Mathematics of Discrete Structures for Computer Science

Number theory is concerned with the properties of the natural numbers: 1, 2, 3 … During the seventeenth and eighteenth centuries, number theory became established through the work of Fermat, Euler and Gauss. With the hand calculators and computers of today the results of extensive numerical work are instantly available and the road leading to their discoveries may be traversed with comparative care. Now in its second edition, this book consists of a sequence of exercises that will lead readers from quite simple number work to the point where they can prove algebraically the classical results of elementary number theory for themselves. A modern secondary school course in mathematics is sufficient background for the whole book which is designed to be used as an undergraduate course in number theory to be pursued by independent study without supporting lectures.

Paul Dirac, who died in 1984, was without question one of the greatest physicists of the twentieth century. His revolutionary contribution to modern quantum theory is remembered for its insight and creativity. He is especially famous for his prediction of the magnetic moment and spin of the electron and for the existence of antiparticles. He was awarded the Nobel Prize for physics in 1933 at the age of 31. In this memorial volume, 24 of Dirac's friends, colleagues and contemporaries remember him with affection. There are chapters describing Dirac's personality, and many anecdotes about the man with a reputation for silence. Other chapters describe Dirac's science and its impact on modern physics.

Uncover the evidence-based science to slowing the effects of aging, from the New York Times bestselling author of the How Not to Die seriesWhen Dr. Michael Greger, founder of NutritionFacts.org, dove into the top peer-reviewed anti-aging medical research, he realized that diet could regulate every one of the most promising strategies for combating the effects of aging. We don’t need Big Pharma to keep us feeling young―we already have the tools. In How Not to Age, the internationally renowned physician and nutritionist breaks down the science of aging and chronic illness and explains how to help avoid the diseases most commonly encountered in our journeys through life.Physicians have long treated aging as a malady, but getting older does not have to mean getting sicker. There are eleven pathways for aging in our bodies’ cells and we can disrupt each of them. Processes like autophagy, the upcycling of unusable junk, can be boosted with spermidine, a compound found in tempeh, mushrooms, a

This ground-breaking volume explores a series of inter-related key themes in Saharan archaeology and history. Migration and identity formation can both be approached from the perspective of funerary archaeology, using the combined evidence of burial structures, specific rites and funerary material culture, and integrated methods of skeletal analysis including morphometrics, palaeopathology and isotopes. Burial traditions from various parts of the Sahara are compared and contrasted with those of the Nile Valley, the Maghreb and West Africa. Several chapters deal with the related evidence of human migration derived from linguistic study. The volume presents the state of the field of funerary archaeology in the Sahara and its neighbouring regions and sets the agenda for future research on mobility, migration and identity. It will be a seminal reference point for Mediterranean and African archaeologists, historians and anthropologists as well as archaeologists interested in burial and migr

Coastal exposures of the Santa Cruz Formation in southern Patagonia have been a fertile ground for recovery of Early Miocene vertebrates for more than 100 years. This volume presents a comprehensive compilation of important mammalian groups which continue to thrive today. It includes the most recent fossil finds as well as important new interpretations based on ten years of fieldwork by the authors. A key focus is placed on the paleoclimate and paleoenvironment during the time of deposition in the Middle Miocene Climatic Optimum (MMCO) between twenty and fifteen million years ago. The authors present the first reconstruction of what climatic conditions were like and present important new evidence of the geochronological age, habits and community structures of fossil bird and mammal species. Academic researchers and graduate students in paleontology, paleobiology, paleoecology, stratigraphy, climatology and geochronology will find this a valuable source of information about this fascina

Monarchy was widespread as a political system in the ancient world. This volume offers a substantial discussion of ancient monarchies from the viewpoint of the ruler's court. The monarchies treated are Achaemenid and Sassanian Persia, the empire of Alexander, Rome under both the early and later Caesars, the Han rulers of China and Egypt's Eighteenth Dynasty. A comparative approach is adopted to major aspects of ancient courts, including their organisation and physical setting, their role as a vehicle for display, and their place in monarchial structures of power and control. This approach is broadly inspired by work on courts in later periods of history, especially early-modern France. The case studies confirm that ancient monarchies created the conditions for the emergence of a court and court society. The culturally specific conditions in which these monarchies functioned meant variety in the character of the ruler's court from one society to another.

