Mathematics Books

Book SynopsisGroup actions are an efficient way of describing symmetries in objects by defining the essential elements of a given object as a set. The symmetries of the object are then defined as the symmetry group of this set. This title explores group actions on the simplest closed manifold, the circle.

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Book SynopsisRanging from math to literature to philosophy, Uncountable explains how numbers triumphed as the basis of knowledge—and compromise our sense of humanity.Trade Review"Ricardo and David Nirenberg, father and son scholars of mathematics and history, have teamed up in a breathtaking voyage examining the foundations and limits of knowledge in western thought. Not content with secondary sources, they have translated from the literature in their original languages: Arabic, French, German, Greek, Hebrew, Italian, Latin, and Spanish. In particular, they target mathematics and the natural sciences, and the way the concepts of sameness and differences affect our understanding of the natural world. But in the process, the authors touch upon many other facets of human endeavor, all named after their Greek roots: poetry, philosophy, psychology, economy. Along this wildly entertaining journey, we meet dozens of erudite thinkers, scientists, and writers such as Anaximander, Al-Farabi, Fyodor Dostoevsky, Ludwig Wittgenstein, Werner Heisenberg, and Reiner Maria Rilke. The book arrives just in time to give us ammunition as attempts are being made to put truth itself into the supercollider. It is a source of inspiration and comfort to learn how the far-flung ideas about numbers, our existence, and the world we live in have been debated in the past."--Joachim Frank, Columbia University, Nobel Prize in ChemistryTable of ContentsIntroduction: Playing with Pebbles 1 World War Crisis 2 The Greeks: A Protohistory of Theory 3 Plato, Aristotle, and the Future of Western Thought 4 Monotheism’s Math Problem 5 From Descartes to Kant: An Outrageously Succinct History of Philosophy 6 What Numbers Need: Or, When Does 2 + 2 = 4? 7 Physics (and Poetry): Willing Sameness and Difference 8 Axioms of Desire: Economics and the Social Sciences 9 Killing Time 10 Ethical Conclusions Acknowledgments Notes Bibliography Index of Names

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Book SynopsisThe principles of symmetry and self-symmetry are expressed in fractals, the subject of study in dimension theory. This book introduces an area of research which has recently appeared in the interface between dimension theory and the theory of dynamical systems, focusing on invariant fractals.

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Book SynopsisIn this innovative approach to the practice of social science, Charles Ragin explores the use of fuzzy sets to bridge the divide between quantitive and qualitative methods. He argues that fuzzy sets allow a far richer dialogue between ideas and evidence in social research than previously possible.

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Book SynopsisIn mathematics, 'buildings' are geometric structures that represent groups of Lie type over an arbitrary field. This book presents an introduction to mathematical buildings. It is suitable for those doing research or teaching courses on Lie-type groups, on finite groups, or on discrete groups.Trade Review"Ronan's account of the classification of affine buildings is both interesting and stimulating, and his book is highly recommended to those who already have some knowledge and enthusiasm for the theory of buildings." - Bulletin of the London Mathematical Society "[This book] belongs in every research library. Ronan's book will do more [than other books on the subject] to initiate the already motivated reader into current research on buildings and groups." - Bulletin of the American Mathematical Society"

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Book SynopsisOne is a science, the other an art; one useful, the other seemingly decorative, but mathematics and music share common origins in cult and mystery. This work explains how mathematics makes sense of space, how music tells a story, how theories are constructed, how melody is shaped. It argues that they are images of the mind at work and play.Trade Review"Expect luminous rewards by the end and exhilaration throughout the journey." - Hugh Kenner, Wall Street Journal "Provocative and exciting.... Rothstein writes this book as a foreign correspondent, sending dispatches from a remote and mysterious locale as a guide for the intellectually adventurous. The remarkable fact about his work is not that it is profound, as much of the writing is, but that it is so accessible." - Christian Science Monitor "Lovely, wistful.... Rothstein is a wonderful guide to the architecture of musical space, its tensions and relations, its resonances and proportions.... His account of what is going on in the music is unfailingly felicitous." - New Yorker"

