Mathematics Books

Book SynopsisOne of the most unfathomable mysteries of quantum physics... could the answer be much closer than ever we thought?Trade Review'A delightful account of one of the deepest and most fascinating explorations going on today.' —Carlo Rovelli'The renowned science writer George Musser has taken on one of our time’s greatest issues: AI, how it works, and what makes it so powerful. This masterfully written book shows a surprising connection with theoretical physics.' —Max Tegmark, author of Life 3.0‘Musser is to be applauded for tackling both consciousness and the quantum realm... He joins a distinguished list of thinkers... Musser's book is readable and enthusiastic, packed with first-person anecdotes.’ —TLS'[Musser] has assembled a vast array of ideas from developments in artificial intelligence, heterodox interpretations of modern physics, and philosophies of science and mind, and has interviewed many of the scientists and philosophers behind these theories.' —Washington Post 'The philosopher Immanuel Kant wrote once: "The starry heavens begin at the place I occupy in the external world of sense, and they broaden the connection in which I stand into an unbounded magnitude of worlds beyond worlds." In this captivating book, George Musser takes us on a fascinating tour of the modern, surprising connections scientists discover between the cosmos and our inner world of consciousness.' —Mario Livio, astrophysicist and author of The Golden Ratio‘If you’re interested in how your mind works, what its limitations are and how it connects to the rest of the cosmos, [this is] a fascinating read.’ —BBC Sky at Night, ****'I couldn't put this book down. The science of what makes reality tick, and what makes us conscious, all explored with lively, inviting prose that draws the reader in, from cover to cover.' —Susan Schneider, author of Artificial You: AI and the Future of the Mind'Putting Ourselves Back in the Equation is a remarkable book. It offers a wonderful treatment of bleeding edge issues in the physics of consciousness, asking whether we are sentient observers of the universe or whether the universe emerges from our sentient observations. George Musser leaves the reader with burning questions about our place in the universe (or vice versa)—questions whose answers seem tantalizingly within reach.' —Karl J. Friston FRS, professor of neuroscience at UCL'Fifty years ago, the great theoretical physicist P. W. Anderson wrote an essay titled "More is different." He tried to explain how when "more" is large enough, it begets "new phenomena" entirely unlike the entities of which there are "more." In this book, George Musser entices the reader to ask whether in the gap between consciousness, qualia, and free will, on the one hand, and neurons, networks, electrophysiology, quantum mechanics, and neuroanatomy on the other, there might now be a new scientific synthesis necessary. Putting Ourselves Back in the Equation is sprightly, a good read, and beguiled this reader into thinking once again about "More is different."' —John Hopfield, professor emeritus at Princeton University and former president of the American Physical Society'George Musser is one of my favourite science writers of all time. Putting Ourselves Back in the Equation is an important book that will inform both the future of physics and the philosophy of mind.' —Annaka Harris, author of Conscious: A Brief Guide to the Fundamental Mystery of the Mind'George Musser delivers stunning clarity on mother nature’s toughest puzzles. The reader will discover some things they thought they understood they don't. And mercifully, some things they thought they would never understand they now do. Putting Ourselves Back in the Equation is a great book.' —Michael S. Gazzaniga, author of The Consciousness Instinct'In Putting Ourselves Back in the Equation, George Musser takes us on a fascinating journey that links the deepest mechanisms of human consciousness to the most advanced developments in AI.' —Guido Tonelli, author of Genesis

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Book SynopsisA need for a deeper understanding of the convergence properties of augmented Lagrangian algorithms and of their relationship to operator-splitting methods such as alternating-methods direction and the development of more efficient algorithms prompted the authors to write this book. The volume is oriented to applications in continuum mechanics. This volume deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator-splitting methods (coupled to finite-element approximations). It begins with a description of the mechanical and mathematical frameworks of the considered applications as well as a general analysis of the basic numerical methods additionally used to study them. These ideas are then applied to specific classes of mechanical problems.