Monarchy was widespread as a political system in the ancient world. This volume offers a substantial discussion of ancient monarchies from the viewpoint of the ruler's court. The monarchies treated are Achaemenid and Sassanian Persia, the empire of Alexander, Rome under both the early and later Caesars, the Han rulers of China and Egypt's Eighteenth Dynasty. A comparative approach is adopted to major aspects of ancient courts, including their organisation and physical setting, their role as a vehicle for display, and their place in monarchial structures of power and control. This approach is broadly inspired by work on courts in later periods of history, especially early-modern France. The case studies confirm that ancient monarchies created the conditions for the emergence of a court and court society. The culturally specific conditions in which these monarchies functioned meant variety in the character of the ruler's court from one society to another.

Peter Mack examines the impact of humanist training in rhetoric and argument on a range of Elizabethan prose texts, including political orations, histories, romances, conduct manuals, privy council debates and personal letters. Elizabethan Rhetoric reconstructs the knowledge, skills and approaches which an Elizabethan would have acquired in order to participate in the political and religious debates of the time: the approaches to an audience, analysis and replication of textual structures, organisation of arguments and tactics for disputation. Study of the rhetorical codes and conventions in terms of which debates were conducted is currently a major area of historical and literary enquiry, and Mack provides a wealth of new information about what was taught and how these conventions were exploited in personal memoranda, court depositions, sermons and political and religious pamphlets. This important book will be invaluable for all those interested in the culture, literature and politica

For Michel Foucault, philosophy was a way of questioning the allegedly necessary truths that underpin the practices and institutions of modern society. He carried this out in a series of deeply original and strikingly controversial studies on the origins of modern medical and social scientific disciplines. These studies have raised fundamental questions about the nature of human knowledge and its relation to power structures, and have become major topics of discussion throughout the humanities and social sciences. The essays in this volume provide a comprehensive overview of Foucault's major themes and texts, from his early work on madness through his history of sexuality. Special attention is also paid to thinkers and movements, from Kant through current feminist theory, that are particularly important for understanding his work and its impact. This revised edition contains five new essays and revisions of many others, and the extensive bibliography has been updated.

This book describes the stochastic method for ocean wave analysis. This method provides a route to predicting the characteristics of random ocean waves - information vital for the design and safe operation of ships and ocean structures. Assuming a basic knowledge of probability theory, the book begins with a chapter describing the essential elements of wind-generated random seas from the stochastic point of view. The following three chapters introduce spectral analysis techniques, probabilistic predictions of wave amplitudes, wave height and periodicity. A further four chapters discuss sea severity, extreme sea state, the directional wave energy spreading in random seas and special wave events such as wave breaking and group phenomena. Finally the stochastic properties of non-Gaussian waves are presented. Useful appendices and an extensive reference list are included. Examples of practical applications of the theories presented can be found throughout the text. This book will be suitab

For Michel Foucault, philosophy was a way of questioning the allegedly necessary truths that underpin the practices and institutions of modern society. He carried this out in a series of deeply original and strikingly controversial studies on the origins of modern medical and social scientific disciplines. These studies have raised fundamental questions about the nature of human knowledge and its relation to power structures, and have become major topics of discussion throughout the humanities and social sciences. The essays in this volume provide a comprehensive overview of Foucault's major themes and texts, from his early work on madness through his history of sexuality. Special attention is also paid to thinkers and movements, from Kant through current feminist theory, that are particularly important for understanding his work and its impact. This revised edition contains five new essays and revisions of many others, and the extensive bibliography has been updated.

