamics brings the unique perspective of a leading geophysicist to the solution of a wide array of problems in geodynamics. The approach emphasizes the use of advanced mathematics, in particular the Fourier transform, to obtain a quantitative understanding of the processes involved in shaping the Earth's surface. The advanced mathematical approach not only enhances the elegance of the solutions, but it enables the consideration of many problems not accessible with less sophisticated mathematical methods. The choice of problems benefits from the deep physical insights of the author to their solutions. The book discusses the physical processes involved in plate tectonics and the earthquake cycle and provides the latest relevant observational data sets. An emphasis is also placed on the use of gravity data to learn about these processes. The book is the product of decades of teaching by the author and is a must read for students of the physics of the Earth with the appropriate mathematical background.' Gerald Schubert, University of California, Los Angeles; co-author of Geodynamics\u003cbr\u003e'Most authors would find writing a sequel to Turcotte and Schubert's classic book on Geodynamics a daunting task. Not so for David Sandwell, whose first book is a wonderful mix of observations and theory, elegant mathematics and a focus on the oceans and the Fourier method which together help illuminate some of the fundamental physical processes that underlie plate tectonics.' Tony Watts, University of Oxford; author of Isostasy and Flexure of the Lithosphere\u003cbr\u003e'Advanced Geodynamics: The Fourier Transform Method by David Sandwell is a godsend for advanced undergraduate students, graduate students, and researchers actively engaged in the broad area of geodynamics. It complements the classic Geodynamics book by Turcotte \u0026amp; Schubert in a way nothing else could: by elevating the treatment to real, cutting-edge research problems via Fourier transforms that deliver simple and elegant solutions to complicated science problems.' Paul Wessel, University of Hawaii\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1. Observations Related to Plate Tectonics; 2. Fourier Transform Methods in Geophysics; 3. Plate Kinematics; 4. Marine Magnetic Anomalies; 5. Cooling of the Oceanic Lithosphere; 6. A Brief Review of Elasticity; 7. Crustal Structure, Isostasy, Swell Push Force, and Rheology; 8. Flexure of the Lithosphere; 9. Flexure Examples; 10. Elastic Solutions for Strike-Slip Faulting; 11. Heat Flow Paradox; 12. The Gravity Field of the Earth, Part I; 13. Reference Earth Model: WGS84; 14. Laplace's Equation in Spherical Coordinates; 15. Laplace's Equation in Cartesian Coordinates and Satellite Altimetry; 16. Poisson's Equation in Cartesian Coordinates; 17. Gravity\/Topography Transfer Function and Isostatic Geoid Anomalies; 18. Postglacial Rebound; 19. Driving Forces of Plate Tectonics; References; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48738562703703,"sku":"9781316519622","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781316519622.jpg?v=1720049478"},{"product_id":"mathematical-modeling-and-computation-in-finance-with-exercises-and-python-and-matlab-computer-codes-9781786347947","title":"Mathematical Modeling And Computation In Finance:","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis book discusses the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The stochastic models, numerical valuation techniques, computational aspects, financial products, and risk management applications presented will enable readers to progress in the challenging field of computational finance.When the behavior of financial market participants changes, the corresponding stochastic mathematical models describing the prices may also change. Financial regulation may play a role in such changes too. The book thus presents several models for stock prices, interest rates as well as foreign-exchange rates, with increasing complexity across the chapters. As is said in the industry, 'do not fall in love with your favorite model.' The book covers equity models before moving to short-rate and other interest rate models. We cast these models for interest rate into the Heath-Jarrow-Morton framework, show relations between the different models, and explain a few interest rate products and their pricing.The chapters are accompanied by exercises. Students can access solutions to selected exercises, while complete solutions are made available to instructors. The MATLAB and Python computer codes used for most tables and figures in the book are made available for both print and e-book users. This book will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance. The topics that are discussed are relevant for MSc and PhD students, academic researchers, and for quants in the financial industry.Supplementary Material:Solutions Manual is available to instructors who adopt this textbook for their courses.  Please contact sales@wspc.com.","brand":"World Scientific Europe Ltd","offers":[{"title":"Default Title","offer_id":48741447631191,"sku":"9781786347947","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781786347947.jpg?v=1720057615"},{"product_id":"science-by-simulation-volume-1-a-mezze-of-mathematical-models-9781800611214","title":"Science By Simulation - Volume 1: A Mezze Of","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eA 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.","brand":"World Scientific Europe Ltd","offers":[{"title":"Default Title","offer_id":48741753520471,"sku":"9781800611214","price":40.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781800611214.jpg?v=1720058692"},{"product_id":"introduction-to-multiscale-mathematical-modeling-9781800612310","title":"Introduction To Multiscale Mathematical Modeling","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis book introduces the reader to multiscale mathematical modeling that starts by describing a physical process at the microscopic level, and is followed by the macroscopic description of that process. There are two preliminary chapters introducing the main equations of mathematical physics and serves as revision of all of the necessary mathematical notions needed to navigate the domain of multiscale research.The author gives a rigorous presentation of the tools of mathematical modeling, as well as an evaluation of the errors of the method. This allows readers to analyze the limitations and accuracy of the method.The book is accessible to a wide range of readers, from specialists in engineering to applied mathematicians working in the applications of materials science, biophysics and medicine.","brand":"World Scientific Europe Ltd","offers":[{"title":"Default Title","offer_id":48741754405207,"sku":"9781800612310","price":63.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781800612310.jpg?v=1720058695"},{"product_id":"basic-stochastic-processes-9781848218826","title":"Basic Stochastic Processes","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis book presents basic stochastic processes, stochastic calculus including Lévy processes on one hand, and Markov and Semi Markov models on the other. From the financial point of view, essential concepts such as the Black and Scholes model, VaR indicators, actuarial evaluation, market values, fair pricing play a central role and will be presented.\u003c\/p\u003e \u003cp\u003eThe authors also present basic concepts so that this series is relatively self-contained for the main audience formed by actuaries and particularly with ERM (enterprise risk management) certificates, insurance risk managers, students in Master in mathematics or economics and people involved in Solvency II for insurance companies and in Basel II and III for banks.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003eINTRODUCTION  xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 1. BASIC PROBABILISTIC TOOLS FOR STOCHASTIC MODELING 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1. Probability space and random variables 1\u003c\/p\u003e \u003cp\u003e1.2. Expectation and independence 4\u003c\/p\u003e \u003cp\u003e1.3. Main distribution probabilities 7\u003c\/p\u003e \u003cp\u003e1.3.1. Binomial distribution 7\u003c\/p\u003e \u003cp\u003e1.3.2. Negative exponential distribution 8\u003c\/p\u003e \u003cp\u003e1.3.3. Normal (or Laplace–Gauss) distribution 8\u003c\/p\u003e \u003cp\u003e1.3.4. Poisson distribution 11\u003c\/p\u003e \u003cp\u003e1.3.5. Lognormal distribution 11\u003c\/p\u003e \u003cp\u003e1.3.6. Gamma distribution 12\u003c\/p\u003e \u003cp\u003e1.3.7. Pareto distribution 13\u003c\/p\u003e \u003cp\u003e1.3.8. Uniform distribution 16\u003c\/p\u003e \u003cp\u003e1.3.9. Gumbel distribution 16\u003c\/p\u003e \u003cp\u003e1.3.10. Weibull distribution 16\u003c\/p\u003e \u003cp\u003e1.3.11. Multi-dimensional normal distribution 17\u003c\/p\u003e \u003cp\u003e1.3.12. Extreme value distribution 19\u003c\/p\u003e \u003cp\u003e1.4. The normal power (NP) approximation 28\u003c\/p\u003e \u003cp\u003e1.5. Conditioning 31\u003c\/p\u003e \u003cp\u003e1.6. Stochastic processes 39\u003c\/p\u003e \u003cp\u003e1.7. Martingales 43\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 2. HOMOGENEOUS AND NON-HOMOGENEOUS RENEWAL MODELS 47\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1. Introduction 47\u003c\/p\u003e \u003cp\u003e2.2. Continuous time non-homogeneous convolutions 49\u003c\/p\u003e \u003cp\u003e2.2.1. Non-homogeneous convolution product 49\u003c\/p\u003e \u003cp\u003e2.3. Homogeneous and non-homogeneous renewal processes 53\u003c\/p\u003e \u003cp\u003e2.4. Counting processes and renewal functions 56\u003c\/p\u003e \u003cp\u003e2.5. Asymptotical results in the homogeneous case 61\u003c\/p\u003e \u003cp\u003e2.6. Recurrence times in the homogeneous case 63\u003c\/p\u003e \u003cp\u003e2.7. Particular case: the Poisson process 66\u003c\/p\u003e \u003cp\u003e2.7.1. Homogeneous case 66\u003c\/p\u003e \u003cp\u003e2.7.2. Non-homogeneous case 68\u003c\/p\u003e \u003cp\u003e2.8. Homogeneous alternating renewal processes 69\u003c\/p\u003e \u003cp\u003e2.9. Solution of non-homogeneous discrete timevevolution equation 71\u003c\/p\u003e \u003cp\u003e2.9.1. General method 71\u003c\/p\u003e \u003cp\u003e2.9.2. Some particular formulas 73\u003c\/p\u003e \u003cp\u003e2.9.3. Relations between discrete time and continuous time renewal equations 74\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 3. MARKOV CHAINS 77\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1. Definitions 77\u003c\/p\u003e \u003cp\u003e3.2. Homogeneous case 78\u003c\/p\u003e \u003cp\u003e3.2.1. Basic definitions 78\u003c\/p\u003e \u003cp\u003e3.2.2. Markov chain state classification 81\u003c\/p\u003e \u003cp\u003e3.2.3. Computation of absorption probabilities 87\u003c\/p\u003e \u003cp\u003e3.2.4. Asymptotic behavior 88\u003c\/p\u003e \u003cp\u003e3.2.5. Example: a management problem in an insurance company 93\u003c\/p\u003e \u003cp\u003e3.3. Non-homogeneous Markov chains 95\u003c\/p\u003e \u003cp\u003e3.3.1. Definitions 95\u003c\/p\u003e \u003cp\u003e3.3.2. Asymptotical results 98\u003c\/p\u003e \u003cp\u003e3.4. Markov reward processes 99\u003c\/p\u003e \u003cp\u003e3.4.1. Classification and notation 99\u003c\/p\u003e \u003cp\u003e3.5. Discrete time Markov reward processes (DTMRWPs) 102\u003c\/p\u003e \u003cp\u003e3.5.1. Undiscounted case 102\u003c\/p\u003e \u003cp\u003e3.5.2. Discounted case 105\u003c\/p\u003e \u003cp\u003e3.6. General algorithms for the DTMRWP 111\u003c\/p\u003e \u003cp\u003e3.6.1. Homogeneous MRWP 112\u003c\/p\u003e \u003cp\u003e3.6.2. Non-homogeneous MRWP 112\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 4. HOMOGENEOUS AND NON-HOMOGENEOUS SEMI-MARKOV MODELS 113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1. Continuous time semi-Markov processes 113\u003c\/p\u003e \u003cp\u003e4.2. The embedded Markov chain 117\u003c\/p\u003e \u003cp\u003e4.3. The counting processes and the associated semi-Markov process 118\u003c\/p\u003e \u003cp\u003e4.4. Initial backward recurrence times 120\u003c\/p\u003e \u003cp\u003e4.5. Particular cases of MRP 122\u003c\/p\u003e \u003cp\u003e4.5.1. Renewal processes and Markov chains 