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Book SynopsisThis definitive synthesis of mathematician Gregory Margulis's research brings together leading experts to cover the breadth and diversity of disciplines Margulis's work touches upon. This edited collection highlights the foundations and evolution of research by widely influential Fields Medalist Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics; his ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. Dynamics, Geometry, Number Theory introduces these areas, their development, their use in current research, and the connections between them. Divided into four broad sectionsArithmeticity, Superrigidity, Normal Subgroups; Discrete Subgroups; Expanders, Representations, Spectral Theory; and Homogeneous Dynamicsthe chapters have all been written by the foremost experts on each topic with a view to making them accessible bothTrade Review"Margulis is without a doubt one of the most influential mathematicians of the past fifty years. The book Dynamics, Geometry, Number Theory is vast in scope and provides an excellent introduction to Margulis's work and the research that it has inspired. It will be of great interest not only to specialists, but to graduate students and researchers interested in ergodic theory, Lie theory, geometry, and number theory." * MAA Reviews *"The chapters have all been written by the foremost experts on each topic with a view to making them accessible both to graduate students and to experts in other parts of mathematics. This was no simple feat: Margulis’s work stands out in part because of its depth, but also because it brings together ideas from different areas of mathematics. Few can be experts in all of these fields, and this diversity of ideas can make it challenging to enter Margulis’s area of research. Dynamics, Geometry, Number Theory provides one remedy to that challenge." * zbMath *“Margulis is one of the great mathematicians of the twentieth century and the first decades of this century, whose work is central today. This valuable book collects reflections on his work by some of the most prominent scholars in the area. Uniquely broad in scope, the whole collection is very strong, and the whole is greater than the parts. Terrific!” -- Shmuel Weinberger, University of Chicago“A superb contribution in every regard: purely scientifically; expounding upon the many deep works of Margulis and thereby appropriately honoring him and his work; and putting the contributions in context and sorting them in appropriate categories, while explaining the deep connections between them. The intellectual level of this book is astounding. I will recommend it to all my associates, graduate students, postdocs, and other researchers, and surely to my library.” -- Ralf Spatzier, University of Michigan“Margulis’s work has had a tremendous impact on mathematics, and this book will be read by scholars from a broad cross-section of mathematical backgrounds connected to the four sections of the volume and beyond. It will serve as a go-to collection for specialists and graduate students alike.” -- Alan Reid, Rice UniversityTable of ContentsIntroductionDavid FisherPART I || Arithmeticity, superrigidity, normal subgroups1. Superrigidity, arithmeticity, normal subgroups: results, ramifications, and directions David Fisher2. An extension of Margulis’s superrigidity theoremUri Bader and Alex Furman3. The normal subgroup theorem through measure rigidityAaron Brown, Federico Rodriguez Hertz, and Zhiren WangPART II || Discrete subgroups4. Proper actions of discrete subgroups of affine transformationsJeffrey Danciger, Todd A. Drumm, William M. Goldman, and Ilia Smilga5. Maximal subgroups of countable groups: a surveyTsachik Gelander, Yair Glasner, and Gregory SoiferPART III || Expanders, representations, spectral theory6. Tempered homogeneous spaces IIYves Benoist and Toshiyuki Kobayashi7. Expansion in simple groupsEmmanuel Breuillard and Alexander Lubotzky8. Elements of a metric spectral theoryAnders KarlssonPART IV || Homogeneous dynamics9. Quantitative nondivergence and Diophantine approximation on manifolds Victor Beresnevich and Dmitry Kleinbock10. Margulis functions and their applicationsAlex Eskin and Shahar Mozes11. Recent progress on rigidity properties of higher rank diagonalizable actions and applicationsElon Lindenstrauss12. Effective arguments in unipotent dynamicsManfred Einsiedler and Amir Mohammadi13. Effective equidistribution of closed hyperbolic subspaces in congruence quotients of hyperbolic spacesManfred Einsiedler and Philipp Wirth14. Dynamics for discrete subgroups of SL2(C)Hee Oh

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Book SynopsisOtto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of history of mathematics and presented calculus as an organic evolution of ideas. Through this approach, Toeplitz elucidated mathematical advances that contributed to modern calculus. This work deals with this topic.Trade Review"There is much that all of us can learn about the teaching of calculus from this book....It is above all a delightful and entertaining introduction to mathematical problems that have inspired the creation of calculus. Read it for the sheer enjoyment of well-crafted explanations. Read it to learn something new." - from the Foreword by David Bressoud"