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Book SynopsisShaping everyday landscapes from cities to factories, the grid - an arrangement of individual elements along perpendicular lines - has been a basic structure of modern life. This book traces the relationship of these different yet intertwined methods of organizing the visual world and how we represent it in art.

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Book SynopsisFrom IB Publishing, in cooperation with Hodder Education.Help students to understand the key and related concepts and build the skills they need to reach the highest level of the assessment criteria.IB Skills is an innovative new series of resources for years 4 and 5 of the MYP.These resources aim to:- introduce students to key and related concepts that are relevant within and across the subject areas- develop interdisciplinary and disciplinary skills that are essential to the understanding of both concepts and subject content- help students to understand key features of the MYP-global contexts, approaches to learning (ATL), inquiry and reflection.These practical, subject-specific guides include a wide variety of topics designed to engage and motivate students. Each chapter in the books is designed to deepen conceptual understanding and to allow students to practice the skills that they will need to reach the highest level of the assessment criteria.

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Book SynopsisOften it is more instructive to know ''what can go wrong'' and to understand ''why a result fails'' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples - some of them both surprising and amusing - showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a self-contained, non-technical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for self-study as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to René Schilling''s other book Measures, Integrals and Martingales (www.cambridge.org/9781316620243).Trade Review'This book is an admirable counterpart, both to the first author's well-known text Measures, Integrals and Martingales (Cambridge, 2005/2017), and to the books on counter-examples in analysis (Gelbaum and Olmsted), topology (Steen and Seebach) and probability (Stoyanov). To paraphrase the authors' preface: in a good theory, it is valuable and instructive to probe the limits of what can be said by investigating what cannot be said. The task is thus well-conceived, and the execution is up to the standards one would expect from the books of the first author and of their papers. I recommend it warmly.' N. H. Bingham, Imperial College'… an excellent reference text and companion reader for anyone interested in deepening their understanding of measure theory.' John Ross, MAA Reviews'… the unique nature of the book makes it an essential acquisition for any university with a doctoral program in pure mathematics … Essential.' M. Bona, Choice Connect'The book is well written, the demonstrations are clear and the bibliographic references are competent. We appreciate this work as extremely useful for those interested in measure theory and integration, starting with beginners and extending even to advanced researchers in the field.' Liviu Constantin Florescu, Mathematical Reviews/MathSciNet'Counterexamples in Measure and Integration is an ideal companion to help better understand canonically problematic examples in analysis … This collection of counterexamples is an excellent resource to researchers who rely on measure and integration theory. It would be helpful for students studying for their analysis qualifying exam as it draws on common misconceptions and enables readers to build intuition about why a given counterexample works and how conditions can be changed to make a particular statement hold.' Katelynn Kochalski, Notices of the AMS'This is a remarkable book covering Measure and Integration, perhaps one of the most important parts of Mathematics. It is written in a master style by following the best traditions in writing this kind of books. The authors are passionate about the topic. Look at the great care with which each of the counterexamples is presented. It is done in a way to help maximally the reader. The names of the counterexamples are chosen very carefully. Any name can be considered as a 'door' behind which is a treasure!' Jordan M. Stoyanov, zbMATH'… compendia of counterexamples remain a useful and thought-provoking resource, and this new text is a high-quality example in an analytic direction.' Dominic Yeo, The Mathematical GazetteTable of ContentsPreface; User's guide; List of topics and phenomena; 1. A panorama of Lebesgue integration; 2. A refresher of topology and ordinal numbers; 3. Riemann is not enough; 4. Families of sets; 5. Set functions and measures; 6. Range and support of a measure; 7. Measurable and non-measurable sets; 8. Measurable maps and functions; 9. Inner and outer measure; 10. Integrable functions; 11. Modes of convergence; 12. Convergence theorems; 13. Continuity and a.e. continuity; 14. Integration and differentiation; 15. Measurability on product spaces; 16. Product measures; 17. Radon–Nikodým and related results; 18. Function spaces; 19. Convergence of measures; References; Index.