Peter Mack examines the impact of humanist training in rhetoric and argument on a range of Elizabethan prose texts, including political orations, histories, romances, conduct manuals, privy council debates and personal letters. Elizabethan Rhetoric reconstructs the knowledge, skills and approaches which an Elizabethan would have acquired in order to participate in the political and religious debates of the time: the approaches to an audience, analysis and replication of textual structures, organisation of arguments and tactics for disputation. Study of the rhetorical codes and conventions in terms of which debates were conducted is currently a major area of historical and literary enquiry, and Mack provides a wealth of new information about what was taught and how these conventions were exploited in personal memoranda, court depositions, sermons and political and religious pamphlets. This important book will be invaluable for all those interested in the culture, literature and politica

This book describes the stochastic method for ocean wave analysis. This method provides a route to predicting the characteristics of random ocean waves - information vital for the design and safe operation of ships and ocean structures. Assuming a basic knowledge of probability theory, the book begins with a chapter describing the essential elements of wind-generated random seas from the stochastic point of view. The following three chapters introduce spectral analysis techniques, probabilistic predictions of wave amplitudes, wave height and periodicity. A further four chapters discuss sea severity, extreme sea state, the directional wave energy spreading in random seas and special wave events such as wave breaking and group phenomena. Finally the stochastic properties of non-Gaussian waves are presented. Useful appendices and an extensive reference list are included. Examples of practical applications of the theories presented can be found throughout the text. This book will be suitab

In this authoritative study of international economic relations, first published in 1991, László Csaba examines the power structures, economic reforms and economic developments within Eastern Europe. He explores the history of intra-regional cooperation and conflicts and international trade, evaluating the changes within the system created by the standards and requirements of the world economy. Particular attention is paid to Soviet-East European relations, assessing the merits and limitations of recent policies and the implications for Eastern Europe of the change and challenge of Gorbachev's reforms. The author addresses many key issues of the economic system. These include price formation in intra-CMEA trade; the impact of the settlement on transferable rouble accounts on intra-CMEA prices and finance; the consequences the CMEA's complex programme of 1971 has had for trade and development and its long-term target programmes initiated in 1976. Csaba looks forward to the new preoccupa

Join Liko and Roy on their journey to become real Pokémon Trainers as they embark on a series of training battles.This simple story book is accessible to young readers who are learning to read independently.Liko, Sprigatito, Roy, and Fuecoco are now official members of the Rising Volt Tacklers and ask Friede to train them, but Friede has an electrifying surprise in store for them. Will they manage to dig deep and uncover what it takes to become true Pokémon Trainers?This Level 2 reader includes longer sentence structures, more challenging vocabulary, paragraphs and short chapter lengths.

Most object-oriented or functional languages are higher order languages, i.e. ones in which the means of manipulation (e.g. object or function) can itself be manipulated. This 1998 book contains a collection of original articles about recent developments in operational semantics for higher order programming languages by some of the leading researchers in the field. Operational techniques are important because they are closer to implementations and language definitions than more abstract mathematical techniques such as denotational semantics. One of the exciting developments reflected by the book is that mathematical structures and techniques used in denotational semantics (such as fixpoint induction) may be recovered from a purely operational starting point. The book surveys and introduces techniques such as contextual equivalence, applicative bisimulation, logical relations, improvement relations, explicit models of memory management, and labelling techniques for confluence properties

A science-based approach for transforming ailments of both body and mind through cold-water swimming.The belief that swimming in cold water can improve one's health is hardly new. For centuries, people from all over the world have reported that immersing themselves in cold water alleviates their pain and improves their overall well-being. Even Katharine Hepburn famously claimed to treat her winter colds by swimming in the icy waters of the Pacific Ocean. But until now, the practice has been treated lightly by the scientific community, the curative effects all but dismissed by doctors seeking medicine-centered solutions for their patients' illnesses.In Chill, expert anesthetist and researcher Dr. Mark Harper delivers long-awaited evidence that cold-water swimming can, in fact, achieve powerful, tangible health benefits. Combining science with case studies and stories from the lives of patients, Dr. Harper illuminates the ways in which cold water can impact us physiologically and mentall