122\u003c\/p\u003e \u003cp\u003e4.5.2. MRP of zero-order (PYKE (1962)) 122\u003c\/p\u003e \u003cp\u003e4.5.3. Continuous Markov processes 124\u003c\/p\u003e \u003cp\u003e4.6. Examples 124\u003c\/p\u003e \u003cp\u003e4.7. Discrete time homogeneous and non-homogeneous semi-Markov processes 127\u003c\/p\u003e \u003cp\u003e4.8. Semi-Markov backward processes in discrete time 129\u003c\/p\u003e \u003cp\u003e4.8.1. Definition in the homogeneous case 129\u003c\/p\u003e \u003cp\u003e4.8.2. Semi-Markov backward processes in discrete time for the non-homogeneous case 130\u003c\/p\u003e \u003cp\u003e4.8.3. DTSMP numerical solutions 133\u003c\/p\u003e \u003cp\u003e4.9. Discrete time reward processes 137\u003c\/p\u003e \u003cp\u003e4.9.1. Undiscounted SMRWP 137\u003c\/p\u003e \u003cp\u003e4.9.2. Discounted SMRWP 141\u003c\/p\u003e \u003cp\u003e4.9.3. General algorithms for DTSMRWP 144\u003c\/p\u003e \u003cp\u003e4.10. Markov renewal functions in the homogeneous case 146\u003c\/p\u003e \u003cp\u003e4.10.1. Entrance times 146\u003c\/p\u003e \u003cp\u003e4.10.2. The Markov renewal equation 150\u003c\/p\u003e \u003cp\u003e4.10.3. Asymptotic behavior of an MRP 151\u003c\/p\u003e \u003cp\u003e4.10.4. Asymptotic behavior of SMP 153\u003c\/p\u003e \u003cp\u003e4.11. Markov renewal equations for the non-homogeneous case 158\u003c\/p\u003e \u003cp\u003e4.11.1. Entrance time 158\u003c\/p\u003e \u003cp\u003e4.11.2. The Markov renewal equation 162\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 5. STOCHASTIC CALCULUS  165\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1. Brownian motion 165\u003c\/p\u003e \u003cp\u003e5.2. General definition of the stochastic integral 167\u003c\/p\u003e \u003cp\u003e5.2.1. Problem of stochastic integration 167\u003c\/p\u003e \u003cp\u003e5.2.2. Stochastic integration of simple predictable processes and semi-martingales 168\u003c\/p\u003e \u003cp\u003e5.2.3. General definition of the stochastic integral 170\u003c\/p\u003e \u003cp\u003e5.3. Itô’s formula 177\u003c\/p\u003e \u003cp\u003e5.3.1. Quadratic variation of a semi-martingale 177\u003c\/p\u003e \u003cp\u003e5.3.2. Itô’s formula 179\u003c\/p\u003e \u003cp\u003e5.4. Stochastic integral with standard Brownian motion as an integrator process 180\u003c\/p\u003e \u003cp\u003e5.4.1. Case of simple predictable processes 181\u003c\/p\u003e \u003cp\u003e5.4.2. Extension to general integrator processes 183\u003c\/p\u003e \u003cp\u003e5.5. Stochastic differentiation 184\u003c\/p\u003e \u003cp\u003e5.5.1. Stochastic differential 184\u003c\/p\u003e \u003cp\u003e5.5.2. Particular cases 184\u003c\/p\u003e \u003cp\u003e5.5.3. Other forms of Itô’s formula 185\u003c\/p\u003e \u003cp\u003e5.6. Stochastic differential equations 191\u003c\/p\u003e \u003cp\u003e5.6.1. Existence and unicity general theorem 191\u003c\/p\u003e \u003cp\u003e5.6.2. Solution of stochastic differential equations 195\u003c\/p\u003e \u003cp\u003e5.6.3. Diffusion processes 199\u003c\/p\u003e \u003cp\u003e5.7. Multidimensional diffusion processes 202\u003c\/p\u003e \u003cp\u003e5.7.1. Definition of multidimensional Itô and diffusion processes 203\u003c\/p\u003e \u003cp\u003e5.7.2. Properties of multidimensional diffusion processes 203\u003c\/p\u003e \u003cp\u003e5.7.3. Kolmogorov equations 205\u003c\/p\u003e \u003cp\u003e5.7.4. The Stroock–Varadhan martingale characterization of diffusion processes 208\u003c\/p\u003e \u003cp\u003e5.8. Relation between the resolution of PDE and SDE problems. The Feynman–Kac formula 209\u003c\/p\u003e \u003cp\u003e5.8.1. Terminal payoff 209\u003c\/p\u003e \u003cp\u003e5.8.2. Discounted payoff function 210\u003c\/p\u003e \u003cp\u003e5.8.3. Discounted payoff function and payoff rate 210\u003c\/p\u003e \u003cp\u003e5.9. Application to option theory 213\u003c\/p\u003e \u003cp\u003e5.9.1. Options 213\u003c\/p\u003e \u003cp\u003e5.9.2. Black and Scholes model 216\u003c\/p\u003e \u003cp\u003e5.9.3. The Black and Scholes partial differential equation (BSPDE) and the BS formula 216\u003c\/p\u003e \u003cp\u003e5.9.4. Girsanov theorem 219\u003c\/p\u003e \u003cp\u003e5.9.5. The risk-neutral measure and the martingale property 221\u003c\/p\u003e \u003cp\u003e5.9.6. The risk-neutral measure and the evaluation of derivative products 224\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 6. LÉVY PROCESSES 227\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1. Notion of characteristic functions 227\u003c\/p\u003e \u003cp\u003e6.2. Lévy processes 228\u003c\/p\u003e \u003cp\u003e6.3. Lévy–Khintchine formula 230\u003c\/p\u003e \u003cp\u003e6.4. Subordinators 234\u003c\/p\u003e \u003cp\u003e6.5. Poisson measure for jumps 234\u003c\/p\u003e \u003cp\u003e6.5.1. The Poisson random measure 234\u003c\/p\u003e \u003cp\u003e6.5.2. The compensated Poisson process 235\u003c\/p\u003e \u003cp\u003e6.5.3. Jump measure of a Lévy process 236\u003c\/p\u003e \u003cp\u003e6.5.4. The Itô–Lévy decomposition 236\u003c\/p\u003e \u003cp\u003e6.6. Markov and martingale properties of Lévy processes 237\u003c\/p\u003e \u003cp\u003e6.6.1. Markov property 237\u003c\/p\u003e \u003cp\u003e6.6.2. Martingale properties 239\u003c\/p\u003e \u003cp\u003e6.6.3. Itô formula 240\u003c\/p\u003e \u003cp\u003e6.7. Examples of Lévy processes 240\u003c\/p\u003e \u003cp\u003e6.7.1. The lognormal process: Black and Scholes process 240\u003c\/p\u003e \u003cp\u003e6.7.2. The Poisson process 241\u003c\/p\u003e \u003cp\u003e6.7.3. Compensated Poisson process 242\u003c\/p\u003e \u003cp\u003e6.7.4. The compound Poisson process 242\u003c\/p\u003e \u003cp\u003e6.8. Variance gamma (VG) process 244\u003c\/p\u003e \u003cp\u003e6.8.1. The gamma distribution 244\u003c\/p\u003e \u003cp\u003e6.8.2. The VG distribution 245\u003c\/p\u003e \u003cp\u003e6.8.3. The VG process 246\u003c\/p\u003e \u003cp\u003e6.8.4. The Esscher transformation 247\u003c\/p\u003e \u003cp\u003e6.8.5. The Carr–Madan formula for the European call 249\u003c\/p\u003e \u003cp\u003e6.9. Hyperbolic Lévy processes 250\u003c\/p\u003e \u003cp\u003e6.10. The Esscher transformation 252\u003c\/p\u003e \u003cp\u003e6.10.1. Definition 252\u003c\/p\u003e \u003cp\u003e6.10.2. Option theory with hyperbolic Lévy processes 253\u003c\/p\u003e \u003cp\u003e6.10.3. Value of the European option call 255\u003c\/p\u003e \u003cp\u003e6.11. The Brownian–Poisson model with jumps 256\u003c\/p\u003e \u003cp\u003e6.11.1. Mixed arithmetic Brownian–Poisson and geometric Brownian–Poisson processes 256\u003c\/p\u003e \u003cp\u003e6.11.2. Merton model with jumps 258\u003c\/p\u003e \u003cp\u003e6.11.3. Stochastic differential equation (SDE) for mixed arithmetic Brownian–Poisson and geometric Brownian–Poisson processes 261\u003c\/p\u003e \u003cp\u003e6.11.4. Value of a European call for the lognormal Merton model 264\u003c\/p\u003e \u003cp\u003e6.12. Complete and incomplete markets 264\u003c\/p\u003e \u003cp\u003e6.13. Conclusion 265\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCHAPTER 7. ACTUARIAL EVALUATION, VAR AND STOCHASTIC INTEREST RATE MODELS 267\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1. VaR technique 267\u003c\/p\u003e \u003cp\u003e7.2. Conditional VaR value 271\u003c\/p\u003e \u003cp\u003e7.3. Solvency II 276\u003c\/p\u003e \u003cp\u003e7.3.1. The SCR indicator 276\u003c\/p\u003e \u003cp\u003e7.3.2. Calculation of MCR 278\u003c\/p\u003e \u003cp\u003e7.3.3. ORSA approach 279\u003c\/p\u003e \u003cp\u003e7.4. Fair value 280\u003c\/p\u003e \u003cp\u003e7.4.1. Definition 280\u003c\/p\u003e \u003cp\u003e7.4.2. Market value of financial flows 281\u003c\/p\u003e \u003cp\u003e7.4.3. Yield curve 281\u003c\/p\u003e \u003cp\u003e7.4.4. Yield to maturity for a financial investment and a bond 283\u003c\/p\u003e \u003cp\u003e7.5. Dynamic stochastic time continuous time model for instantaneous interest rate 284\u003c\/p\u003e \u003cp\u003e7.5.1. Instantaneous deterministic interest rate 284\u003c\/p\u003e \u003cp\u003e7.5.2. Yield curve associated with a deterministic instantaneous interest rate 285\u003c\/p\u003e \u003cp\u003e7.5.3. Dynamic stochastic continuous time model for instantaneous interest rate 286\u003c\/p\u003e \u003cp\u003e7.5.4. The OUV stochastic model 287\u003c\/p\u003e \u003cp\u003e7.5.5. The CIR model 289\u003c\/p\u003e \u003cp\u003e7.6. Zero-coupon pricing under the assumption of no arbitrage 292\u003c\/p\u003e \u003cp\u003e7.6.1. Stochastic dynamics of zero-coupons 292\u003c\/p\u003e \u003cp\u003e7.6.2. The CIR process as rate dynamic 295\u003c\/p\u003e \u003cp\u003e7.7. Market evaluation of financial flows 298\u003c\/p\u003e \u003cp\u003eBIBLIOGRAPHY 301\u003c\/p\u003e \u003cp\u003eINDEX 309\u003c\/p\u003e","brand":"ISTE Ltd and John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48742234456407,"sku":"9781848218826","price":125.06,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781848218826.jpg?v=1723812509"},{"product_id":"special-relativity-an-introduction-with-200-problems-and-solutions-9783030273460","title":"Special Relativity: An Introduction with 200","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis textbook develops Special Relativity in a systematic way and offers problems with detailed solutions to empower students to gain a real understanding of this core subject in physics.  This new edition has been thoroughly updated and has new sections on relativistic fluids, relativistic kinematics and on four-acceleration. The problems and solution section has been significantly expanded and short history sections have been included throughout the book.\u003c\/p\u003e\u003cp\u003eThe approach is structural in the sense that it develops Special Relativity in Minkowski space following the parallel steps as the development of Newtonian Physics in Euclidian space. A second characteristic of the book is that it discusses the mathematics of the theory independently of the physical principles, so that the reader will appreciate their role in the development of the physical theory.\u003c\/p\u003e\u003cp\u003eThe book is intended to be used both as a textbook for an advanced undergraduate teaching course in Special Relativity but also as a reference book for the future. \u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eMathematical Part.- The Structure of the Theories of Physics.- Newtonian Physics.- The Foundation of Special Relativity.- The Physics of the Position Four-Vector.- Relativistic Kinematics.- Four-Acceleration.- Paradoxes.- Mass – Four-Momentum.- Relativistic Reactions.- Four-Force.- Irreducible Decompositions.- The Electromagnetic Field.- Relativistic Angular Momentum.- The Covariant Lorentz Transformation.- Geometric Description of Relativistic Interactions.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743028228439,"sku":"9783030273460","price":72.64,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030273460.jpg?v=1791480468"},{"product_id":"a-primer-on-mathematical-modelling-9783030445409","title":"A Primer on Mathematical Modelling","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eIn this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eA broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eThis book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https:\/\/paola-gervasio.unibs.it\/quarteroni-gervasio\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book is addressed to any student interested in learning how to construct and apply mathematical models.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“The book is extremely well written and is spectacular in its beauty. It is full with colorful pictures and figures, with many clear graphs, algorithms, codes (written in Octave) and tables, which makes reading the book a real joy. … This is a superb book for readers doing their initial steps in the wonderful world of modeling. I recommended it to my 17-year-old nephew, who is now reading it with great enthusiasm.” (Dan Givoli, IACM Expressions, Issue 50, July, 2022)\u003cbr\u003e“It is thus appropriate for junior college students. It is even suitable for self-study and independent research projects. … Professors Quarteroni and Gervasio have written a nice and fun book, which also constitutes a useful toolbox for anyone who wants to get acquainted with the methods of Applied Mathematics.” (Fernando Tohmé, zbMATH 1475.00018, 2022)\u003cbr\u003e\u003cbr\u003e“The book is an outstanding document from an educational point of view. ... The interaction of the simplicity of mathematical methods and the sophistication of the three main applications is very well done. In summary, this new book is highly recommended for both undergraduate and graduate students who are interested in mathematical modeling … .” (Thomas Wick, SIAM Review, Vol. 63 (3), September, 2021)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003e1. A warm-up to models.