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Book SynopsisPoint-counting results for sets in real Euclidean space have found remarkable applications to diophantine geometry, enabling significant progress on the AndréOort and ZilberPink conjectures. The results combine ideas close to transcendence theory with the strong tameness properties of sets that are definable in an o-minimal structure, and thus the material treated connects ideas in model theory, transcendence theory, and arithmetic. This book describes the counting results and their applications along with their model-theoretic and transcendence connections. Core results are presented in detail to demonstrate the flexibility of the method, while wider developments are described in order to illustrate the breadth of the diophantine conjectures and to highlight key arithmetical ingredients. The underlying ideas are elementary and most of the book can be read with only a basic familiarity with number theory and complex algebraic geometry. It serves as an introduction for postgraduate studTable of Contents1. Introduction; Part I. Point-Counting and Diophantine Applications: 2. Point-counting; 3. Multiplicative Manin–Mumford; 4. Powers of the Modular Curve as Shimura Varieties; 5. Modular André–Oort; 6. Point-Counting and the André–Oort Conjecture; Part II. O-Minimality and Point-Counting: 7. Model theory and definable sets; 8. O-minimal structures; 9. Parameterization and point-counting; 10. Better bounds; 11. Point-counting and Galois orbit bounds; 12. Complex analysis in O-minimal structures; Part III. Ax–Schanuel Properties: 13. Schanuel's conjecture and Ax–Schanuel; 14. A formal setting; 15. Modular Ax–Schanuel; 16. Ax–Schanuel for Shimura varieties; 17. Quasi-periods of elliptic curves; Part IV. The Zilber–Pink Conjecture: 18. Sources; 19. Formulations; 20. Some results; 21. Curves in a power of the modular curve; 22. Conditional modular Zilber–Pink; 23. O-minimal uniformity; 24. Uniform Zilber–Pink; References; List of notation; Index.

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Book SynopsisA graduate-level introduction to advanced topics in Markov chain Monte Carlo (MCMC), as applied broadly in the Bayesian computational context. The topics covered have emerged as recently as the last decade and include stochastic gradient MCMC, non-reversible MCMC, continuous time MCMC, and new techniques for convergence assessment. A particular focus is on cutting-edge methods that are scalable with respect to either the amount of data, or the data dimension, motivated by the emerging high-priority application areas in machine learning and AI. Examples are woven throughout the text to demonstrate how scalable Bayesian learning methods can be implemented. This text could form the basis for a course and is sure to be an invaluable resource for researchers in the field.

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Book SynopsisIntended for first- or second-year graduate students in mathematics, as well as researchers working in algebraic geometry or combinatorics, this text introduces techniques that are essential in several areas of modern mathematics. With numerous exercises and examples, it covers the core notions and applications of equivariant cohomology.Trade Review'This book is a much-needed introduction to a powerful and central tool in algebraic geometry and related subjects. The authors are masters of clarity and rigor. The important theorems and examples are thoroughly explained, and illuminated with well-chosen exercises. This book is an essential companion for anyone wanting to understand group actions in algebraic geometry.' Ravi Vakil, Stanford University'Equivariant Cohomology is a tool from algebraic topology that becomes available when groups act on spaces. In Algebraic geometry, the groups are algebraic groups, including tori, and typical spaces are toric varieties and homogeneous varieties such as Grassmannians and flag varieties. This book introduces and studies equivariant cohomology (actually equivariant Chow groups) from the perspective of algebraic geometry, beginning with the artful replacement of Borel's classifying spaces by Totaro's finite-dimensional approximations. After developing the main properties of equivariant Chow groups, including localization and GKM theory, the authors investigate equivariant Chow groups of toric varieties and flag varieties, and the equivariant classes of Schubert varieties. Reflecting the interests of the authors, special attention is paid to Schubert calculus and the links between degeneracy loci and equivariant cohomology. The text also serves as an introduction to flag varieties, their Schubert varieties, and the calculus of Schubert classes in equivariant cohomology.' Frank Sottile, Texas A&M University'Equivariant Cohomology in Algebraic Geometry by David Anderson and William Fulton offers a comprehensive, accessible exploration of the development, standard examples, and recent contributions in this fascinating field. The authors have successfully struck a balance between rigor and approachability, making it an excellent resource for young researchers in the field. The book's real strength lies in its application to toric varieties and Schubert varieties across various settings, including Grassmannians, flag varieties, degeneracy loci, and extensions to other classical types and Kac–Moody groups. The authors' treatment of Bott-Samelson desingularizations of Schubert varieties is particularly noteworthy, displaying elegance and coherence within the context of the book's material. With over 450 pages of content, Equivariant Cohomology in Algebraic Geometry offers a comprehensive resource for researchers and scholars. It is poised to become a standard reference in the field, leaving a lasting impact on the flourishing area of research for years to come.' Sara Billey, University of WashingtonTable of Contents1. Preview; 2. Defining equivariant cohomology; 3. Basic properties; 4. Grassmannians and flag varieties; 5. Localization I; 6. Conics; 7. Localization II; 8. Toric varieties; 9. Schubert calculus on Grassmannians; 10. Flag varieties and Schubert polynomials; 11. Degeneracy loci; 12. Infinite-dimensional flag varieties; 13. Symplectic flag varieties; 14. Symplectic Schubert polynomials; 15. Homogeneous varieties; 16. The algebra of divided difference operators; 17. Equivariant homology; 18. Bott–_Samelson varieties and Schubert varieties; 19. Structure constants; A. Algebraic topology; B. Specialization in equivariant Borel–_Moore homology; C. Pfaffians and Q-polynomials; D. Conventions for Schubert varieties; E. Characteristic classes and equivariant cohomology; References; Notation index; Subject index.