Deep Wheel Orcadia is, effortlessly, a first: a science-fiction verse-novel written in the Orcadian dialect, it's also the first full-length book in the Orkney language in over fifty years.Astrid is returning home from art school on Mars, looking for inspiration. Darling is fleeing a life that never fit, searching for somewhere to hide. They meet on Deep Wheel Orcadia, a distant space station struggling for survival as the pace of change threatens to leave the community behind.Deep Wheel Orcadia is a magical first: a science-fiction verse-novel written in the Orkney dialect. This unique adventure in minority language poetry comes with a parallel translation into playful and vivid English, so the reader will miss no nuance of the original. The rich and varied cast weaves a compelling, lyric and effortlessly readable story around place and belonging, work and economy, generation and gender politics, love and desire - all with the lightness of touch, fluency and musicality one might expec

Barron's SAT Premium Study Guide with 7 Practice Tests provides detailed review, online practice, and expert advice from experienced teachers who know the test. Step-by-step review helps you master the content, and full-length practice tests in the book and online help you feel ready for the actual SAT. This edition includes: Four full-length practice tests in the bookTwo full-length online practice testsOne full-length diagnostic test to help identify strengths and weaknesses so you can pinpoint your trouble spots and focus your studyBarron's extensive vocabulary list in online flashcard formatAn overview of the SAT, an explanation of the test's scoring method, and study advice from experienced teachersTest-taking tactics for the exam as a whole, and special strategies for each part of the test, including detailed instruction in writing the SAT essaySubject reviews covering all sections of the test, including Reading, Writing and Language, and Mathematics

Optimization methods play a central role in financial modeling. This textbook is devoted to explaining how state-of-the-art optimization theory, algorithms, and software can be used to efficiently solve problems in computational finance. It discusses some classical mean–variance portfolio optimization models as well as more modern developments such as models for optimal trade execution and dynamic portfolio allocation with transaction costs and taxes. Chapters discussing the theory and efficient solution methods for the main classes of optimization problems alternate with chapters discussing their use in the modeling and solution of central problems in mathematical finance. This book will be interesting and useful for students, academics, and practitioners with a background in mathematics, operations research, or financial engineering. The second edition includes new examples and exercises as well as a more detailed discussion of mean–variance optimization, multi-period models, and add

Scientists need statistics. Increasingly this is accomplished using computational approaches. Freeing readers from the constraints, mysterious formulas and sophisticated mathematics of classical statistics, this book is ideal for researchers who want to take control of their own statistical arguments. It demonstrates how to use spreadsheet macros to calculate the probability distribution predicted for any statistic by any hypothesis. This enables readers to use anything that can be calculated (or observed) from their data as a test statistic and hypothesize any probabilistic mechanism that can generate data sets similar in structure to the one observed. A wide range of natural examples drawn from ecology, evolution, anthropology, palaeontology and related fields give valuable insights into the application of the described techniques, while complete example macros and useful procedures demonstrate the methods in action and provide starting points for readers to use or modify in their ow

How should one choose the best restaurant to eat in? Can one really make money at gambling? Or predict the future? Naive Decision Making presents the mathematical basis for making decisions where the outcome may be uncertain or the interests of others have to taken into consideration. Professor Körner takes the reader on an enjoyable journey through many aspects of mathematical decision making, with pithy observations, anecdotes and quotations. Topics include probability, statistics, Arrow's theorem, Game Theory and Nash equilibrium. Readers will also gain a great deal of insight into mathematics in general and the role it can play within society. Intended for those with elementary calculus, this book is ideal as a supplementary text for undergraduate courses in probability, game theory and decision making. Engaging and intriguing, it will also appeal to all those of a mathematical mind. To aid understanding, many exercises are included, with solutions available online.