- 2. Getting started.- 3. Reckoning with the computer.- 4. A virtual surfer for the web.- 5. A network of capillaries.- 6. Predators and preys in the maths ocean.- 7. Take-home message.- 8. Solutions to exercises.\u003c\/p\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743036551511,"sku":"9783030445409","price":33.24,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030445409.jpg?v=1791480485"},{"product_id":"non-local-cell-adhesion-models-symmetries-and-bifurcations-in-1-d-9783030671136","title":"Non-Local Cell Adhesion Models: Symmetries and","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis monograph considers the mathematical modeling of cellular adhesion, a key interaction force in cell biology. While deeply grounded in the biological application of cell adhesion and tissue formation, this monograph focuses on the mathematical analysis of non-local adhesion models. The novel aspect is the non-local term (an integral operator), which accounts for forces generated by long ranged cell interactions. The analysis of non-local models has started only recently, and it has become a vibrant area of applied mathematics. This monograph contributes a systematic analysis of steady states and their bifurcation structure, combining global bifurcation results pioneered by Rabinowitz, equivariant bifurcation theory, and the symmetries of the non-local term. These methods allow readers to analyze and understand cell adhesion on a deep level.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“Modelers who wish to use similar approaches in their modeling will find this a good source of base information, as well as a valuable guide for initiating similar analyses for their own models. Analysts wishing to expand our understanding … will find this book a fine building block. It could also prove a useful resource for graduate students looking for potential projects … . this monograph is an admirable attempt … and hopefully will inspire significant further study.” (Kevin Painter, SIAM Review, Vol. 64 (1), March, 2022)\u003cbr\u003e\u003cbr\u003e“The detailed analysis, as presented here, shows a stimulating interaction between model symmetries, mathematical analysis, and biological reality, which probably are inspired the authors and hopefully the readers of this book too.” (Andrey Zahariev, zbMATH 1473.92001, 2021)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction.- Preliminaries.- The Periodic Problem.- Basic Properties.- Local Bifurcation.- Global Bifurcation.- Non-local Equations with Boundary Conditions.- No-flux Boundary Conditions.- Discussion and future directions.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743044415831,"sku":"9783030671136","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030671136.jpg?v=1791480515"},{"product_id":"measuring-professional-competence-for-the-teaching-of-mathematical-modelling-a-test-instrument-9783030780708","title":"Measuring Professional Competence for the","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis open access book presents a structural model and an associated test instrument designed to provide a detailed analysis of professional competences for teaching mathematical modelling. The conceptualisation is based on the COACTIV model, which describes aspects, areas and facets of professional competences of teachers. The manual provides an overview of the essential teaching skills in application-related contexts and offers the tools needed to capture these aspects. It discusses the objectives and application areas of the instrument, as well as the development of the test. In addition, it describes the implementation and evaluates the quality and results of the structural equation analysis of the model.\u003c\/p\u003e  Teaching mathematical modelling is a cognitively challenging activity for (prospective) teachers. Thus, teacher education requires a detailed analysis of professional competence for teaching mathematical modelling. Measuring this competence requires theoretical models that accurately describe requirements placed upon teachers, as well as appropriate evaluation tools that adequately capture skills and abilities in this field. This book presents an instrument that measures the professional competences in a sample of 349 prospective teachers.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003eIntroduction.- Objectives and application areas.- Test development.- Implementation of the test.- Test quality.- Selected results.- References.- Attachment.- Modelling experiences.- Beliefs about mathematical modelling.- Self-efficacy about assesing mathematical modelling.- Modelling specific pedagogical content knowledge.- Test booklet.\u003c\/p\u003e\u003cbr\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743049462103,"sku":"9783030780708","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030780708.jpg?v=1791480533"},{"product_id":"recent-advances-in-industrial-and-applied-mathematics-9783030862381","title":"Recent Advances in Industrial and Applied","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress.\u003cb\u003e\u003c\/b\u003e\u003c\/p\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003e1 M. Berger, Asteroid-Generated Tsunamis: A Review.- 2 A. Bermúdez, Some Case Studies in Environmental and Industrial Mathematics.- 3 Z. Cai et al., Hyperbolic Model Reduction for Kinetic Equations.- 4 A. Cohen et al., State Estimation - The Role of Reduced Models.- 5 C. Conca, Modelling Our Sense Of Smell.- 6 L. Edelstein-Keshet, Pattern formation inside living cells.- 7 M. Garzon et al., Efficient Algorithms for Tracking Moving Interfaces.- 8 K. Lauter, Private AI: Machine Learning on Encrypted Data.- 9 C. Le Bris, Mathematical approaches for contemporary materials science: Addressing defects in the microstructure.- 10 H. Leng et al., An iterative thresholding method for topology optimization for the Navier-Stokes flow.- 11 K. Sako, Cryptography and Digital Transformation.- 12 H. Suito et al., Numerical Study for Blood Flows in Thoracic Aorta.- 13 J.A.C. Weideman, Dynamics of Complex Singularities of Nonlinear PDEs: Analysis and Computation.\u003c\/p\u003e\u003cbr\u003e","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743055032663,"sku":"9783030862381","price":33.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030862381.jpg?v=1720063913"},{"product_id":"novel-mathematics-inspired-by-industrial-challenges-9783030961756","title":"Novel Mathematics Inspired by Industrial","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis contributed volume convenes a rich selection of works with a focus on innovative mathematical methods with applications in real-world, industrial problems. Studies included in this book are all motivated by a relevant industrial challenge, and demonstrate that mathematics for industry can be extremely rewarding, leading to new mathematical methods and sometimes even to entirely new fields within mathematics.\u003cbr\u003eThe book is organized into two parts: Computational Sciences and Engineering, and Data Analysis and Finance. In every chapter, readers will find a brief description of why such work fits into this volume; an explanation on which industrial challenges have been instrumental for their inspiration; and which methods have been developed as a result. All these contribute to a greater unity of the text, benefiting not only practitioners and professionals seeking information on novel techniques but also graduate students in applied mathematics, engineering, and related fields.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePart I:  Computational Science and Engineering.- Multirate Schemes — An Answer of Numerical Analysis to a Demand from Applications.- Electronic Circuit Simulation and the Development of New Krylov-Subspace Methods.- Modular time integration of coupled problems in system dynamics.- Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems.- Fast Numerical Methods to Compute Periodic Solutions of Electromagnetic Models.- Challenges in the Simulation of Radio Frequency Circuits.- An integrated data-driven computational pipeline with model order reduction for industrial and applied mathematics.- From rotating fluid masses and Ziegler’s paradox to Pontryagin- and Krein spaces and bifurcation theory.- Part II: Data Analysis and finance.- Topological Data Analysis.- Prediction Models with Functional Data for Variables related with Energy Production.- Quantization Methods for Stochastic Differential Equations.","brand":"Springer Nature Switzerland AG","offers":[{"title":"Default Title","offer_id":48743061586263,"sku":"9783030961756","price":71.24,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783030961756.jpg?v=1720063941"},{"product_id":"model-order-reduction-and-applications-cetraro-italy-2021-9783031295621","title":"Model Order Reduction and Applications: Cetraro,","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis book addresses the state of the art of reduced order methods for modelling and computational reduction of complex parametrised systems, governed by ordinary and\/or partial differential equations, with a special emphasis on real time computing techniques and applications in various fields.\u003cp\u003eConsisting of  four contributions presented at the CIME summer school, the book presents several points of view and techniques to solve demanding problems of increasing complexity. The focus is on theoretical investigation and applicative algorithm development for reduction in the complexity – the dimension, the degrees of freedom, the data – arising in these models.\u003c\/p\u003eThe book is addressed to graduate students, young researchers and people interested in the field. It is a good companion for graduate\/doctoral classes.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e- 1. The Reduced Basis Method in Space and Time: Challenges, Limits and Perspectives. - 2. Inverse Problems: A Deterministic Approach Using Physics-Based Reduced Models. - 3. Model Order Reduction for Optimal Control Problems. - 4. Machine Learning Methods for Reduced Order Modeling.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743079739735,"sku":"9783031295621","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031295621.jpg?v=1720064021"},{"product_id":"uncertain-rule-based-fuzzy-systems-introduction-and-new-directions-2nd-edition-9783319513690","title":"Uncertain Rule-Based Fuzzy Systems: Introduction","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThe second edition of this textbook provides a fully updated approach to fuzzy sets and systems that can model uncertainty — i.e., “type-2” fuzzy sets and systems. The author demonstrates how to overcome the limitations of classical fuzzy sets and systems, enabling a wide range of applications from time-series forecasting to knowledge mining to control. In this new edition, a bottom-up approach is presented that begins by introducing classical (type-1) fuzzy sets and systems, and then explains how they can be modified to handle uncertainty. The author covers fuzzy rule-based systems – from type-1 to interval type-2 to general type-2 – in one volume. For hands-on experience, the book provides information on accessing MatLab and Java software to complement the content. The book features a full suite of classroom material.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003eIntroduction.- Part 1: Type-1 Fuzzy Sets and Systems.- Short Primers on Type-1 Fuzzy Sets and Fuzzy Logic.- Type-1 Fuzzy Logic Systems.- Part 2: Type-2 Fuzzy Sets.- Sources of Uncertainty.- Type-2 Fuzzy Sets.- Operations on and Properties OF Type-2 Fuzzy Sets.- Type-2 Relations and Compositions.