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Book SynopsisPsychological Statistics: The Basics walks the reader through the core logic of statistical inference and provides a solid grounding in the techniques necessary to understand modern statistical methods in the psychological and behavioral sciences. This book is designed to be a readable account of the role of statistics in the psychological sciences. Rather than providing a comprehensive reference for statistical methods, Psychological Statistics: The Basics gives the reader an introduction to the core procedures of estimation and model comparison, both of which form the cornerstone of statistical inference in psychology and related fields. Instead of relying on statistical recipes, the book gives the reader the big picture and provides a seamless transition to more advanced methods, including Bayesian model comparison.Psychological Statistics: The Basics not only serves as an excellent primer for beginners but it is also the perfectTrade Review"This book cuts to the very heart of the core principles of statistical inference and does so in a way that is accessible and easily digestible. I honestly wish a book like this one had existed when I was a student – I would have clutched it hard and never let it go!" -- Dr. Ruth Horry, Senior Lecturer in Psychology, Swansea University, UK"I see this book as a very useful resource, not only for those who have just started their journey at the university, but also for senior students to experience "aha!" moments while recapping the basics from a unique and nicely presented perspective. I am looking forward to recommending this book to my students as soon as it is available." -- Dr. Krzysztof Cipora, Lecturer in Mathematical Cognition, Loughborough University, UK"As a new graduate student, I was suddenly faced with academic papers presenting statistical methods. But with hardly any statistical understanding myself, I struggled to do this well. I longed for a book that I could easily refer back to. This is that book. The explanations are very accessible, the examples are relatable, and the book is concise. I thoroughly recommend it." -- Jennifer Read, Graduate Student in Education, University of Derby, UK"If you want to understand why we use statistics in psychology, this is the book for you!" -- Dawn Short, Ph.D. student in Psychology, Abertay University, UK"This is an accessible and helpful educational tool that students with a variety of backgrounds will enjoy. The author incorporates clear examples and is able to frame advanced concepts in a simple and straightforward way." -- Dr. Dawn Weatherford, Associate Professor of Psychology, Texas A&M University - San Antonio, USATable of Contents1. A (Very) Brief Introduction to Statistical Inference 2. Describing the Observed Data 3. Modeling the Observed Data 4. How Likely is the Observed Data? 5. Comparing Statistical Models 6. Introduction to the t-test 7. Bayesian Model Comparison 8. Recap and Next Steps