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Book SynopsisTrade Review"There are myriad introductory books on special relativity. This one distinguishes itself by working through the mathematics of relativity in a very detailed yet conversational fashion. . . . Highly recommended." * Choice *“Introducing students in small, careful steps toward an understanding of the notation and physics behind special relativity has not been undertaken at this level since the text by Taylor and Wheeler from thirty years ago. Goldberg’s approach of encouraging the reader to see the simplicity behind the seemingly complex is welcome.” -- Christopher G. Tully, author of "Elementary Particle Physics in a Nutshell"“This engaging book will shape the education of a generation of physicists and astrophysicists. It defines the conceptual and mathematical stage—spacetime—on which physics is performed. From contemporary notation in the early chapters to sophisticated applications in the late chapters, Goldberg's book will not only propel students to more advanced classes, it will ease their entry into research.” -- Daniel Fabrycky, Department of Astronomy and Astrophysics, University of Chicago“Goldberg slings the reader straight in at the deep end . . . but with enough masterly wit to keep you afloat.” * Nature, on "The Universe in the Rearview Mirror" *“Reading this book is like taking a class with the most awesome science professor ever.” -- Annalee Newitz, founding editor of io9, on "The Universe in the Rearview Mirror"“Most physics books can’t really be described as ‘rollicking,’ but most physics books aren't written by Dave Goldberg.” -- Sean Carroll, theoretical physicist at Caltech, author of "The Particle at the End of the Universe," on "The Universe in the Rearview Mirror"

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Book SynopsisTrade Review“Mathematics has undergone tremendous changes, especially during the twentieth century, when it pushed ever deeper into the realm of abstraction. This upheaval even involved a redefinition of the definition itself, as Steingart explains in Axiomatics. A historian of science, Steingart sees this revolution as central to the modernist movements that dominated the mid-twentieth century in the arts and social sciences, particularly in the United States.” * Nature *“Steingart provides a history of mathematical thinking over the twentieth century: a compelling review of the increased abstraction of mathematical thought as well as its embrace of deep exploration of alternative axiomatic systems.” * Public Books *“Steingart takes a wide-angle view on mid-twentieth-century mathematics, connecting the axiomatic movement with high abstraction in modern art, structuralism in the social sciences, the New Criticism in literary criticism, and the deep unease felt by many scientists and mathematicians in the wake of World War II as their research became ever more entangled with military applications. Unfailingly lucid and alert to sympathetic resonances between apparently disparate realms, Steingart positions modern mathematics squarely in the center of high modernism.” -- Lorraine Daston, author of Rules: A Short History of What We Live By“This sophisticated and wide-ranging book examines mid-century American mathematics as a species of high modernism, both in its pure form and in applied mathematics. It looks at how it was supported, why it was advocated, how and why it was compared to contemporary abstract art, how the evolving ideas of abstraction played out in the Cold War, and how this even affected the writing of the history of mathematics. It is a major addition to and critique of the literature that presents modern mathematics as a species of modernism, and it should be read by every historian of modern science and indeed by anyone interested in how abstract ideas have shaped the modern world.” -- Jeremy Gray, author of Plato’s Ghost: The Modernist Transformation of Mathematics“American mathematics was in the midst of a puzzling contradiction at midcentury: applied mathematics appeared triumphant even as many mathematicians promoted abstraction and rejected the idea that utility was important. Steingart’s brilliant book has finally resolved this puzzle. Far from standing in opposition, mathematics’ utility and idealism, its calculations and foundations, were historically intertwined with the concept of axiomatics. By masterfully weaving together the work of artists and mathematicians, mundane academic conference proceedings and philosophical treatises, Steingart has written an essential guide to the transformation of postwar mathematics.” -- Christopher J. Phillips, author of The New Math: A Political History“The push for axiomatic reasoning, so central to twentieth-century mathematics, extended by 1950 to elite social science. But the power of this abstract logic, never absolute, was in retreat by the 1990s. Although the most familiar of these challenges took form as a new cult of data, Steingart’s most engaging arguments explore a new fascination with mathematical historicism.” -- Theodore M. Porter, author of Trust in Numbers: The Pursuit of Objectivity in Science and Public Life"Alma Steingart’s Axiomatics: Mathematical Thought and High Modernism is an attempt to combine the story of abstraction with developments outside of mathematics. . . . she presents this material from a very interesting and well-informed perspective." * American Mathematical Monthly *Table of ContentsNote to Readers Introduction 1. Pure Abstraction: Mathematics as Modernism 2. Applied Abstraction: Axiomatics and the Meaning of Mathematization 3. Human Abstraction: “The Mathematics of Man” and Midcentury Social Sciences 4. Creative Abstraction: Abstract Art, Pure Mathematics, and Cold War Ideology 5. Unreasonable Abstraction: The Meaning of Applicability, or the Miseducation of the Applied Mathematician 6. Historical Abstraction: Kuhn, Skinner, and the Problem of the Weekday Platonist Epilogue Acknowledgments Archival Collections Notes Index

