Математика
Различные книги в жанре МатематикаElements of Partial Differential Equations
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent study will particularly appreciate the worked examples that appear throughout the text.
Diophantine Approximations
This self-contained treatment originated as a series of lectures delivered to the Mathematical Association of America. It covers basic results on homogeneous approximation of real numbers; the analogue for complex numbers; basic results for nonhomogeneous approximation in the real case; the analogue for complex numbers; and fundamental properties of the multiples of an irrational number, for both the fractional and integral parts.The author refrains from the use of continuous fractions and includes basic results in the complex case, a feature often neglected in favor of the real number discussion. Each chapter concludes with a bibliographic account of closely related work; these sections also contain the sources from which the proofs are drawn.
Concepts of Probability Theory
This approach to the basics of probability theory employs the simple conceptual framework of the Kolmogorov model, a method that comprises both the literature of applications and the literature on pure mathematics. The author also presents a substantial introduction to the idea of a random process. Intended for college juniors and seniors majoring in science, engineering, or mathematics, the book assumes a familiarity with basic calculus.After a brief historical introduction, the text examines a mathematical model for probability, random variables and probability distributions, sums and integrals, mathematical expectation, sequence and sums of random variables, and random processes. Problems with answers conclude each chapter, and six appendixes offer supplementary material. This text provides an excellent background for further study of statistical decision theory, reliability theory, dynamic programming, statistical game theory, coding and information theory, and classical sampling statistics.
Einstein on Cosmic Religion and Other Opinions and Aphorisms
Science and religion are compatible, declares the famous physicist. In these essays, Einstein views science as the basis for a «cosmic» religion, embraced by scientists, theologians, and all who share a sense of wonder in the rationality and beauty of the universe. In the course of his career, Einstein wrote more than 300 scientific and 150 nonscientific publications. These essays date from the 1930s and 40s. In direct, everyday language the author develops a coherent view that transcends both the antiquated religion of fear and the modern religion of ethics. His concept of cosmic religion combines science and religion, with science forming the basis for a more enlightened religion. In these essays and aphorisms, Einstein also reflects on pacifism, disarmament, and Zionism. In addition to a brief biography of the author, this volume includes a warm appreciation by George Bernard Shaw.
Molecular Feminisms
�Should feminists clone?� �What do neurons think about?� �How can we learn from bacterial writing?� These provocative questions have haunted neuroscientist and molecular biologist Deboleena Roy since her early days of research when she was conducting experiments on an in vitro cell line using molecular biology techniques. An expert natural scientist as well as an intrepid feminist theorist, Roy takes seriously the expressive capabilities of biological �objects��such as bacteria and other human, nonhuman, organic, and inorganic actants�in order to better understand processes of becoming. She also suggests that renewed interest in matter and materiality in feminist theory must be accompanied by new feminist approaches that work with the everyday, nitty-gritty research methods and techniques in the natural sciences.By practicing science as feminism at the lab bench, Roy creates an interdisciplinary conversation between molecular biology, Deleuzian philosophies, science and technology studies, feminist theory, posthumanism, and postcolonial and decolonial studies. In Molecular Feminisms she brings insights from feminist and cultural theory together with lessons learned from the capabilities and techniques of bacteria, subcloning, and synthetic biology to o er tools for how we might approach nature anew. In the process she demonstrates that learning how to see the world around us is also always about learning how to encounter that world.