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Book SynopsisLibrarians understand the need to store, use and analyze data related to their collection, patrons and institution, and there has been consistent interest over the last 10 years to improve data management, analysis, and visualization skills within the profession. However, librarians find it difficult to move from out-of-the-box proprietary software applications to the skills necessary to perform the range of data science actions in code. This book will focus on teaching R through relevant examples and skills that librarians need in their day-to-day lives that includes visualizations but goes much further to include web scraping, working with maps, creating interactive reports, machine learning, and others. While there's a place for theory, ethics, and statistical methods, librarians need a tool to help them acquire enough facility with R to utilize data science skills in their daily work, no matter what type of library they work at (academic, public or special). By walking through eTable of Contents1. Introduction 2. Using RStudio’s IDE 3. Tidying data with dplyr 4. Visualizing your project with ggplot2 5. Webscraping with rvest 6. Mapping with tmap 7. Textual Analysis with tidytext 8. Creating Dynamic Documents with rmarkdown 9. Creating a flexdashboard 10. Creating an interactive dashboard with shiny 11. Using tidymodels to Understand Machine Learning 12. Conclusion Appendix A. Dependencies Appendix B. Additional Skills

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Book SynopsisBayesian Inference: Theory, Methods, Computations provides a comprehensive coverage of the fundamentals of Bayesian inference from all important perspectives, namely theory, methods and computations.All theoretical results are presented as formal theorems, corollaries, lemmas etc., furnished with detailed proofs. The theoretical ideas are explained in simple and easily comprehensible forms, supplemented with several examples. A clear reasoning on the validity, usefulness, and pragmatic approach of the Bayesian methods is provided. A large number of examples and exercises, and solutions to all exercises, are provided to help students understand the concepts through ample practice. The book is primarily aimed at first or second semester master students, where parts of the book can also be used at Ph.D. level or by research community at large. The emphasis is on exact cases. However, to gain further insight into the core concepts, an entire chapter is dedicated to

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Book SynopsisAs probably the most successful scientific theory ever created, quantum theory has profoundly changed our view of the world and extended the limits of our knowledge, impacting both the theoretical interpretation of a tremendous range of phenomena and the practical development of a host of technological breakthroughs. Yet for all its success, quantum theory remains utterly baffling.Quantum Reality: Theory and Philosophy, Second Edition cuts through much of the confusion to provide readers with an exploration of quantum theory that is as authoritatively comprehensive as it is intriguingly comprehensible. The book has been fully updated throughout to include the latest results in quantum entanglement, the theory and practical applications of quantum computing, quantum cosmology and quantum gravity. Needing little more than a school level physics and mathematics background, this volume requires only an interest in understanding how quantum theory came to be and tTable of ContentsIntroduction. Chapter 1. Our First Encounter with the Quantum World: Light. Chapter 2. Particles. Chapter 3. Quantum States. Chapter 4. Amplitudes. Chapter 5. Measurement. Chapter 6. Interference. Chapter 7. Free Particles. Chapter 8. Identical Particles. Chapter 9. Scattering Identical Bosons. Chapter 10. Spin. Chapter 11. Fermion States. Chapter 12. Continuous Bases. Chapter 13. Uncertainty. Chapter 14. The Equations of Quantum Theory. Chapter 15. Constrained Particles. Chapter 16. Genealogy. Chapter 17. Planck and Einstein. Chapter 18. Bohr. Chapter 19. Heisenberg. Chapter 20. De Broglie & Schrödinger. Chapter 21. Dirac. Chapter 22. Conclusions. Chapter 23. Quantum Correlations. Chapter 24. Quantum Computing. Chapter 25. Density Operators. Chapter 26. Interpretations. Chapter 27. The Copenhagen Interpretation. Chapter 28. The Many Worlds Interpretation. Chapter 29. Assorted Alternatives. Chapter 30. Consistent Histories. Chapter 31. The Ontological Interpretation. Chapter 32. Quantum Field Theory. Chapter 33. Personal Conclusions. Appendix.