- Centroid of a Type-2 Fuzzy Set: Type-Reduction.- Part 3: Type-2 Fuzzy Logic Systems.- Mamdani Interval Type-2 Fuzzy Logic Systems (IT2 FLSS).- TSK Interval Type-2 Fuzzy Logic Systems.- General Type-2 Fuzzy Logic Systems (GT2 FLSS).- Conclusion.\u003c\/p\u003e","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743097303383,"sku":"9783319513690","price":74.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"modeling-life-the-mathematics-of-biological-systems-9783319597300","title":"Modeling Life: The Mathematics of Biological","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions.\u003c\/p\u003e  Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking.\u003cp\u003e\u003c\/p\u003e  \u003cp\u003eExamples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“The book can serve as an introduction to the field of modeling not only for university students but for any person interested in the field with little or no knowledge of calculus. … This book is a very interesting deviation from this prevailing paradigm. It takes the essence of calculus and presents it in a way which is accessible and usable in the practice of life sciences professionals.” (Svetoslav Markov, zbMATH 1397.92001, 2018)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1. Modeling, Change, and Simulation.- 2. Derivatives and Integrals.- 3. Equilibrium Behavior.- 4. Non-Equilibrium Dynamics: Oscillation.- 5. Chaos.- 6. Linear Algebra.- 7. Multivariable Systems.- Bibliography.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743099236695,"sku":"9783319597300","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319597300.jpg?v=1791481727"},{"product_id":"modeling-life-the-mathematics-of-biological-systems-9783319866895","title":"Modeling Life: The Mathematics of Biological","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions.\u003c\/p\u003e  Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking.\u003cp\u003e\u003c\/p\u003e  \u003cp\u003eExamples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e“The book can serve as an introduction to the field of modeling not only for university students but for any person interested in the field with little or no knowledge of calculus. … This book is a very interesting deviation from this prevailing paradigm. It takes the essence of calculus and presents it in a way which is accessible and usable in the practice of life sciences professionals.” (Svetoslav Markov, zbMATH 1397.92001, 2018)\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1. Modeling, Change, and Simulation.- 2. Derivatives and Integrals.- 3. Equilibrium Behavior.- 4. Non-Equilibrium Dynamics: Oscillation.- 5. Chaos.- 6. Linear Algebra.- 7. Multivariable Systems.- Bibliography.- Index.","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48743107952983,"sku":"9783319866895","price":47.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783319866895.jpg?v=1791481750"},{"product_id":"learning-mathematics-through-modelling-and-simulation-an-investigative-approach-9789393330383","title":"Learning Mathematics Through Modelling and","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eLearning Mathematics through Modelling and Simulation: An Investigative Approach, offers the readers a hands-on experience of discovering the beautiful aspects of mathematics through the use of technology. Three powerful tools falling into the categories of spreadsheet programs (Microsoft Excel),They are applied in the book to enable the readers to independently explore, visualise, conjecture, reason and solve problems.","brand":"Universities Press","offers":[{"title":"Default Title","offer_id":48743256326487,"sku":"9789393330383","price":23.74,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789393330383.jpg?v=1791379147"},{"product_id":"stability-and-control-of-nonlinear-time-varying-systems-9789811089077","title":"Stability and Control of Nonlinear Time-varying","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThis book presents special systems derived from industrial models, including the complex saturation nonlinear functions and the delay nonlinear functions. It also presents typical methods, such as the classical Liapunov and Integral Inequalities methods. Providing constructive qualitative and stability conditions for linear systems with saturated inputs in both global and local contexts, it offers practitioners more concise model systems for modern saturation nonlinear techniques, which have the potential for future applications. 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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.","brand":"World Scientific Publishing Co Pte Ltd","offers":[{"title":"Default Title","offer_id":48743278313815,"sku":"9789811224874","price":31.5,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811224874.jpg?v=1720064891"},{"product_id":"risk-based-engineering-an-integrated-approach-to-complex-systems-special-reference-to-nuclear-plants-9789811300882","title":"Risk-Based Engineering: An Integrated Approach to","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThe book comprehensively covers the various aspects of risk modeling and analysis in technological contexts. It pursues a systems approach to modeling risk and reliability concerns in engineering, and covers the key concepts of risk analysis and mathematical tools used to assess and account for risk in engineering problems. The relevance of incorporating risk-based structures in design and operations is also stressed, with special emphasis on the human factor and behavioral risks. \u003c\/p\u003e  The book uses the nuclear plant, an extremely complex and high-precision engineering environment, as an example to develop the concepts discussed. The core mechanical, electronic and physical aspects of such a complex system offer an excellent platform for analyzing and creating risk-based models. The book also provides real-time case studies in a separate section to demonstrate the use of this approach. There are many limitations when it comes to applications of risk-based approaches to engineering problems. The book is structured and written in a way that addresses these key gap areas to help optimize the overall methodology. \u003cp\u003e\u003c\/p\u003e  \u003cp\u003eThis book serves as a textbook for graduate and advanced undergraduate courses on risk and reliability in engineering. It can also be used outside the classroom for professional development courses aimed at practicing engineers or as an introduction to risk-based engineering for professionals, researchers, and students interested in the field.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface.- Chapter 1: Introduction.- Chapter 2: Risk Characterization.- Chapter 3: Probabilistic Approach to Reliability Engineering.- Chapter 4: System Reliability Modelling.- Chapter 5: Life Prediction.- Chapter 6: Probabilistic Risk Assessment.- Chapter 7: Risk-based Design.- Chapter 8: Fatigue and Fracture Risk Assessment- A Probabilistic Framework.- Chapter 9: Uncertainty Modeling.- Chapter 10: Human Reliability Analysis.- Chapter 11: Digital system reliability.- Chapter 12: Physics of Failure.- Chapter 13: Prognostics and Health Management.- Chapter 14: Risk Informed Decisions.- Chapter 15: Risk-based \/ Risk-informed Applications.- Appendix: Statistical Tables.\u003cbr\u003e","brand":"Springer Verlag, Singapore","offers":[{"title":"Default Title","offer_id":48743286571351,"sku":"9789811300882","price":82.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9789811300882.jpg?v=1791483944"},{"product_id":"applied-statistics-with-r-a-practical-guide-for-the-life-sciences-9780198869337","title":"Applied Statistics with R A Practical Guide for","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThis book uses the statistical language R, which is the choice of ecologists worldwide and is rapidly becoming the 'go-to' stats program throughout the life-sciences. Furthermore, by using a single, real-world dataset throughout the book, readers are encouraged to become deeply familiar with an imperfect but realistic set of data.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eApplied Statistics with R will keep you engaged with its humor and humility while teaching the fundamentals of modern biological data analysis. * Morgan W. Tingley, The Quarterly Review of Biology *\u003cbr\u003eThis book excels at...taking away the fear of coding that seems to be an epidemic among students. It is written in a very conversational tone and the author explains every line of code, avoiding any technical language. * Julia Balogh, Goethe-Universität Frankfurt am Main, Germany, ISBE Newsletter Vol 36 *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface 1: Introduction to R 2: Before You Begin (aka Thoughts on Proper Data Analysis) 3: Exploratory Data Analysis and Data Summarization 4: Introduction to Plotting 5: Basic Statistical Analyses using R 6: More Linear Models in R! 7: Generalized Linear Models 8: Mixed Effects Models 9: Advanced Data Wrangling and Plotting 10: Writing Loops and Functions in R 11: Final Thoughts","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":48864219005271,"sku":"9780198869337","price":999.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780198869337.jpg?v=1791454548"},{"product_id":"understanding-and-managing-model-risk-9780470977613","title":"Understanding and Managing Model Risk","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cb\u003eA guide to the validation and risk management of quantitative models used for pricing and hedging\u003c\/b\u003e\u003cbr\u003e \u003cbr\u003e   \u003cp\u003eWhereas the majority of quantitative finance books focus on mathematics and risk management books focus on regulatory aspects, this book addresses the elements missed by this literature--the risks of the models themselves. This book starts from regulatory issues, but translates them into practical suggestions to reduce the likelihood of model losses, basing model risk and validation on market experience and on a wide range of real-world examples, with a high level of detail and precise operative indications.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgements xix\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Theory and Practice of Model Risk Management\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Understanding Model Risk 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 What Is Model Risk? 3\u003c\/p\u003e \u003cp\u003e1.1.1 The Value Approach 4\u003c\/p\u003e \u003cp\u003e1.1.2 The Price Approach 6\u003c\/p\u003e \u003cp\u003e1.1.3 A Quant Story of the Crisis 9\u003c\/p\u003e \u003cp\u003e1.1.4 A Synthetic View on Model Risk 17\u003c\/p\u003e \u003cp\u003e1.2 Foundations of Modelling and the Reality of Markets 22\u003c\/p\u003e \u003cp\u003e1.2.1 The Classic Framework 22\u003c\/p\u003e \u003cp\u003e1.2.2 Uncertainty and Illiquidity 30\u003c\/p\u003e \u003cp\u003e1.3 Accounting for Modellers 38\u003c\/p\u003e \u003cp\u003e1.3.1 Fair Value 38\u003c\/p\u003e \u003cp\u003e1.3.2 The Liquidity Bubble and the Accountancy Boards 40\u003c\/p\u003e \u003cp\u003e1.3.3 Level 1, 2, 3 .go? 41\u003c\/p\u003e \u003cp\u003e1.3.4 The Hidden Model Assumptions in ‘vanilla’ Derivatives 42\u003c\/p\u003e \u003cp\u003e1.4 What Regulators Said After the Crisis 48\u003c\/p\u003e \u003cp\u003e1.4.1 Basel New Principles: The Management Process 49\u003c\/p\u003e \u003cp\u003e1.4.2 Basel New Principles: The Model, The Market and The Product 51\u003c\/p\u003e \u003cp\u003e1.4.3 Basel New Principles: Operative Recommendations 52\u003c\/p\u003e \u003cp\u003e1.5 Model Validation and Risk Management: Practical Steps 53\u003c\/p\u003e \u003cp\u003e1.5.1 A Scheme for Model Validation 54\u003c\/p\u003e \u003cp\u003e1.5.2 Special Points in Model Risk Management 59\u003c\/p\u003e \u003cp\u003e1.5.3 The Importance of Understanding Models 60\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Model Validation and Model Comparison: Case Studies 63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Practical Steps of Model Comparison 63\u003c\/p\u003e \u003cp\u003e2.2 First Example: The Models 65\u003c\/p\u003e \u003cp\u003e2.2.1 The Credit Default Swap 66\u003c\/p\u003e \u003cp\u003e2.2.2 Structural First-Passage Models 67\u003c\/p\u003e \u003cp\u003e2.2.3 Reduced-Form Intensity Models 69\u003c\/p\u003e \u003cp\u003e2.2.4 Structural vs Intensity: Information 72\u003c\/p\u003e \u003cp\u003e2.3 First Example: The Payoff. Gap Risk in a Leveraged Note 74\u003c\/p\u003e \u003cp\u003e2.4 The Initial Assessment 77\u003c\/p\u003e \u003cp\u003e2.4.1 First Test: Calibration to Liquid Relevant Products 77\u003c\/p\u003e \u003cp\u003e2.4.2 Second Test: a Minimum Level of Realism 78\u003c\/p\u003e \u003cp\u003e2.5 The Core Risk in the Product 81\u003c\/p\u003e \u003cp\u003e2.5.1 Structural Models: Negligible Gap Risk 82\u003c\/p\u003e \u003cp\u003e2.5.2 Reduced-Form Models: Maximum Gap Risk 82\u003c\/p\u003e \u003cp\u003e2.6 A Deeper Analysis: Market Consensus and Historical Evidence 85\u003c\/p\u003e \u003cp\u003e2.6.1 What to Add to the Calibration Set 85\u003c\/p\u003e \u003cp\u003e2.6.2 Performing Market Intelligence 86\u003c\/p\u003e \u003cp\u003e2.6.3 The Lion and the Turtle. Incompleteness in Practice 86\u003c\/p\u003e \u003cp\u003e2.6.4 Reality Check: Historical Evidence and Lack of it 87\u003c\/p\u003e \u003cp\u003e2.7 Building a Parametric Family of Models 88\u003c\/p\u003e \u003cp\u003e2.7.1 Understanding Model Implications 93\u003c\/p\u003e \u003cp\u003e2.8 Managing Model Uncertainty: Reserves, Limits, Revisions 95\u003c\/p\u003e \u003cp\u003e2.9 Model Comparison: Examples from Equity and Rates 99\u003c\/p\u003e \u003cp\u003e2.9.1 Comparing Local and Stochastic Volatility Models in Pricing Equity Compound and Barrier Options 99\u003c\/p\u003e \u003cp\u003e2.9.2 Comparing Short Rate and Market Models in Pricing Interest Rate Bermudan Options 105\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Stress Testing and the Mistakes of the Crisis 111\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Learning Stress Test from the Crisis 111\u003c\/p\u003e \u003cp\u003e3.1.1 The Meaning of Stress Testing 112\u003c\/p\u003e \u003cp\u003e3.1.2 Portfolio Stress Testing 113\u003c\/p\u003e \u003cp\u003e3.1.3 Model Stress Testing 116\u003c\/p\u003e \u003cp\u003e3.2 The Credit Market and the ‘Formula that Killed Wall Street’ 118\u003c\/p\u003e \u003cp\u003e3.2.1 The CDO Payoff 118\u003c\/p\u003e \u003cp\u003e3.2.2 The Copula 119\u003c\/p\u003e \u003cp\u003e3.2.3 Applying the Copula to CDOs 122\u003c\/p\u003e \u003cp\u003e3.2.4 The Market Quotation Standard 124\u003c\/p\u003e \u003cp\u003e3.3 Portfolio Stress Testing and the Correlation Mistake 125\u003c\/p\u003e \u003cp\u003e3.3.1 From Flat Correlation Towards a Realistic Approach 126\u003c\/p\u003e \u003cp\u003e3.3.2 A Correlation Parameterization to Stress the Market Skew 131\u003c\/p\u003e \u003cp\u003e3.4 Payoff Stress and the Liquidity Mistake 136\u003c\/p\u003e \u003cp\u003e3.4.1 Detecting the Problem: Losses Concentrated in Time 137\u003c\/p\u003e \u003cp\u003e3.4.2 The Problem in Practice 139\u003c\/p\u003e \u003cp\u003e3.4.3 A Solution. From Copulas to Real Models 145\u003c\/p\u003e \u003cp\u003e3.4.4 Conclusions 150\u003c\/p\u003e \u003cp\u003e3.5 Testing with Historical Scenarios and the Concentration Mistake 151\u003c\/p\u003e \u003cp\u003e3.5.1 The Mapping Methods for Bespoke Portfolios 152\u003c\/p\u003e \u003cp\u003e3.5.2 The Lehman Test 156\u003c\/p\u003e \u003cp\u003e3.5.3 Historical Scenarios to Test Mapping Methods 157\u003c\/p\u003e \u003cp\u003e3.5.4 The Limits of Mapping and the Management of Model Risk 164\u003c\/p\u003e \u003cp\u003e3.5.5 Conclusions 168\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Preparing for Model Change. Rates and Funding in the New Era 171\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Explaining the Puzzle in the Interest Rates Market and Models 171\u003c\/p\u003e \u003cp\u003e4.1.1 The Death of a Market Model: 9 August 2007 173\u003c\/p\u003e \u003cp\u003e4.1.2 Finding the New Market Model 174\u003c\/p\u003e \u003cp\u003e4.1.3 The Classic Risk-free Market Model 178\u003c\/p\u003e \u003cp\u003e4.1.4 A Market Model with Stable Default Risk 182\u003c\/p\u003e \u003cp\u003e4.1.5 A Market with Volatile Credit Risk 192\u003c\/p\u003e \u003cp\u003e4.1.6 Conclusions 200\u003c\/p\u003e \u003cp\u003e4.2 Rethinking the Value of Money: The Effect of Liquidity in Pricing 201\u003c\/p\u003e \u003cp\u003e4.2.1 The Setting 204\u003c\/p\u003e \u003cp\u003e4.2.2 Standard DVA: Is Something Missing? 206\u003c\/p\u003e \u003cp\u003e4.2.3 Standard DVA plus Liquidity: Is Something Duplicated? 207\u003c\/p\u003e \u003cp\u003e4.2.4 Solving the Puzzle 207\u003c\/p\u003e \u003cp\u003e4.2.5 Risky Funding for the Borrower 208\u003c\/p\u003e \u003cp\u003e4.2.6 Risky Funding for the Lender and the Conditions for Market Agreement 209\u003c\/p\u003e \u003cp\u003e4.2.7 Positive Recovery Extension 210\u003c\/p\u003e \u003cp\u003e4.2.8 Two Ways of Looking at the Problem: Default Risk or Funding Benefit? The Accountant vs the Salesman 211\u003c\/p\u003e \u003cp\u003e4.2.9 Which Direction for Future Pricing? 214\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Snakes in the Grass: Where Model Risk Hides\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Hedging 219\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Model Risk and Hedging 219\u003c\/p\u003e \u003cp\u003e5.2 Hedging and Model Validation: What is Explained by P\u0026amp;L Explain? 221\u003c\/p\u003e \u003cp\u003e5.2.1 The Sceptical View 222\u003c\/p\u003e \u003cp\u003e5.2.2 The Fundamentalist View and Black and Scholes 222\u003c\/p\u003e \u003cp\u003e5.2.3 Back to Reality 224\u003c\/p\u003e \u003cp\u003e5.2.4 Remarks: Recalibration, Hedges and Model Instability 226\u003c\/p\u003e \u003cp\u003e5.2.5 Conclusions: from Black and Scholes to Real Hedging 228\u003c\/p\u003e \u003cp\u003e5.3 From Theory to Practice: Real Hedging 229\u003c\/p\u003e \u003cp\u003e5.3.1 Stochastic Volatility Models: SABR 231\u003c\/p\u003e \u003cp\u003e5.3.2 Test Hedging Behaviour Leaving Nothing Out 232\u003c\/p\u003e \u003cp\u003e5.3.3 Real Hedging for Local Volatility Models 238\u003c\/p\u003e \u003cp\u003e5.3.4 Conclusions: the Reality of Hedging Strategies 241\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Approximations 243\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Validate and Monitor the Risk of Approximations 243\u003c\/p\u003e \u003cp\u003e6.2 The Swaption Approximation in the Libor Market Model 245\u003c\/p\u003e \u003cp\u003e6.2.1 The Three Technical Problems in Interest Rate Modelling 245\u003c\/p\u003e \u003cp\u003e6.2.2 The Libor Market Model and the Swaption Market 247\u003c\/p\u003e \u003cp\u003e6.2.3 Pricing Swaptions 250\u003c\/p\u003e \u003cp\u003e6.2.4 Understanding and Deriving the Approximation 253\u003c\/p\u003e \u003cp\u003e6.2.5 Testing the Approximation 257\u003c\/p\u003e \u003cp\u003e6.3 Approximations for CMS and the Shape of the Term Structure 264\u003c\/p\u003e \u003cp\u003e6.3.1 The CMS Payoff 265\u003c\/p\u003e \u003cp\u003e6.3.2 Understanding Convexity Adjustments 266\u003c\/p\u003e \u003cp\u003e6.3.3 The Market Approximation for Convexity Adjustments 267\u003c\/p\u003e \u003cp\u003e6.3.4 A General LMM Approximation 269\u003c\/p\u003e \u003cp\u003e6.3.5 Comparing and Testing the Approximations 271\u003c\/p\u003e \u003cp\u003e6.4 Testing Approximations Against Exact. Dupire’s Idea 276\u003c\/p\u003e \u003cp\u003e6.4.1 Perfect Positive Correlation 278\u003c\/p\u003e \u003cp\u003e6.4.2 Perfect Negative Correlation 280\u003c\/p\u003e \u003cp\u003e6.5 Exercises on Risk in Computational Methods 283\u003c\/p\u003e \u003cp\u003e6.5.1 Approximation 283\u003c\/p\u003e \u003cp\u003e6.5.2 Integration 285\u003c\/p\u003e \u003cp\u003e6.5.3 Monte Carlo 285\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Extrapolations 287\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Using the Market to Complete Information: Asymptotic Smile 288\u003c\/p\u003e \u003cp\u003e7.1.1 The Indetermination in the Asymptotic Smile 288\u003c\/p\u003e \u003cp\u003e7.1.2 Pricing CMS with a Smile: Extrapolating to Infinity 292\u003c\/p\u003e \u003cp\u003e7.1.3 Using CMS Information to Transform Extrapolation into Interpolation and Fix the Indetermination 293\u003c\/p\u003e \u003cp\u003e7.2 Using Mathematics to Complete Information: Correlation Skew 295\u003c\/p\u003e \u003cp\u003e7.2.1 The Expected Tranched Loss 295\u003c\/p\u003e \u003cp\u003e7.2.2 Properties for Interpolation 298\u003c\/p\u003e \u003cp\u003e7.2.3 Properties for Turning Extrapolation into Interpolation 298\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Correlations 303\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 The Technical Difficulties in Computing Correlations 303\u003c\/p\u003e \u003cp\u003e8.1.1 Correlations in Interest Rate Modelling 305\u003c\/p\u003e \u003cp\u003e8.1.2 Cross-currency Correlations 307\u003c\/p\u003e \u003cp\u003e8.1.3 Stochastic Volatility Correlations 312\u003c\/p\u003e \u003cp\u003e8.2 Fundamental Errors in Modelling Correlations 315\u003c\/p\u003e \u003cp\u003e8.2.1 The Zero-correlation Error 316\u003c\/p\u003e \u003cp\u003e8.2.2 The 1-Correlation Error 319\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Calibration 323\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Calibrating to Caps\/Swaptions and Pricing Bermudans 324\u003c\/p\u003e \u003cp\u003e9.1.1 Calibrating Caplets 325\u003c\/p\u003e \u003cp\u003e9.1.2 Understanding the Term Structure of Volatility 326\u003c\/p\u003e \u003cp\u003e9.1.3 Different Parameterizations 329\u003c\/p\u003e \u003cp\u003e9.1.4 The Evolution of the Term Structure of Volatility 332\u003c\/p\u003e \u003cp\u003e9.1.5 The Effect on Early-Exercise Derivatives 334\u003c\/p\u003e \u003cp\u003e9.1.6 Reducing Our Indetermination in Pricing Bermudans: Liquid European Swaptions 335\u003c\/p\u003e \u003cp\u003e9.2 The Evolution of the Forward Smiles 340\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 When the Payoff is Wrong 347\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 The Link Between Model Errors and Payoff Errors 347\u003c\/p\u003e \u003cp\u003e10.2 The Right Payoff at Default: The Impact of the Closeout Convention 348\u003c\/p\u003e \u003cp\u003e10.2.1 How Much Will be Paid at Closeout, Really? 350\u003c\/p\u003e \u003cp\u003e10.2.2 What the Market Says and What the ISDA Says 352\u003c\/p\u003e \u003cp\u003e10.2.3 A Quantitative Analysis of the Closeout 353\u003c\/p\u003e \u003cp\u003e10.2.4 A Summary of the Findings and Some Conclusions on Payoff Uncertainty 360\u003c\/p\u003e \u003cp\u003e10.3 Mathematical Errors in the Payoff of Index Options 362\u003c\/p\u003e \u003cp\u003e10.3.1 Too Much Left Out 364\u003c\/p\u003e \u003cp\u003e10.3.2 Too Much Left In 365\u003c\/p\u003e \u003cp\u003e10.3.3 Empirical Results with the Armageddon Formula 365\u003c\/p\u003e \u003cp\u003e10.3.4 Payoff Errors and Armageddon Probability 367\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Model Arbitrage 371\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 371\u003c\/p\u003e \u003cp\u003e11.2 Capital Structure Arbitrage 373\u003c\/p\u003e \u003cp\u003e11.2.1 The Credit Model 373\u003c\/p\u003e \u003cp\u003e11.2.2 The Equity Model 375\u003c\/p\u003e \u003cp\u003e11.2.3 From Barrier Options to Equity Pricing 377\u003c\/p\u003e \u003cp\u003e11.2.4 Capital-structure Arbitrage and Uncertainty 381\u003c\/p\u003e \u003cp\u003e11.3 The Cap-Swaption Arbitrage 391\u003c\/p\u003e \u003cp\u003e11.4 Conclusion: Can We Use No-Arbitrage Models to Make Arbitrage? 