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Book SynopsisTrade Review"There are myriad introductory books on special relativity. This one distinguishes itself by working through the mathematics of relativity in a very detailed yet conversational fashion. . . . Highly recommended." * Choice *“Introducing students in small, careful steps toward an understanding of the notation and physics behind special relativity has not been undertaken at this level since the text by Taylor and Wheeler from thirty years ago. Goldberg’s approach of encouraging the reader to see the simplicity behind the seemingly complex is welcome.” -- Christopher G. Tully, author of "Elementary Particle Physics in a Nutshell"“This engaging book will shape the education of a generation of physicists and astrophysicists. It defines the conceptual and mathematical stage—spacetime—on which physics is performed. From contemporary notation in the early chapters to sophisticated applications in the late chapters, Goldberg's book will not only propel students to more advanced classes, it will ease their entry into research.” -- Daniel Fabrycky, Department of Astronomy and Astrophysics, University of Chicago“Goldberg slings the reader straight in at the deep end . . . but with enough masterly wit to keep you afloat.” * Nature, on "The Universe in the Rearview Mirror" *“Reading this book is like taking a class with the most awesome science professor ever.” -- Annalee Newitz, founding editor of io9, on "The Universe in the Rearview Mirror"“Most physics books can’t really be described as ‘rollicking,’ but most physics books aren't written by Dave Goldberg.” -- Sean Carroll, theoretical physicist at Caltech, author of "The Particle at the End of the Universe," on "The Universe in the Rearview Mirror"

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Book SynopsisTrade Review“Beautifully bringing together historical and contemporary research on representations in science with themes from aesthetics and the philosophy of art, Suárez’s book is an outstanding interdisciplinary contribution to the philosophy of science. It is essential reading for anyone interested in modeling practices, their connections with the arts, and what this insightful combination of science, art, and practice might bring to the epistemology of science.” -- Chiara Ambrosio, University College London“Suárez has been a leading voice in the philosophy of modeling for the last two decades. This book is a wonderfully clear and compelling presentation of his ‘inferentialist theory of representation.’ The book will be a central resource for advanced undergraduate and graduate students, and required reading for every philosopher of science.” -- Martin Kusch, University of Vienna“Suárez has written a brilliant account of the inferential conception of scientific representation, its historical roots, and its application to contemporary scientific modeling. What stands out is his deflationist approach toward metaphysics, the streamlined account in terms of representational force and inferential capacity, and the connection to the phenomenology of artistic perception. A magnificent work.” -- Bas C. van Fraassen, Princeton University“Inference and Representation makes a strong case for an inferential conception of scientific modeling. It argues that the effectiveness of a model lies in its providing an orientation that facilitates fruitful scientific reasoning. It is a valuable contribution to the literature on modeling.” -- Catherine Z. Elgin, Harvard University“This much-anticipated book is the culmination of over twenty years of pioneering work by Suárez. It is a must-read for anyone wishing to think carefully about models and representations in science. Suárez gives a careful, insightful, and comprehensive exposition and defence of his inferential conception of representation, and he now develops it in an expressly pragmatist direction with a helpful focus on the uses of models. What emerges is a compelling deflationary account of ‘representation without metaphysics,’ engaging fully with the complex realities of inferential practices. Suárez argues that common notions of representation based on similarity or isomorphism are ill-fitting and inadequate, and shows how the activity of representation pervades all sorts of scientific practices. His discussion is clear and systematic throughout, and successfully combines philosophical acuity and historical awareness. In the course of presenting his own position he also gives a fair, critical summing-up and evaluation of the considerable existing literature on models and representation. This landmark work should appeal to philosophers, historians of science and practicing scientists alike.” -- Hasok Chang, University of Cambridge“During the past quarter-century, philosophers of science have come to appreciate the importance of models and modeling practices in the sciences. Suárez has been one of the pioneers in this work, specifically in investigating how models represent aspects of the world. The present book is the culmination of insights accumulated over more than two decades. It provides a convincing account of representation, one emphasizing the uses to which models are put and the inferences they allow. Suárez develops his views with welcome precision, focuses on an admirably wide range of types of models, and offers numerous insights about the historical development of modeling. His final two chapters explore the notion of representation more broadly, with a lucid and well-informed discussion of representation in visual art, and draw out the implications for several large issues in the philosophy of science. This book is an outstanding contribution to the field.” -- Philip Kitcher, Columbia UniversityTable of ContentsPreface and Acknowledgments 1 Introducing Scientific Representation Part I Modeling 2 The Modeling Attitude: A Genealogy 3 Models and Their Uses Part II Representation 4 Theories of Representation 5 Against Substance 6 Scientific Theories and Deflationary Representation 7 Representation as Inference Part III Implications 8 Lessons from the Philosophy of Art 9 Scientific Epistemology Transformed Notes References Index