How should one choose the best restaurant to eat in? Can one really make money at gambling? Or predict the future? Naive Decision Making presents the mathematical basis for making decisions where the outcome may be uncertain or the interests of others have to taken into consideration. Professor Körner takes the reader on an enjoyable journey through many aspects of mathematical decision making, with pithy observations, anecdotes and quotations. Topics include probability, statistics, Arrow's theorem, Game Theory and Nash equilibrium. Readers will also gain a great deal of insight into mathematics in general and the role it can play within society. Intended for those with elementary calculus, this book is ideal as a supplementary text for undergraduate courses in probability, game theory and decision making. Engaging and intriguing, it will also appeal to all those of a mathematical mind. To aid understanding, many exercises are included, with solutions available online.

During the past two decades there has been active interplay between geometric measure theory and Fourier analysis. This book describes part of that development, concentrating on the relationship between the Fourier transform and Hausdorff dimension. The main topics concern applications of the Fourier transform to geometric problems involving Hausdorff dimension, such as Marstrand type projection theorems and Falconer's distance set problem, and the role of Hausdorff dimension in modern Fourier analysis, especially in Kakeya methods and Fourier restriction phenomena. The discussion includes both classical results and recent developments in the area. The author emphasises partial results of important open problems, for example, Falconer's distance set conjecture, the Kakeya conjecture and the Fourier restriction conjecture. Essentially self-contained, this book is suitable for graduate students and researchers in mathematics.

General relativity is now an essential part of undergraduate and graduate courses in physics, astrophysics and applied mathematics. This simple, user-friendly introduction to relativity is ideal for a first course in the subject. Beginning with a comprehensive but simple review of special relativity, the book creates a framework from which to launch the ideas of general relativity. After describing the basic theory, it moves on to describe important applications to astrophysics, black hole physics, and cosmology. Several worked examples, and numerous figures and images, help students appreciate the underlying concepts. There are also 180 exercises which test and develop students' understanding of the subject. The textbook presents all the necessary information and discussion for an elementary approach to relativity. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521735612.

General relativity is now an essential part of undergraduate and graduate courses in physics, astrophysics and applied mathematics. This simple, user-friendly introduction to relativity is ideal for a first course in the subject. Beginning with a comprehensive but simple review of special relativity, the book creates a framework from which to launch the ideas of general relativity. After describing the basic theory, it moves on to describe important applications to astrophysics, black hole physics, and cosmology. Several worked examples, and numerous figures and images, help students appreciate the underlying concepts. There are also 180 exercises which test and develop students' understanding of the subject. The textbook presents all the necessary information and discussion for an elementary approach to relativity. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521735612.

For the last thirty years, international summer schools in plasma physics have been held at Culham Laboratory, site of the Joint European Torus fusion project. This book has been developed from lectures given at these schools, and provides a wide-ranging introduction to the subject. The first few chapters deal with the fundamentals of plasma physics. In subsequent chapters, the applications and properties of man-made and naturally occurring plasmas are discussed. In addition, there are chapters devoted to general phenomena such as turbulence and chaos. The computational techniques employed in modelling plasma behaviour are also described. Since no prior knowledge of plasma physics is assumed, this book will act as an ideal introduction to the subject for final year undergraduates and beginning graduate students in physics, astronomy, mathematics and engineering.

When new ideas like chaos first move into the mathematical limelight, the early textbooks tend to be very difficult. The concepts are new and it takes time to find ways to present them in a form digestible to the average student. This process may take a generation, but eventually, what originally seemed far too advanced for all but the most mathematically sophisticated becomes accessible to a much wider readership. This book takes some major steps along that path of generational change. It presents ideas about chaos in discrete time dynamics in a form where they should be accessible to anyone who has taken a first course in undergraduate calculus. More remarkably, it manages to do so without discarding a commitment to mathematical substance and rigour. The book evolved from a very popular one-semester middle level undergraduate course over a period of several years and has therefore been well class-tested.