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Book SynopsisA concise treatment of the fundamentals of thermodynamics is presented in this book. In particular, emphasis is placed on discussions of the second law, a unique feature of thermodynamics, which states the limitations of converting thermal energy into mechanical energy. The entropy function that permits the loss in the potential of a real thermodynamic process to be assessed, the maximum possible work in a process, and irreversibility and equilibrium are deduced from the law through physical and intuitive considerations. They are applicable in mitigating waste heat and are useful for solving energy, power, propulsion and climate-related issues.The treatment is not restricted to properties and functions of ideal gases. The ideal gas assumption is invoked as a limiting case. Reversible paths between equilibrium states are obtained using reversible heat engines and reversible heat pumps between environment and systems to determine the entropy changes and the maximum work. The coTable of Contents1. Fundamental Concepts. 2. Equation of State. 3. First Law of Thermodynamics. 4. Second Law of Thermodynamics. 5. Entropy. 6. Reversible Work, Availability and Irreversibility. 7. Thermodynamic State Functions. 8. Thermodynamic Coefficients and Specific Heats. 9. Thermodynamic Equilibrium. 10. Equilibrium of Species in a Chemically Reacting System. 11. Statistical Thermodynamics.

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Book SynopsisThe book equips students with the end-to-end skills needed to do data science. That means gathering, cleaning, preparing, and sharing data, then using statistical models to analyse data, writing about the results of those models, drawing conclusions from them, and finally, using the cloud to put a model into production, all done in a reproducible way.At the moment, there are a lot of books that teach data science, but most of them assume that you already have the data. This book fills that gap by detailing how to go about gathering datasets, cleaning and preparing them, before analysing them. There are also a lot of books that teach statistical modelling, but few of them teach how to communicate the results of the models and how they help us learn about the world. Very few data science textbooks cover ethics, and most of those that do, have a token ethics chapter. Finally, reproducibility is not often emphasised in data science books. This book is based around a straight-forward workflow conducted in an ethical and reproducible way: gather data, prepare data, analyse data, and communicate those findings. This book will achieve the goals by working through extensive case studies in terms of gathering and preparing data, and integrating ethics throughout. It is specifically designed around teaching how to write about the data and models, so aspects such as writing are explicitly covered. And finally, the use of GitHub and the open-source statistical language R are built in throughout the book.Key Features: Extensive code examples. Ethics integrated throughout. Reproducibility integrated throughout. Focus on data gathering, messy data, and cleaning data. Extensive formative assessment throughout. Trade Review"This clean and fun book covers a wide range of topics on statistical communication, programming, and modeling in a way that should be a useful supplement to any statistics course or self-learning program. I absolutely love this book!"- Andrew Gelman, Columbia University"An excellent book. Communication and reproducibility are of increasing concern in statistics, and this book covers these topics and more in a practical, appealing, and truly unique way."- Daniela Witten, University of Washington"Many data science texts tell you how to perform perfunctory calculations. Instead, Telling Stories with Data tells you how to engage in the mindset and process of analysis. By arming students with the computational, statistical and philosophical skills needed to use data in sense-making and story-telling, this book stands out from the pack as uniquely actionable and empowering."- Emily Riederer, Capital One"This is not another statistics book. It is much better than that. It is a book about doing quantitative research, about scientific justification, about quality control, about communication and epistemic humility. It's a valuable supplement to any methods curriculum, and useful for self-learners as well."- Richard McElreath, Max Planck Institute for Evolutionary Anthropology"Telling Stories with Data is a thoughtful guide to using data to learn and affect positive change. The book includes each stage of the process and can serve as a long-lasting companion to many data scientists and future data story tellers."- Christopher Peters, Zapier“A clever career choice is to pick a field where your skills are complementary with a growing resource. In the coming decades, those who are adept in analysing data will flourish. That means crunching statistics and telling compelling stories. Rohan Alexander’s book will help you do both.”- Andrew Leigh, Member of the Australian Parliament and author of Randomistas: How Radical Researchers Are Changing Our World"Every data analyst has to tell stories with data, and yet traditional textbooks focus on statistical methods alone. Telling Stories with Data teaches the entire data science workflow, including data acquisition, communication, and reproducibility. I highly recommend this unique book!"- Kosuke Imai, Harvard University"This is an extraordinary, wonderful, book, full of wise advice for anyone starting in data science. Intermixing concepts and code means the ideas are immediately made concrete, and the emphasis on reproducible workflows brings a welcome dose of rigor to a rapidly developing field."- David Spiegelhalter, The University of CambridgeTable of Contents1. Telling stories with data 2. Drinking from a fire hose 3. Reproducible workflows Part 1. Foundations 4. Writing research 5. Static communication Part 2. Communication 6. Farm data 7. Gather data 8. Hunt data Part 3. Acquisition 9. Clean and prepare 10. Store and share Part 4. Preparation 11. Exploratory data analysis 12. Linear models 13. Generalized linear models 14. Causality from observational data 15. Multilevel regression with post-stratification 16. Text as data 17. Concluding remarks