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Book SynopsisThis text provides topologists with a new way of looking at the classification theory of singular spaces. Divided into three parts, the book begins with an overview of high-dimensional manifold theory. It then offers the parallel theory for stratified spaces. Applications are also included.Table of ContentsPart 1 Manifold theory: algebraic K-theory and topology; surgery theory; spacification and functoriality; applications. Part 2 General theory: definitions and examples; classification of stratified spaces; transverse stratified classification; PT category; controlled topology; proof of main theorems in topology. Part 3 Applications and illustrations: manifolds and embedding theory revisited; supernormal spaces and varieties; group actions; rigidity conjectures.

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Book SynopsisA guide for any student of vector analysis, this text separates those relationships which are topologically invariant from those which are not. Based on the essentially geometric nature of the subject, this approach builds consistently on students' prior knowledge and geometrical intuition.

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Book SynopsisFrom the author of the landmark bestseller The-Thirty-Six-Hour-Day comes a lucid, engaging, and nuanced treatment of one of the essential questions in science, medicine, and life: "Why?"Trade ReviewPeter Rabins shows incredible breadth of knowledge and his thesis-that there are three distinct approaches to causation, appropriate for different types of questions-is compelling. His writing is engaging, and the subject matter is deeply relevant. -- Simon Levin, Princeton University, author of Fragile Dominion: Complexity and the Commons Peter Rabin's book draws upon science, statistics, philosophy, and religion to stretch readers' thinking about the 'why' and 'how' of what happens. It provides a remarkably lucid synthesis of diverse ideas about causality based on superb scholarship and is always entertaining. I heartily recommend it. -- David Reuben, MD, David Geffen School of Medicine, University of California, Los Angeles From the two year old child's endlessly nested 'why' questions to the Old Testament and the modern scientist, and through many philosophers in between, Peter Rabins takes us on a fascinating quest in search of answers to that seemingly simplest of all questions: Why? Simple but enigmatic because, like the two year old, how do we know when to be satisfied and how do we know when we know? Throughout The Why of Things, Rabins examines fundamental aspects of how we know-or don't. In his erudite yet accessible book, readers will learn everything from philosophical categorization to nonlinear dynamics in a way that will suddenly make sense, even if they never do find out exactly why. -- Stuart Firestein, Columbia University, author of Ignorance: How It Drives Science if you're looking to learn how to better reason things out through logic and comparative analysis, then this one may be for you. Lifelong Dewey Blog Quite simply, wow. This is one of the most complex, mind-boggling and ultimately satisfying books I have read in a very long time. The Garden Window Blog A most enjoyable read and source of inspiration. The book constitutes a noteworthy addition to Professor Rabins' academic production... Philosophers of science - and perhaps more specifically philosophers interested in causality, explanation, or medicine - would gain a lot in reading it. MetascienceTable of ContentsPreface Introduction 1. Historical Overview: The Four Approaches to Causality 2. The Three-Facet Model: An Overview 3. The Answer Is Either "No" or "Yes": Causality as a Categorical Concept 4. Probabilities 5. A Third Model of Causality: The Emergent 6. Empirical: The Physical Sciences 7. Empirical: The Biological Sciences 8. Empirical: Epidemiology 9. Narrative Truth: The Empathic Method 10. Cause in the Ecclesiastic Tradition 11. Seeking the Why of Things: The Model Applied References Index