394\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Appendix 397\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Random Variables 397\u003c\/p\u003e \u003cp\u003e12.1.1 Generating Variables from Uniform Draws 397\u003c\/p\u003e \u003cp\u003e12.1.2 Copulas 397\u003c\/p\u003e \u003cp\u003e12.1.3 Normal and Lognormal 398\u003c\/p\u003e \u003cp\u003e12.2 Stochastic Processes 399\u003c\/p\u003e \u003cp\u003e12.2.1 The Law of Iterated Expectation 399\u003c\/p\u003e \u003cp\u003e12.2.2 Diffusions, Brownian Motions and Martingales 400\u003c\/p\u003e \u003cp\u003e12.2.3 Poisson Process 403\u003c\/p\u003e \u003cp\u003e12.2.4 Time-dependent Intensity 404\u003c\/p\u003e \u003cp\u003e12.3 Useful Results from Quantitative Finance 405\u003c\/p\u003e \u003cp\u003e12.3.1 Black and Scholes (1973) and Black (1976) 405\u003c\/p\u003e \u003cp\u003e12.3.2 Change of Numeraire 407\u003c\/p\u003e \u003cp\u003eBibliography 409\u003c\/p\u003e \u003cp\u003eIndex 417 \u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48864643678551,"sku":"9780470977613","price":63.65,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470977613.jpg?v=1722272866"},{"product_id":"a-biologists-guide-to-mathematical-modeling-in-ecology-and-evolution-9780691123448","title":"A Biologists Guide to Mathematical Modeling in","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eServes as a how-to guide for developing mathematical models in biology. Starting at an elementary level of mathematical modeling, this title gradually builds from classic models in ecology and evolution to more intricate class-structured and probabilistic models. It provides primers with instructive exercises.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eHonorable Mention for the 2007 Best Professional\/Scholarly Book in Biological Sciences, Association of American Publishers \"A gentle but thorough introduction to the mathematical techniques employed in ecological and evolutionary theory. Readers who ... finish this well-written book will be prepared to read and understand a sizeable fraction of the current literature.\"--Donald L. DeAngelis, Quarterly Review of Biology \"At long last, Sally Otto and Troy Day have provided relief for biologists and epidemiologists in search of an easily read, practical, and thorough starting point from which to learn mathematical modeling... We would recommend this book over shorter texts that are labeled as 'introductory'... The depth and detail that Otto and Day have included in this text arc appealing rather than intimidating, and the structure of the text is empowering rather than didactic or formulaic.\"--Sanjay Basu and Alison P. Galvani, Siam Review \"[T]he great value of the Otto\/Day book is that it attempts pedagogical soundness, and so is useful for teaching. Besides being perfectly readable, it engages and impresses the reader quickly not only with the subject matter, but also with the quality of printing and layout which have to be seen to be believed. These praises may sound lavish by many a reader of these columns but first see the book or better still buy the volume and you will see our passion and rage for going all out in praise of this volume.\"--Current Engineering Practice \"I highly recommend this book for every university biology department because it provides both a unique, and often uplifting, introduction and a comprehensive reference of techniques for building and analysing mathematical models.\"--Volker Grimm, Basic and Applied Ecology \"I cannot help but think that future textbook authors will want to have Otto and Day front and center on the work desk, for this is a valuable source of material... This book stands out, and its contribution is quite apparent. In sum, this book is a valuable contribution to the literature, and one to which I expect to refer regularly in connection with my teaching and writing duties.\"--Steven G. Krantz, UMAP Journal \"[A] great textbook... [M]asterful use of figures and illustrations and exercises ... provide the reader with valuable practice in constructing models and implementing related mathematical techniques. I certainly recommend this text and can attest to its usefulness for budding researchers in the biological sciences.\"--Jason M. Graham, MAA Reviews\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface ix    Chapter 1: Mathematical Modeling in Biology 1 1.1 Introduction 1 1.2 HIV 2 1.3 Models of HIV\/AIDS 5 1.4 Concluding Message 14   Chapter 2: How to Construct a Model 17 2.1 Introduction 17 2.2 Formulate the Question 19 2.3 Determine the Basic Ingredients 19 2.4 Qualitatively Describe the Biological System 26 2.5 Quantitatively Describe the Biological System 33 2.6 Analyze the Equations 39 2.7 Checks and Balances 47 2.8 Relate the Results Back to the Question 50 2.9 Concluding Message 51   Chapter 3: Deriving Classic Models in Ecology and Evolutionary Biology 54 3.1 Introduction 54 3.2 Exponential and Logistic Models of Population Growth 54 3.3 Haploid and Diploid Models of Natural Selection 62 3.4 Models of Interactions among Species 72 3.5 Epidemiological Models of Disease Spread 77 3.6 Working Backward--Interpreting Equations in Terms of the Biology 79 3.7 Concluding Message 82   Primer 1: Functions and Approximations 89 P1.1 Functions and Their Forms 89 P1.2 Linear Approximations 96 P1.3 The Taylor Series 100   Chapter 4: Numerical and Graphical Techniques--Developing a Feeling for Your Model 110 4.1 Introduction 110 4.2 Plots of Variables Over Time 111 4.3 Plots of Variables as a Function of the Variables Themselves 124 4.4 Multiple Variables and Phase-Plane Diagrams 133 4.5 Concluding Message 145   Chapter 5: Equilibria and Stability Analyses--One-Variable Models 151 5.1 Introduction 151 5.2 Finding an Equilibrium 152 5.3 Determining Stability 163 5.4 Approximations 176 5.5 Concluding Message 184   Chapter 6: General Solutions and Transformations--One-Variable Models 191 6.1 Introduction 191 6.2 Transformations 192 6.3 Linear Models in Discrete Time 193 6.4 Nonlinear Models in Discrete Time 195 6.5 Linear Models in Continuous Time 198 6.6 Nonlinear Models in Continuous Time 202 6.7 Concluding Message 207   Primer 2: Linear Algebra 214 P2.1 An Introduction to Vectors and Matrices 214 P2.2 Vector and Matrix Addition 219 P2.3 Multiplication by a Scalar 222 P2.4 Multiplication of Vectors and Matrices 224 P2.5 The Trace and Determinant of a Square Matrix 228 P2.6 The Inverse 233 P2.7 Solving Systems of Equations 235 P2.8 The Eigenvalues of a Matrix 237 P2.9 The Eigenvectors of a Matrix 243   Chapter 7: Equilibria and Stability Analyses--Linear Models with Multiple Variables 254 7.1 Introduction 254 7.2 Models with More than One Dynamic Variable 255 7.3 Linear Multivariable Models 260 7.4 Equilibria and Stability for Linear Discrete-Time Models 279 7.5 Concluding Message 289   Chapter 8: Equilibria and Stability Analyses--Nonlinear Models with Multiple Variables 294 8.1 Introduction 294 8.2 Nonlinear Multiple-Variable Models 294 8.3 Equilibria and Stability for Nonlinear Discrete-Time Models 316 8.4 Perturbation Techniques for Approximating Eigenvalues 330 8.5 Concluding Message 337   Chapter 9: General Solutions and Tranformations--Models with Multiple Variables 347 9.1 Introduction 347 9.2 Linear Models Involving Multiple Variables 347 9.3 Nonlinear Models Involving Multiple Variables 365 9.4 Concluding Message 381   Chapter 10: Dynamics of Class-Structured Populations 386 10.1 Introduction 386 10.2 Constructing Class-Structured Models 388 10.3 Analyzing Class-Structured Models 393 10.4 Reproductive Value and Left Eigenvectors 398 10.5 The Effect of Parameters on the Long-Term Growth Rate 400 10.6 Age-Structured Models--The Leslie Matrix 403 10.7 Concluding Message 418   Chapter 11: Techniques for Analyzing Models with Periodic Behavior 423 11.1 Introduction 423 11.2 What Are Periodic Dynamics? 423 11.3 Composite Mappings 425 11.4 Hopf Bifurcations 428 11.5 Constants of Motion 436 11.6 Concluding Message 449   Chapter 12: Evolutionary Invasion Analysis 454 12.1 Introduction 454 12.2 Two Introductory Examples 455 12.3 The General Technique of Evolutionary Invasion Analysis 465 12.4 Determining How the ESS Changes as a Function of Parameters 478 12.5 Evolutionary Invasion Analyses in Class-Structured Populations 485 12.6 Concluding Message 502   Primer 3: Probability Theory 513 P3.1 An Introduction to Probability 513 P3.2 Conditional Probabilities and Bayes' Theorem 518 P3.3 Discrete Probability Distributions 521 P3.4 Continuous Probability Distributions 536 P3.5 The (Insert Your Name Here) Distribution 553   Chapter 13: Probabilistic Models 567 13.1 Introduction 567 13.2 Models of Population Growth 568 13.3 Birth-Death Models 573 13.4 Wright-Fisher Model of Allele Frequency Change 576 13.5 Moran Model of Allele Frequency Change 581 13.6 Cancer Development 584 13.7 Cellular Automata--A Model of Extinction and Recolonization 591 13.8 Looking Backward in Time--Coalescent Theory 594 13.9 Concluding Message 602   Chapter 14: Analyzing Discrete Stochastic Models 608 14.1 Introduction 608 14.2 Two-State Markov Models 608 14.3 Multistate Markov Models 614 14.4 Birth-Death Models 631 14.5 Branching Processes 639 14.6 Concluding Message 644   Chapter 15: Analyzing Continuous Stochastic Models--Diffusion in Time and Space 649 15.1 Introduction 649 15.2 Constructing Diffusion Models 649 15.3 Analyzing the Diffusion Equation with Drift 664 15.4 Modeling Populations in Space Using the Diffusion Equation 684 15.5 Concluding Message 687 Epilogue: The Art of Mathematical Modeling in Biology 692   Appendix 1: Commonly Used Mathematical Rules 695 A1.1 Rules for Algebraic Functions 695 A1.2 Rules for Logarithmic and Exponential Functions 695 A1.3 Some Important Sums 696 A1.4 Some Important Products 696 A1.5 Inequalities 697   Appendix 2: Some Important Rules from Calculus 699 A2.1 Concepts 699 A2.2 Derivatives 701 A2.3 Integrals 703 A2.4 Limits 704   Appendix 3: The Perron-Frobenius Theorem 709 A3.1: Definitions 709 A3.2: The Perron-Frobenius Theorem 710   Appendix 4: Finding Maxima and Minima of Functions 713 A4.1 Functions with One Variable 713 A4.2 Functions with Multiple Variables 714   Appendix 5: Moment-Generating Functions 717   Index of Definitions, Recipes, and Rules 725 General Index 727","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":48865518584151,"sku":"9780691123448","price":69.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691123448.jpg?v=1722274357"},{"product_id":"neuro-design-9780749478889","title":"Neuro Design","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cb\u003eDarren Bridger\u003c\/b\u003e is a consultant to designers and marketers, advising on using and analyzing data that tap into consumers' non-conscious thinking and motivations. He was one of the original pioneers of the Consumer Neuroscience industry, helping to pioneer two of the first companies in the field then joining the world's largest agency, Neurofocus (now part of the Nielsen company). He is currently Head of Insights at NeuroStrata. \u003ci\u003e\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\"A super, easy-to-read book demystifying the world of neuro design, addressing the balance between the role of human creativity and that of neuroscience in modern design. If you think neuro design is about creating bland designs by deconstructing beauty, you need to read this book. It's not about that at all. Darren Bridger introduces all the major themes, key methods and tools underlying the science in engaging, manageable chunks. Any book that explains the allure of memes has to get five stars from me.\" * Jamie Croggon, Design Director, SharkNinja *\u003cbr\u003e\"With solid science as the starting point, Darren Bridger provides an eminently practical guide to designing for your customer's brain. Neuro Design is packed with actionable strategies and techniques, and is a must-read for every marketer and designer.\" * Roger Dooley, author of Brainfluence *\u003cbr\u003e\"A topic which should be of great importance to anyone in the business of retailing, advertising and marketing. Darren Bridger deals with complex topics in an engaging and practical manner, covering all aspects of the interplay between brain function and product design. Such an understanding is crucial for ensuring consumers stop and buy, rather than walking on by.\" * Dr David Lewis, Chairman of Mindlab International \u0026amp; Author of The Brain Sell *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cul\u003e\n\u003cli\u003eSection - 01: What is Neuro Design?;\u003c\/li\u003e\n\u003cli\u003eSection - 02: Neuroaesthetics;\u003c\/li\u003e\n\u003cli\u003eSection - 03: Processing Fluency;\u003c\/li\u003e\n\u003cli\u003eSection - 04: How First Impressions Work;\u003c\/li\u003e\n\u003cli\u003eSection - 05: Multisensory and Emotional Design;\u003c\/li\u003e\n\u003cli\u003eSection - 06: Visual Saliency Maps;\u003c\/li\u003e\n\u003cli\u003eSection - 07: Visual Persuasion and Behavioural Economics;\u003c\/li\u003e\n\u003cli\u003eSection - 08: Designing for Screens;\u003c\/li\u003e\n\u003cli\u003eSection - 09: Viral Designs;\u003c\/li\u003e\n\u003cli\u003eSection - 10: Designing Presentation Slides;\u003c\/li\u003e\n\u003cli\u003eSection - 11: Conducting Neuro Design Research;\u003c\/li\u003e\n\u003cli\u003eSection - 12: Conclusion;\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"Kogan Page Ltd","offers":[{"title":"Default Title","offer_id":48865726136663,"sku":"9780749478889","price":24.