The life of trailblazing physicist Mildred Dresselhaus, who expanded our understanding of the physical world.As a girl in New York City in the 1940s, Mildred “Millie” Dresselhaus was taught that there were only three career options open to women: secretary, nurse, or teacher. But sneaking into museums, purchasing three-cent copies of National Geographic, and devouring books on the history of science ignited in Dresselhaus (1930–2017) a passion for inquiry. In Carbon Queen, science writer Maia Weinstock describes how, with curiosity and drive, Dresselhaus defied expectations and forged a career as a pioneering scientist and engineer. Dresselhaus made highly influential discoveries about the properties of carbon and other materials and helped reshape our world in countless ways―from electronics to aviation to medicine to energy. She was also a trailblazer for women in STEM and a beloved educator, mentor, and colleague. Her path wasn’t easy. Dresselhaus’s Bronx childhood was impoverishe

Scientists Making a Difference is a fascinating collection of first-person narratives from the top psychological scientists of the modern era. These readable essays highlight the most important contributions to theory and research in psychological science, show how the greatest psychological scientists formulate and think about their work, and illustrate how their ideas develop over time. In particular, the authors address what they consider their most important scientific contribution, how they got the idea, how the idea matters for the world beyond academic psychology, and what they would like to see as the next steps in research. The contributors, who were chosen from an objectively compiled list of the most eminent psychological scientists, provide a broad range of insightful perspectives. This book is essential reading for students, researchers and professionals interested in learning about the development of the biggest ideas in modern psychological science, described firsthand b

Scientists Making a Difference is a fascinating collection of first-person narratives from the top psychological scientists of the modern era. These readable essays highlight the most important contributions to theory and research in psychological science, show how the greatest psychological scientists formulate and think about their work, and illustrate how their ideas develop over time. In particular, the authors address what they consider their most important scientific contribution, how they got the idea, how the idea matters for the world beyond academic psychology, and what they would like to see as the next steps in research. The contributors, who were chosen from an objectively compiled list of the most eminent psychological scientists, provide a broad range of insightful perspectives. This book is essential reading for students, researchers and professionals interested in learning about the development of the biggest ideas in modern psychological science, described firsthand b

The coastal ocean comprises the semi-enclosed seas on the continental shelf, including estuaries and extending to the shelf break. This region is the focus of many serious concerns, including coastal inundation by tides, storm surges or sea level change; fisheries and aquaculture management; water quality; harmful algal blooms; planning of facilities (such as power stations); port development and maintenance; and oil spills. This book addresses modeling and simulation of the transport, evolution and fate of particles (physical and biological) in the coastal ocean. It is the first to summarize the state of the art in this field and direct it toward diverse applications, for example in measuring and monitoring sediment motion, oil spills and larval ecology. This is an invaluable textbook and reference work for advanced students and researchers in oceanography, geophysical fluid dynamics, marine and civil engineering, computational science and environmental science.

Holmes Rolston challenges the sociobiological orthodoxy that would naturalize science, ethics, and religion. The book argues that genetic processes are not blind, selfish, and contingent, and that nature is therefore not value-free. The author examines the emergence of complex biodiversity through evolutionary history. Especially remarkable in this narrative is the genesis of human beings with their capacities for science, ethics, and religion. A major conceptual task of the book is to relate cultural genesis to natural genesis. There is also a general account of how values are created and transmitted in both natural and human cultural history. The book is written by one of the most well-respected figures in the philosophy of biology and religion.

The concept of Hopf algebras was first introduced in the theory of algebraic topology but in recent years has been developed by many mathematicians and applied to other areas of mathematics such as Lie groups, algebraic groups and Galois theory. This book is an introduction to the basic theory of Hopf algebras for the reader already familiar with the basic ideas of linear algebra and commutative algebra. After introducing and discussing the basic properties of coalgebras, bialgebras and Hopf algebras, the author treats the fundamental structure theorem of bi-modules and Sullivan's proof of the existence and uniqueness of integrals of Hopf algebras. This book will interest graduate students and research workers who specialise in algebra.