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Book SynopsisThis text introduces bad events (incidents and accidents) named as metaphors. The metaphors, called as safety animals, are named as black swan, gray rhino, gray swans, and invisible gorilla.The book analyzes incidents and accidents from the context of the safety management system in the risky industries including aviation, nuclear, chemical, oil, and petroleum. It further uses mathematical analysis of these events (through statistics and probabilities) and presents preventive and corrective measures in dealing with the same.It comprehensively covers important topics including real-time monitoring, reverse stress testing, change management, predictive maintenance, management system, contingency plans, human factors, behavioral safety, anticipatory failure determination, resilience engineering (RE), resilience management (RM), Swiss cheese model, and probability distribution.Aimed at professionals working in the fields of health and safety, quTable of Contents1. Philosophy of Science as Introduction. 2. The Black Swan events. 3. Analysis of the “Fat-tails” in Safety. 4. What to do with BSe in the Risky Industry?. 5. The Gray Rhino events. 6. Specifics of GRe in Risky Industry. 7. The Invisible Gorilla. 8. Other “Safety Animals”. 9. How to fight “Safety Animals”?. 10. Top Management and “Safety Animals”. 11. Final Words.

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Book SynopsisCarl Friedrich Gauss, the foremost of mathematicians, was a land surveyor. Measuring and calculating geodetic networks on the curved Earth was the inspiration for some of his greatest mathematical discoveries. This is just one example of how mathematics and geodesy, the science and art of measuring and mapping our world, have evolved together throughout history.This text is for students and professionals in geodesy, land surveying, and geospatial science who need to understand the mathematics of describing the Earth and capturing her in maps and geospatial data: the discipline known as mathematical geodesy. Map of the World: An Introduction to Mathematical Geodesy aims to provide an accessible introduction to this area, presenting and developing the mathematics relating to maps, mapping, and the production of geospatial data. Described are the theory and its fundamental concepts, its application for processing, analyzing, transforming, and projecting geospatial data, and how these are used in producing charts and atlases. Also touched upon are the multitude of cross-overs into other sciences sharing in the adventure of discovering what our world really looks like.FEATURESâ Written in a fluid and accessible style, replete with exercises; adaptable for courses on different levels.â Suitable for students and professionals in the mapping sciences, but also for lovers of maps and map making.Trade Review"Map of the World: An Introduction to Mathematical Geodesy is organized, written and presented in an impressively accessible style that is replete with exercises -- making it highly adaptable textbook for curriculum courses on different levels. Especially and unreservedly recommended for students and professionals in the mapping sciences, Map of the World will prove to be an ideal and instructive source for non-specialist readers with an interest in maps and map making. While a critically important addition to college and university library collections, it should be noted for personal reading lists that Maps of the World is also available in a digital book format."—Midwest Book Review"This is a textbook covering mathematics applied to geodesy: the measuring and mapping of our ellipsoid spheroid earth that includes an overview of earth measurement and mapping back to remote times. The mathematics of describing the Earth through maps and geospatial data is covered from underpinnings to application. [. . .] This textbook, including some exercises (without solutions), is aimed at students and practitioners in geodesy, land surveying, and geospatial science. It is easy to see this as a reference work. [. . .] this is a concise review of the theory and development of coordinate reference systems."—Tom Schulte, MAA Reviews ". . .