Algebraic Surfaces in Positive Characteristics
Customarily, the framework of algebraic geometry has been worked over an algebraically closed field of characteristic zero, say, over the complex number field. However, over a field of positive characteristics, many unpredictable phenomena arise where analyses will lead to further developments.In the present book, we consider first the forms of the affine line or the additive group, classification of such forms and detailed analysis. The forms of the affine line considered over the function field of an algebraic curve define the algebraic surfaces with fibrations by curves with moving singularities. These fibrations are investigated via the Mordell–Weil groups, which are originally introduced for elliptic fibrations.This is the first book which explains the phenomena arising from purely inseparable coverings and Artin–Schreier coverings. In most cases, the base surfaces are rational, hence the covering surfaces are unirational. There exists a vast, unexplored world of unirational surfaces. In this book, we explain the Frobenius sandwiches as examples of unirational surfaces.Rational double points in positive characteristics are treated in detail with concrete computations. These kinds of computations are not found in current literature. Readers, by following the computations line after line, will not only understand the peculiar phenomena in positive characteristics, but also understand what are crucial in computations. This type of experience will lead the readers to find the unsolved problems by themselves.<b>Contents:</b> <ul><li><b><i>Forms of the Affine Line:</i></b><ul><li>Picard Scheme and Jacobian Variety</li><li>Forms of the Affine Line</li><li>Groups of Russell Type</li><li>Hyperelliptic Forms of the Affine Line</li><li>Automorphisms</li><li>Divisor Class Groups</li></ul></li><li><b><i>Purely Inseparable and Artin–Schreier Coverings:</i></b><ul><li>Vector Fields and Infinitesimal Group Schemes</li><li>Zariski Surfaces</li><li>Quasi-Elliptic or Quasi-Hyperelliptic Fibrations</li><li>Mordell-Weil Groupps of Quasi-Elliptic or Quasi-Hyperelliptic Surfaces</li><li>Artin-Schreier Coverings</li><li>Higher Derivations</li><li>Unified <i>p</i>-Group Scheme</li></ul></li><li><b><i>Rational Double Points:</i></b><ul><li>Basics on Rational Double Points</li><li>Deformation of Rational Double Points</li><li>Open Problems on Rational Double Points in Positive Characteristics</li></ul></li></ul><br><b>Readership:</b> Graduate students and researchers in the fields of Algebraic Geometry, Fields and Rings, and Commutative Algebra.Form of the Affine Line;Zariski Surface;Quasi-Elliptic Fibration;Mordell–Weil Group;Artin–Schreier Covering;Higher Derivation;Unified p-group Scheme;Rational Double Point;Versal Deformation;Equisingular Locus0<b>Key Features:</b><ul><li>The mainstreams of arguments are explained, followed by computations</li><li>Several concrete examples are given to elucidate the stated results</li><li>All in all, the present book is more for practice than learning a general theory</li></ul>
Leaving Truth
"Leaving Truth" offers a radically new, and potentially conclusive, contribution to our ancient science vs. religion debate. It is a collection of five essays, one main and four subsidiary. The collection addresses how we can most coherently select proposals as knowledge, and the limitation from this on the kinds of proposals that we can select. Though at first glance abstruse and academic, addressing this most basic epistemic question seems to yield a very surprising result: That we have been maintaining our concept "truth" either redundantly or as an independent and reason-antithetical basis for knowledge; and that the proposals of all of our authoritarian systems of emotionally seductive irrationality – in particular, but not limited to, our theistic religions – can only be maintained from this basis. "Leaving Truth" suggests that our past 250 years of progress in epistemology can be summarized through the injunction that we should stop asking of any knowledge proposal, "Is this 'true'?" and start asking instead, "Can I honestly qualify this as knowledge?" It then shows how and why our theists cannot do this for their proposals. Its logical core demonstrates that both of the modern epistemological developments that are broadly assumed by theists and atheists alike to support the theists' position (David Hume's dismissal of Induction as our basis for "objective proof", and Karl Popper's demonstration that science can provide only "best present" knowledge, as opposed to certainty) achieve instead the opposite. That they undercut the theists' position at a level from which no coherent defense can be made. Leaving Truth thereby offers atheists and free-thinkers a prospect for the kind clear victory at the intellectual and academic level that we have not dared to hope for since collapse of the Radical Enlightenment.