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Book SynopsisFrom the author of the landmark bestseller The-Thirty-Six-Hour-Day comes a lucid, engaging, and nuanced treatment of one of the essential questions in science, medicine, and life: "Why?"Trade ReviewPeter Rabins shows incredible breadth of knowledge and his thesis-that there are three distinct approaches to causation, appropriate for different types of questions-is compelling. His writing is engaging, and the subject matter is deeply relevant. -- Simon Levin, Princeton University, author of Fragile Dominion: Complexity and the Commons Peter Rabin's book draws upon science, statistics, philosophy, and religion to stretch readers' thinking about the 'why' and 'how' of what happens. It provides a remarkably lucid synthesis of diverse ideas about causality based on superb scholarship and is always entertaining. I heartily recommend it. -- David Reuben, MD, David Geffen School of Medicine, University of California, Los Angeles From the two year old child's endlessly nested 'why' questions to the Old Testament and the modern scientist, and through many philosophers in between, Peter Rabins takes us on a fascinating quest in search of answers to that seemingly simplest of all questions: Why? Simple but enigmatic because, like the two year old, how do we know when to be satisfied and how do we know when we know? Throughout The Why of Things, Rabins examines fundamental aspects of how we know-or don't. In his erudite yet accessible book, readers will learn everything from philosophical categorization to nonlinear dynamics in a way that will suddenly make sense, even if they never do find out exactly why. -- Stuart Firestein, Columbia University, author of Ignorance: How It Drives Science if you're looking to learn how to better reason things out through logic and comparative analysis, then this one may be for you. Lifelong Dewey Blog Quite simply, wow. This is one of the most complex, mind-boggling and ultimately satisfying books I have read in a very long time. The Garden Window Blog A most enjoyable read and source of inspiration. The book constitutes a noteworthy addition to Professor Rabins' academic production... Philosophers of science - and perhaps more specifically philosophers interested in causality, explanation, or medicine - would gain a lot in reading it. MetascienceTable of ContentsPreface Introduction 1. Historical Overview: The Four Approaches to Causality 2. The Three-Facet Model: An Overview 3. The Answer Is Either "No" or "Yes": Causality as a Categorical Concept 4. Probabilities 5. A Third Model of Causality: The Emergent 6. Empirical: The Physical Sciences 7. Empirical: The Biological Sciences 8. Empirical: Epidemiology 9. Narrative Truth: The Empathic Method 10. Cause in the Ecclesiastic Tradition 11. Seeking the Why of Things: The Model Applied References Index

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Book SynopsisA step-by-step strategy for protecting ourselves against the phony claims, trendy pseudoscience, and sloppy thinking that permeate our world.Trade ReviewA Survival Guide to the Misinformation Age is a no-holds-barred paean to the scientific mode of thinking. Helfand's wide-ranging, interdisciplinary, humorously cynical intellect comes through at every turn. -- J. Craig Wheeler, University of Texas at Austin A Survival Guide for the Misinformation Age is an impassioned plea for science literacy. Given the state of the world today, in which scientifically underinformed voters elect scientifically illiterate politicians, David Helfand has written the right book at the right time with the right message. Read it now. The future of our civilization may depend on it. -- Neil deGrasse Tyson, astrophysicist, American Museum of Natural History David Helfand's Survival Guide to the Misinformation Age gives readers a chance to spend time with one this country's clearest and best critical thinkers. Helfand channels Steven Pinker's ability to dissect language with John Alan Paulos's ability to explain numbers with Richard Dawkins' ability to explain our existence (to obtain food, to avoid being food, and to reproduce) with George Carlin's ability to make us laugh. Using personal anecdotes (he's a Red Sox fan), Helfand teaches us how to think through questions as diverse as why the moon doesn't make us lunatics to why it only takes twenty-three people to have a 50:50 chance that two will have the same birthday. A real pleasure. -- Paul Offit, University of Pennsylvania Important and timely. Library Journal Helfand's work is an admirable response to a long-standing problem of sloppy thinking. Publishers Weekly Helfand is a man brimming with incredible insights on the universe. Dave's Universe A must-read for anyone presuming to call themselves a scientist and a should-read for anyone just trying to make sense of the overwhelming volume of data and real and concocted 'proofs' of nearly everything that spews forth from the Internet on demand. This book provides a road map for teaching students how to both celebrate science and how to view their primary source of information with skepticism and caution. Every science teacher should read this book. -- John Ziegler NSTA Recommends For those with an arts and humanities background, this book offers many valuable lessons... For everyone else it provides a vital antidote to the ills of misinformation by teaching systematic and rigorous scientific reasoning. -- Marina Gerner Times Literary Supplement Highly recommended. CHOICE How I wish everyone would read, appreciate, and follow [David J. Helfand's] guidance. Physics TodayTable of ContentsForeword Acknowledgments Introduction: Information, Misinformation, and Our Planet's Future 1. A Walk in the Park 2. What Is Science? 3. A Sense of Scale Interlude 1: Numbers 4. Discoveries on the Back of an Envelope 5. Insights in Lines and Dots Interlude 2: Language and Logic 6. Expecting the Improbable 7. Lies, Damned Lies, and Statistics 8. Correlation, Causation ... Confusion and Clarity 9. Definitional Features of Science 10. Applying Scientific Habits of Mind to Earth's Future 11. What Isn't Science 12. The Triumph of Misinformation; The Peril of Ignorance 13. The Unfinished Cathedral Appendix: Practicing Scientific Habits of Mind Notes Index