(T)his text, by a geodesist (Vermeer) and a mathematician (Rasila), focuses primarily on the mathematics enabling map projections, coordinate systems, and transformation of three-dimensional coordinate representations, ranging from Euclidean to Reimannian geometries. Although the geometry is beyond what most geography students would need to address, the detailed mathematics offers a bridge for integration of collaborative teaching appropriate for upper-level mathematics and physics students, with applications to both cartography and geophysics. Each chapter concludes with exercises that provide an opportunity for learning the explicit mathematics behind the calculation presented. Interesting historical anecdotes about mathematicians and the evolution of geodesy are also included throughout. Students and readers of mathematics and geophysics as well as scientists working in the interdisciplinary area of geodesy will appreciate this book."– Choice Review, C. A. Badurek, SUNY Cortland"Map of the World: An Introduction to Mathematical Geodesy is organized, written and presented in an impressively accessible style that is replete with exercises -- making it highly adaptable textbook for curriculum courses on different levels. Especially and unreservedly recommended for students and professionals in the mapping sciences, Map of the World will prove to be an ideal and instructive source for non-specialist readers with an interest in maps and map making. While a critically important addition to college and university library collections, it should be noted for personal reading lists that Maps of the World is also available in a digital book format."—Midwest Book Review"This is a textbook covering mathematics applied to geodesy: the measuring and mapping of our ellipsoid spheroid earth that includes an overview of earth measurement and mapping back to remote times. The mathematics of describing the Earth through maps and geospatial data is covered from underpinnings to application. [. . .] This textbook, including some exercises (without solutions), is aimed at students and practitioners in geodesy, land surveying, and geospatial science. It is easy to see this as a reference work. [. . .] this is a concise review of the theory and development of coordinate reference systems."—Tom Schulte, MAA Reviews Table of Contents1. A Brief History of Mapping. 2. Popular Conformal Map Projections. 3. The Complex Plane and Conformal Mappings. 4. Complex Analysis. 5. Conformal Mappings. 6. Transversal Mercator Projections. 7. Sperical Trigonometry. 8. The Geometry of the Ellipsoid of Revolution. 9. Three-dimensional Co-ordinates and Transformations. 10. Co-ordinate Reference Systems. 11. Co-ordinates of Heaven and Earth. 12. The Orbital Motion of Satellites. 13. The Surface Theory of Gauss. 14. Riemann Surfaces and Charts. 15. Map Projections in the Light of Surface Theory. 16. Appendices

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Book SynopsisThis book is the very first one in the English language entirely dedicated to the Lambert W function, its generalizations, and its applications. One goal is to promote future research on the topic. The book contains all the information one needs when trying to find a result. The most important formulas and results are framed. The Lambert W function is a multi-valued inverse function with plenty of applications in areas like molecular physics, relativity theory, fuel consumption models, plasma physics, analysis of epidemics, bacterial growth models, delay differential equations, fluid mechanics, game theory, statistics, study of magnetic materials, and so on.The first part of the book gives a full treatise of the W function from theoretical point of view.The second part presents generalizations of this function which have been introduced by the need of applications where the classical W function is insufficient.The third part presents a large number of app

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Book SynopsisEvery finance professional wants and needs a competitive edge. A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it. Many are notâand that is the competitive edge these books offer the astute reader.Published under the collective title of Foundations of Quantitative Finance, this set of ten books develops the advanced topics in mathematics that finance professionals need to advance their careers. These books expand the theory most do not learn in graduate finance programs, or in most financial mathematics undergraduate and graduate courses.As an investment executive and authoritative instructor, Robert R. Reitano presents the mathematical theories he encountered and used in nearly three decades in the financial services industry and two decades in academia where he taught in highly respected graduate programs.Readers should be quantitatively literate and familiar with the development

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