Foundations of Modern Econometrics
Modern economies are full of uncertainties and risk. Economics studies resource allocations in an uncertain market environment. As a generally applicable quantitative analytic tool for uncertain events, probability and statistics have been playing an important role in economic research. Econometrics is statistical analysis of economic and financial data. In the past four decades or so, economics has witnessed a so-called 'empirical revolution' in its research paradigm, and as the main methodology in empirical studies in economics, econometrics has been playing an important role. It has become an indispensable part of training in modern economics, business and management.This book develops a coherent set of econometric theory, methods and tools for economic models. It is written as a textbook for graduate students in economics, business, management, statistics, applied mathematics, and related fields. It can also be used as a reference book on econometric theory by scholars who may be interested in both theoretical and applied econometrics.<b>Contents:</b> <ul><li>Preface</li><li>Introduction to Econometrics</li><li>General Regression Analysis</li><li>Classical Linear Regression Models</li><li>Linear Regression Models with Independent Observations</li><li>Linear Regression Models with Dependent Observations</li><li>Linear Regression Models Under Conditional Heteroskedasticity and Autocorrelation</li><li>Instrumental Variables Regression</li><li>Generalized Method of Moments Estimation</li><li>Maximum Likelihood Estimation and Quasi-Maximum Likelihood Estimation</li><li>Modern Econometrics: Retrospect and Prospect</li><li>Bibliography</li><li>Index</li></ul><br><b>Readership:</b> Graduate students in economics, business, management, statistics, applied mathematics, and related fields.Econometric;Models;Analytic0<b>Key Features:</b><ul><li>This book has several important features. First, it covers, in a progressive manner, various econometrics models and related methods from conditional means to possibly nonlinear conditional moments to the entire conditional distributions, and this is achieved in a unified and coherent framework. There exists a strong logical link among the materials covered in different chapters of the book</li><li>Second, the book provides various intuitions, explanations and potential applications for important econometric concepts, theories and methods from an economic perspective. Economic examples are also provided to motivate important econometric methods and models. Such training is indispensable in teaching and learning econometrics</li><li>Third, the book emphasizes basic training in asymptotic analysis. It first provides a brief review of asymptotic analytic methods and tools, and then show how they are used to develop the econometric theory in each chapter. Asymptotic analysis helps readers gain deep insight into modern econometric theory, particularly the conditions under which the econometric theory, methods and models are valid and applicable. By going through various chapters in this book progressively, readers will learn how to do asymptotic analysis for econometric models. Such skills are useful not only for those students who intend to work on theoretical econometrics, but also for those who intend to work on applied subjects in economics because with such analytic skills, readers will be able to understand more specialized or more advanced econometrics textbooks</li></ul>
A Healthy, Wealthy, Sustainable World
This book explains to the general reader the roles of chemistry in various areas of life ranging from the entirely personal to the worryingly global. These roles are currently not widely appreciated and certainly not well understood. The book is aimed at educated laypeople who want to know more about the world around them but have little chemical knowledge. The themes relate to the importance of chemistry in everyday life, the benefits they currently bring, and how their use can continue on a sustainable basis. Topics include: Health – conquering the diseases and stresses which still threaten us. Food – the role of agrochemicals and food chemists. Water – drinking water; the seas as a resource of raw materials. Fuels – what are they and from what are they made? Plastics – what are the used for and can they be sustainable? Cities – what role has chemistry in modern life? Sport – chemistry has changed the game. The world stands at a crossroads. What route to the future should we take? The road to a sustainable city beckons, but what effect will this have on chemistry, which appears so dependent on fossil resources? Its products are part of everyday living, and without them we could regress to the world of earlier generations when lives were blighted by disease, famines, dirt, and pain. In fact the industries based on chemistry the chemical, agrochemical, and pharmaceutical industries could be sustainable and not only benefit those in the developed world but could be shared by everyone on this planet and for generations to come. This book shows how it might be achieved.
Scientific Americans
Demonstrating the timely relevance of Theodore Dreiser, Edith Wharton, Jack London and Henry Adams, this book shows how debates about evolution, identity, and a shifting world picture have uncanny parallels with the emerging global systems that shape our own lives. Tracing these systems’ take-off point in the early twentieth century through the lens of popular science journalism, John Bruni makes a valuable contribution to the study of how biopolitical control over life created boundaries among races, classes, genders and species. Rather than accept that these writers get their scientific ideas about evolution second-hand, filtered through a social Darwinist ideology, this study argues that they actively determine what evolution means. Furthermore, the book, examines the ecological concerns that naturalist narratives reflect—such as land and water use, waste management, and environmental pollution—previously unaddressed in a book-length study.