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780749478889.jpg?v=1722275276"},{"product_id":"learning-scientific-programming-with-python-9781108745918","title":"Learning Scientific Programming with Python","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eLearn to master basic programming tasks from scratch with real-life, scientifically relevant examples and solutions drawn from both science and engineering. Students and researchers at all levels are increasingly turning to the powerful Python programming language as an alternative to commercial packages and this fast-paced introduction moves from the basics to advanced concepts in one complete volume, enabling readers to gain proficiency quickly. Beginning with general programming concepts such as loops and functions within the core Python 3 language, and moving on to the NumPy, SciPy and Matplotlib libraries for numerical programming and data visualization, this textbook also discusses the use of Jupyter Notebooks to build rich-media, shareable documents for scientific analysis. The second edition features a new chapter on data analysis with the pandas library and comprehensive updates, and new exercises and examples. A final chapter introduces more advanced topics such as floating-p\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eAcknowledgments; 1. Introduction; 2. The core Python language I; 3. Interlude: simple plots and charts; 4. The core Python language II; 5. IPython and Jupyter Notebook; 6. NumPy; 7. Matplotlib; 8. SciPy; 9. Data analysis with pandas; 10. General scientific programming; Appendix A. Solutions; Appendix B. Differences between Python versions 2 and 3; Appendix C. SciPy's odeint ordinary differential equation solver; Glossary; Index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48866358591831,"sku":"9781108745918","price":37.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781108745918.jpg?v=1722278273"},{"product_id":"entropy-and-diversity-9781108965576","title":"Entropy and Diversity","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003eThe global biodiversity crisis is one of humanity''s most urgent problems, but even quantifying biological diversity is a difficult mathematical and conceptual challenge. This book brings new mathematical rigour to the ongoing debate. It was born of research in category theory, is given strength by information theory, and is fed by the ancient field of functional equations. It applies the power of the axiomatic method to a biological problem of pressing concern, but it also presents new theorems that stand up as mathematics in their own right, independently of any application. The question ''what is diversity?'' has surprising mathematical depth, and this book covers a wide breadth of mathematics, from functional equations to geometric measure theory, from probability theory to number theory. Despite this range, the mathematical prerequisites are few: the main narrative thread of this book requires no more than an undergraduate course in analysis.\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e'The book shows that the theory of diversity measurement is fertile soil for new mathematics, just as much as the neighboring but far more thoroughly worked field of information theory.' Hirokazu Nishimura, ZB Math Reviews\u003cbr\u003e'Each new mathematical concept is introduced from fundamental principles, in a lucid, engaging style, keeping the core biological application in the foreground … Leinster provides us with the tools to clearly assess what we are losing, so that we may focus better on what we can save.' Benjamin Allen, The Quarterly Review of Biology\u003cbr\u003e'The book is a welcome addition to the theory of biodiversity in that it covers the topics of entropy and diversity in a mathematically rigorous yet fairly accessible way … Recommended.' M. Bona, Choice Magazine\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eIntroduction; 1. Fundamental functional equations; 2. Shannon entropy; 3. Relative entropy; 4. Deformations of Shannon entropy; 5. Means; 6. Species similarity and magnitude; 7. Value; 8. Mutual information and metacommunities; 9. Probabilistic methods; 10. Information loss; 11. Entropy modulo a prime; 12. The categorical origins of entropy; Appendix A. Proofs of background facts; Appendix B. Summary of conditions; References; Index of notation; Subject index.","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":48866362458455,"sku":"9781108965576","price":46.27,"currency_code":"GBP","in_stock":true}]},{"product_id":"credit-risk-analytics-9781119143987","title":"Credit Risk Analytics","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cb\u003eThe long-awaited, comprehensive guide to practical credit risk modeling\u003c\/b\u003e \u003cp\u003e\u003ci\u003eCredit Risk Analytics\u003c\/i\u003e provides a targeted training guide for risk managers looking to efficiently build or validate in-house models for credit risk management. Combining theory with practice, this book walks you through the fundamentals of credit risk management and shows you how to implement these concepts using the SAS credit risk management program, with helpful code provided. Coverage includes data analysis and preprocessing, credit scoring; PD and LGD estimation and forecasting, low default portfolios, correlation modeling and estimation, validation, implementation of prudential regulation, stress testing of existing modeling concepts, and more, to provide a one-stop tutorial and reference for credit risk analytics. The companion website offers examples of both real and simulated credit portfolio data to help you more easily implement the concepts discussed, and the expert author team provides\u003cbr\u003e\u003cbr\u003e\u003c\/p\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e\u003cp\u003eAcknowledgments xi\u003c\/p\u003e \u003cp\u003eAbout the Authors xiii\u003c\/p\u003e \u003cp\u003eChapter 1 Introduction to Credit Risk Analytics 1\u003c\/p\u003e \u003cp\u003eChapter 2 Introduction to SAS Software 17\u003c\/p\u003e \u003cp\u003eChapter 3 Exploratory Data Analysis 33\u003c\/p\u003e \u003cp\u003eChapter 4 Data Preprocessing for Credit Risk Modeling 57\u003c\/p\u003e \u003cp\u003eChapter 5 Credit Scoring 93\u003c\/p\u003e \u003cp\u003eChapter 6 Probabilities of Default (PD): Discrete-Time Hazard Models 137\u003c\/p\u003e \u003cp\u003eChapter 7 Probabilities of Default: Continuous-Time Hazard Models 179\u003c\/p\u003e \u003cp\u003eChapter 8 Low Default Portfolios 213\u003c\/p\u003e \u003cp\u003eChapter 9 Default Correlations and Credit Portfolio Risk 237\u003c\/p\u003e \u003cp\u003eChapter 10 Loss Given Default (LGD) and Recovery Rates 271\u003c\/p\u003e \u003cp\u003eChapter 11 Exposure at Default (EAD) and Adverse Selection 315\u003c\/p\u003e \u003cp\u003eChapter 12 Bayesian Methods for Credit Risk Modeling 351\u003c\/p\u003e \u003cp\u003eChapter 13 Model Validation 385\u003c\/p\u003e \u003cp\u003eChapter 14 Stress Testing 445\u003c\/p\u003e \u003cp\u003eChapter 15 Concluding Remarks 475\u003c\/p\u003e \u003cp\u003eIndex 481\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48866387657047,"sku":"9781119143987","price":64.6,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119143987.jpg?v=1722278410"},{"product_id":"models-of-the-mind-9781472966438","title":"Models of the Mind","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eThe human brain is made up of 85 billion neurons, which are connected by over 100 trillion synapses. For more than a century, a diverse array of researchers searched for a language that could be used to capture the essence of what these neurons do and how they communicate  and how those communications create thoughts, perceptions and actions. The language they were looking for was mathematics, and we would not be able to understand the brain as we do today without it.\u003cbr\u003e\u003cbr\u003eIn \u003ci\u003eModels of the Mind\u003c\/i\u003e, author and computational neuroscientist Grace Lindsay explains how mathematical models have allowed scientists to understand and describe many of the brain''s processes, including decision-making, sensory processing, quantifying memory, and more. She introduces readers to the most important concepts in modern neuroscience, and highlights the tensions that arise when the abstract world of mathematical modelling collides with the messy details of biology. \u003cbr\u003e\u003cbr\u003eEach chapter of \u003ci\u003eMo\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eGrace Lindsay provides a \u003cb\u003emasterful \u003c\/b\u003etour of this important frontier, tackling intimidating topics with verve and wit. * Sean Carroll *\u003cbr\u003eThis is \u003cb\u003ea remarkable book\u003c\/b\u003e … an excellent introduction to an area that few of us probably know anything about, and all the more \u003cb\u003efascinating \u003c\/b\u003ebecause of that. * Popular Science *\u003cbr\u003e\u003ci\u003eModels of the Mind\u003c\/i\u003e is a \u003cb\u003egrand tour through the history of computational neuroscience\u003c\/b\u003e, from its humble beginnings in information theory and neuron structure up to its modern manifestations harnessing supercomputers to run large scale convolutional neural networks that model important brain systems. * Women You Should Know *\u003cbr\u003eThe book is not only \u003cb\u003ewide-ranging \u003c\/b\u003ein its choice of topics but is also a \u003cb\u003elively journey\u003c\/b\u003e through the history of these efforts and traces the lives of the eccentric and fascinating scientists who were instrumental in figuring out the brain’s working by using tools ranging from information theory and graph theory to Bayesian modeling and neural networks. * 3 Quarks Daily *\u003cbr\u003e\u003cb\u003e\u003ci\u003e \u003c\/i\u003e\u003c\/b\u003e‘\u003cb\u003eEnthralling, erudite and accessible\u003c\/b\u003e … an engrossing history of science and an enlightening guide to neuroscience’s current frontiers.’ * Liam Drew, Neurobiologist and author of I, Mammal: The Story of What Makes Us Mammals *\u003cbr\u003e‘This book is an anthology of the scientific poetry that has illuminated our studies and conceptions of the brain.’ * Professor Larry Abbott, Center for Theoretical Neuroscience, Columbia University *\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003e1: Spherical Cows 2: How Neurons Get Their Spike 3: Learning to Compute 4: Making and Maintaining Memories 5: Excitation and Inhibition 6: Stages of Sight 7: Cracking the Neural Code 8: Movement in Low Dimensions 9: From Structure to Function 10: Making Rational Decisions 11: How Rewards Guide Actions 12: Grand Unified Theories of the Brain  Mathematical Appendix Acknowledgements Bibliography Index\u003c\/i\u003e\u003c\/p\u003e","brand":"Bloomsbury Publishing PLC","offers":[{"title":"Default Title","offer_id":48867235889495,"sku":"9781472966438","price":12.34,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781472966438.jpg?v=1722282353"},{"product_id":"escape-from-model-land-how-mathematical-models-can-lead-us-astray-and-what-we-can-do-about-it-9781529364873","title":"Escape from Model Land: How Mathematical Models","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003e\u003cb\u003eShortlisted for Best Maths Book of 2022 by \u003ci\u003eChaulkdust Magazine\u003cbr\u003e\u003cbr\u003e\u003c\/i\u003e\u003c\/b\u003e\u003cb\u003e'A brilliant account of how models are so often abused and of how they should be used' John Kay\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eHow do mathematical models shape our world - and how can we harness their power for good?