This well-received textbook has been designed by a team of experts for introductory courses in astronomy and astrophysics. Starting with a detailed discussion of our Galaxy, the Milky Way, it goes on to give a general introduction to normal and active galaxies including models for their formation and evolution. The second part of the book provides an overview of cosmological models, discussing the Big Bang, dark energy and the expansion of the Universe. This second edition has been updated to reflect the latest developments and observations, while still probing the unresolved questions at the forefront of research. It contains numerous learning features such as boxed summaries, exercises with full solutions, a glossary and a supporting website hosting further teaching materials. Written in an accessible style that avoids complex mathematics, and illustrated in colour throughout, this text is suitable for self-study and will appeal to amateur astronomers as well as students.

In recent years the interplay between model theory and other branches of mathematics has led to many deep and intriguing results. In this, the first book on the topic, the theme is the interplay between model theory and the theory of modules. The book is intended to be a self-contained introduction to the subject and introduces the requisite model theory and module theory as it is needed. Dr Prest develops the basic ideas concerning what can be said about modules using the information which may be expressed in a first-order language. Later chapters discuss stability-theoretic aspects of modules, and structure and classification theorems over various types of rings and for certain classes of modules. Both algebraists and logicians will enjoy this account of an area in which algebra and model theory interact in a significant way. The book includes numerous examples and exercises and consequently will make an ideal introduction for graduate students coming to this subject for the first ti

Clays and clay minerals are the most abundant natural reactive solids on the Earth's surface. This comprehensive review considers clay science in the context of the Critical Zone - the Earth's permeable near-surface layer. Providing information on clays and clay minerals related to geological, biological and material sciences in the Critical Zone, it's well suited for graduate students and researchers interested in clay science, and environmental and soil mineralogy. The book starts with an introduction to clays and clay minerals, their historic background, and a review of how clay science impacts the Critical Zone. Examples and applications demonstrate how clays regulate habitats and determine the availability of other resources. These examples are supported by quantitative field data, including numerical and graphical depictions of clay and clay mineral occurrences. The book concludes by covering Critical Zone clay geochemistry and clay sequences, including the industrial, synthetic

The synthesis of symplectic geometry, the calculus of variations and control theory offered in this book provides a crucial foundation for the understanding of many problems in applied mathematics. Focusing on the theory of integrable systems, this book introduces a class of optimal control problems on Lie groups, whose Hamiltonians, obtained through the Maximum Principle of optimality, shed new light on the theory of integrable systems. These Hamiltonians provide an original and unified account of the existing theory of integrable systems. The book particularly explains much of the mystery surrounding the Kepler problem, the Jacobi problem and the Kovalevskaya Top. It also reveals the ubiquitous presence of elastic curves in integrable systems up to the soliton solutions of the non-linear Schroedinger's equation. Containing a useful blend of theory and applications, this is an indispensable guide for graduates and researchers in many fields, from mathematical physics to space control.

A classical theorem of Jordan states that every finite transitive permutation group contains a derangement. This existence result has interesting and unexpected applications in many areas of mathematics, including graph theory, number theory and topology. Various generalisations have been studied in more recent years, with a particular focus on the existence of derangements with special properties. Written for academic researchers and postgraduate students working in related areas of algebra, this introduction to the finite classical groups features a comprehensive account of the conjugacy and geometry of elements of prime order. The development is tailored towards the study of derangements in finite primitive classical groups; the basic problem is to determine when such a group G contains a derangement of prime order r, for each prime divisor r of the degree of G. This involves a detailed analysis of the conjugacy classes and subgroup structure of the finite classical groups.

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in the first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. Volume 1 focuses on the analysis of real-valued functions of a real variable. Volume 2 goes on to consider metric and topological spaces. This third volume develops the classical theory of functions of a complex variable. It carefully establishes the properties of the complex plane, including a proof of the Jordan curve theorem. Lebesgue measure is introduced, and is used as a model for other measure spaces, where the theory of integration is developed. The Radon–Nikodym theorem is proved, and the differentiation of measures discussed.