\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eModels are at the centre of everything we do. Whether we use them or are simply affected by them, they act as metaphors that help us better understand the increasingly complex problems facing us in the modern world. Without models, we couldn't begin to tackle three of the major challenges facing modern society: regulation of the economy, climate change and the COVID-19 pandemic. Yet in recent years, the validity of the models we use has been hotly debated and there has been renewed awareness of the disastrous consequences when the makers and interpreters of models get things wrong.\u003cbr\u003e\u003cbr\u003eDrawing on contemporary examples from finance, climate and health policy, Erica Thompson explores what models are, why we need them, how they work and what happens when they go wrong. This is not a book that argues we should do away with models, but rather, that we need to properly understand how they are constructed - and how some of the assumptions that underlie the models we   use can have significant unintended consequences. Unexpectedly humorous, thought-provoking and passionate, this is essential reading for everyone.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eA brilliant account of how models are so often abused and of how they should be used -- John Kay\u003cbr\u003eA wise, lucid and compelling guide to how mathematical modelling shapes our world. Dr Thompson teaches us how to go from being unthinking consumers of models to sophisticated users, combining a rich variety of vivid examples and case studies with deep conceptual expertise -- Stian Westlake, CEO, Royal Statistical Society\u003cbr\u003eDemystifies the process of making the mathematical models that are increasingly used to make decisions about our lives . . . A thought-provoking and helpful guide for data scientists and decision makers alike -- Stephanie Hare, author of TECHNOLOGY IS NOT NEUTRAL\u003cbr\u003eCarefully researched and beautifully written . . . For an open-minded reader keen to expose, understand and potentially reconstruct their own worldview, \u003ci\u003eEscape from Model Land\u003c\/i\u003e is, at the same time, an uncomfortable and uplifting read. It shines a gentle light on many of our own norms and beliefs -- Kevin Anderson\u003cbr\u003eAn eye-opening account . . . Thompson offers a host of lessons . . . The result is a thoughtful, convincing look at how data works -- Publisher's Weekly\u003cbr\u003eBrilliant . . . a highly engaging work of popular      science -- E\u0026amp;T Magazine\u003cbr\u003e[A] healthy realism about data, algorithms and their limitations . . . Thompson asks data scientists to be conscious of the choices and values in a model's design . . . [offering] the basis for a constructive agenda -- The Economist\u003cbr\u003eData, computing power, AI, and the models that use them will continue to proliferate. The wisdom, life experience, and humility to make the best use of those powerful tools will remain scarce. This delightfully wide-ranging book offers heaps of the latter to help us generate genuine insights from the former -- Charles J. Wheelan, bestselling author of NAKED STATISTICS\u003cbr\u003eOffers a contemplative, densely encapsulated summary of her reflection and research . . . it's up to us to learn from models without being drawn in by their seductive elegance, and to ensure that the lessons from Model Land find substantive expression where it actually matters: in our messy, material, magnificent world -- Wall Street Journal","brand":"John Murray Press","offers":[{"title":"Default Title","offer_id":48867509829975,"sku":"9781529364873","price":999.99,"currency_code":"GBP","in_stock":false}]},{"product_id":"escape-from-model-land-how-mathematical-models-can-lead-us-astray-and-what-we-can-do-about-it-9781529364897","title":"Escape from Model Land: How Mathematical Models","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003e\u003cb\u003e'A brilliant account of how models are so often abused and of how they should be used' John Kay\u003cbr\u003e\u003cbr\u003eHow do mathematical models shape our world - and how can we harness their power for good?\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eModels are at the centre of everything we do. Whether we use them or are simply affected by them, they act as metaphors that help us better understand the increasingly complex problems facing us in the modern world. Without models, we couldn't begin to tackle three of the major challenges facing modern society: regulation of the economy, climate change and the COVID-19 pandemic. Yet in recent years, the validity of the models we use has been hotly debated and there has been renewed awareness of the disastrous consequences when the makers and interpreters of models get things wrong.\u003cbr\u003e\u003cbr\u003eDrawing on contemporary examples from finance, climate and health policy, Erica Thompson explores what models are, why we need them, how they work and what happens when they go wrong. This is not a book that argues we should do away with models, but rather, that we need to properly understand how they are constructed - and how some of the assumptions that underlie the models we   use can have significant unintended consequences. Unexpectedly humorous, thought-provoking and passionate, this is essential reading for everyone.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003eA brilliant account of how models are so often abused and of how they should be used -- John Kay\u003cbr\u003eA wise, lucid and compelling guide to how mathematical modelling shapes our world. Dr Thompson teaches us how to go from being unthinking consumers of models to sophisticated users, combining a rich variety of vivid examples and case studies with deep conceptual expertise -- Stian Westlake, CEO, Royal Statistical Society\u003cbr\u003eDemystifies the process of making the mathematical models that are increasingly used to make decisions about our lives . . . A thought-provoking and helpful guide for data scientists and decision makers alike -- Stephanie Hare, author of TECHNOLOGY IS NOT NEUTRAL\u003cbr\u003eCarefully researched and beautifully written . . . For an open-minded reader keen to expose, understand and potentially reconstruct their own worldview, \u003ci\u003eEscape from Model Land\u003c\/i\u003e is, at the same time, an uncomfortable and uplifting read. It shines a gentle light on many of our own norms and beliefs -- Kevin Anderson\u003cbr\u003eAn eye-opening account . . . Thompson offers a host of lessons . . . The result is a thoughtful, convincing look at how data works -- Publisher's Weekly\u003cbr\u003eBrilliant . . . a highly engaging work of popular      science -- E\u0026amp;T Magazine\u003cbr\u003e[A] healthy realism about data, algorithms and their limitations . . . Thompson asks data scientists to be conscious of the choices and values in a model's design . . . [offering] the basis for a constructive agenda -- The Economist\u003cbr\u003eData, computing power, AI, and the models that use them will continue to proliferate. The wisdom, life experience, and humility to make the best use of those powerful tools will remain scarce. This delightfully wide-ranging book offers heaps of the latter to help us generate genuine insights from the former -- Charles J. Wheelan, bestselling author of NAKED STATISTICS\u003cbr\u003eOffers a contemplative, densely encapsulated summary of her reflection and research . . . it's up to us to learn from models without being drawn in by their seductive elegance, and to ensure that the lessons from Model Land find substantive expression where it actually matters: in our messy, material, magnificent world -- Wall Street Journal","brand":"John Murray Press","offers":[{"title":"Default Title","offer_id":48867510124887,"sku":"9781529364897","price":10.44,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781529364897.jpg?v=1722283623"},{"product_id":"tax-policy-and-uncertainty-modelling-debt-projections-and-fiscal-sustainability-9781800376007","title":"Tax Policy and Uncertainty: Modelling Debt","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003ePresenting innovative modelling approaches to the analysis of fiscal policy and government debt, this book moves beyond previous models that have relied upon the assumption that various age-specific rates and policy variables remain unchanged when it comes to generating government expenditures and tax revenues. As a result of population ageing, current policy settings in many countries are projected to lead to unsustainable levels of public debt; \u003ci\u003eTax Policy and Uncertainty\u003c\/i\u003e explores models that allow for feedbacks and uncertainty to combat this.\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003eApplicable to any country, the models in the book explore the optimal timing and extent of tax changes in the face of anticipated high future debt. Chapters produce stochastic debt projections, including probability distribution of debt ratios at each point in time. It also offers important analysis of fiscal policy trade-offs as well as providing advice on when and by how much tax rates should be increased.\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cbr\u003eEconomics scholars focusing on fiscal policy will appreciate the improved models in this book that allow both for uncertainty and feedback effects arising from responses to increased debt. It will also be helpful to economic policy advisors and economists in government departments.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTrade Review\u003c\/h2\u003e\u003ci\u003e’This book develops important innovations in addressing two problems in determining short term fiscal policy according to long run fiscal projections. The first problem is the difficulty of modelling the complex interactions of macroeconomic variables that generate feedback effects from policy decisions. Second is the potential sunk costs of making irreversible tax and spending decisions in the face of significant uncertainty about future phenomena such as population ageing and climate change. The authors build their analysis carefully and in a very readable style. It should provide a useful manual for fiscal policy makers around the world.’\u003c\/i\u003e\u003cbr\u003e- Ross Guest, Griffith University, Australia -- ’Anyone seeking to understand tax policy modelling under uncertainty will certainly want to consult this book.’- James R. Hines Jr., University of Michigan, US\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003eContents: 1. Introduction  I Deterministic Projection Models  2. Projecting Tax Revenues  3. A Debt Projection Model  II Uncertainty in Tax Models  4. Tax Policy under Uncertainty  III Debt Projections and Uncertainty  5. Stochastic Projections and Debt  6. Optimal Tax Policy  Bibliography   Index","brand":"Edward Elgar Publishing Ltd","offers":[{"title":"Default Title","offer_id":48868515545431,"sku":"9781800376007","price":86.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781800376007.jpg?v=1722288416"},{"product_id":"graph-representation-learning-9783031004605","title":"Graph Representation Learning","description":"\u003ch2\u003eBook Synopsis\u003c\/h2\u003e\u003cp\u003eGraph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis.\u003c\/p\u003e \u003cp\u003eThis book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003ch2\u003eTable of Contents\u003c\/h2\u003ePreface.- Acknowledgments.- Introduction.- Background and Traditional Approaches.- Neighborhood Reconstruction Methods.- Multi-Relational Data and Knowledge Graphs.- The Graph Neural Network Model.- Graph Neural Networks in Practice.- Theoretical Motivations.- Traditional Graph Generation Approaches.- Deep Generative Models.- Conclusion.- Bibliography.- Author's Biography .","brand":"Springer International Publishing AG","offers":[{"title":"Default Title","offer_id":48869362499927,"sku":"9783031004605","price":22.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9783031004605.jpg?v=1791480586"}],"url":"https:\/\/bookcurl.com\/collections\/mathematical-modelling.oembed?page=14","provider":"Book Curl","version":"1.0","type":"link"}