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Book SynopsisA step-by-step strategy for protecting ourselves against the phony claims, trendy pseudoscience, and sloppy thinking that permeate our world.Trade ReviewA Survival Guide to the Misinformation Age is a no-holds-barred paean to the scientific mode of thinking. Helfand's wide-ranging, interdisciplinary, humorously cynical intellect comes through at every turn. -- J. Craig Wheeler, University of Texas at Austin A Survival Guide for the Misinformation Age is an impassioned plea for science literacy. Given the state of the world today, in which scientifically underinformed voters elect scientifically illiterate politicians, David Helfand has written the right book at the right time with the right message. Read it now. The future of our civilization may depend on it. -- Neil deGrasse Tyson, astrophysicist, American Museum of Natural History David Helfand's Survival Guide to the Misinformation Age gives readers a chance to spend time with one this country's clearest and best critical thinkers. Helfand channels Steven Pinker's ability to dissect language with John Alan Paulos's ability to explain numbers with Richard Dawkins' ability to explain our existence (to obtain food, to avoid being food, and to reproduce) with George Carlin's ability to make us laugh. Using personal anecdotes (he's a Red Sox fan), Helfand teaches us how to think through questions as diverse as why the moon doesn't make us lunatics to why it only takes twenty-three people to have a 50:50 chance that two will have the same birthday. A real pleasure. -- Paul Offit, University of Pennsylvania Important and timely. Library Journal Helfand's work is an admirable response to a long-standing problem of sloppy thinking. Publishers Weekly Helfand is a man brimming with incredible insights on the universe. Dave's Universe A must-read for anyone presuming to call themselves a scientist and a should-read for anyone just trying to make sense of the overwhelming volume of data and real and concocted 'proofs' of nearly everything that spews forth from the Internet on demand. This book provides a road map for teaching students how to both celebrate science and how to view their primary source of information with skepticism and caution. Every science teacher should read this book. -- John Ziegler NSTA Recommends For those with an arts and humanities background, this book offers many valuable lessons... For everyone else it provides a vital antidote to the ills of misinformation by teaching systematic and rigorous scientific reasoning. -- Marina Gerner Times Literary Supplement Highly recommended. CHOICE How I wish everyone would read, appreciate, and follow [David J. Helfand's] guidance. Physics TodayTable of ContentsForeword Acknowledgments Introduction: Information, Misinformation, and Our Planet's Future 1. A Walk in the Park 2. What Is Science? 3. A Sense of Scale Interlude 1: Numbers 4. Discoveries on the Back of an Envelope 5. Insights in Lines and Dots Interlude 2: Language and Logic 6. Expecting the Improbable 7. Lies, Damned Lies, and Statistics 8. Correlation, Causation ... Confusion and Clarity 9. Definitional Features of Science 10. Applying Scientific Habits of Mind to Earth's Future 11. What Isn't Science 12. The Triumph of Misinformation; The Peril of Ignorance 13. The Unfinished Cathedral Appendix: Practicing Scientific Habits of Mind Notes Index

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Book SynopsisHow Much Inequality Is Fair? synthesizes concepts from economics, political philosophy, game theory, information theory, statistical mechanics, and systems engineering into a mathematical framework for a fair free-market society. Venkat Venkatasubramanian compares his theory’s predictions to actual inequality data and discusses its implications.Trade ReviewVenkat Venkatasubramanian's unusual argument, which draws on both mathematical and philosophical principles to propose a model of a fair society, is itself worthy of remark. Whether or not you agree with it, it is clearly and fairly presented. It's one of the best books of its kind. -- Simon DeDeo, Carnegie Mellon University A thoughtful book, with unique philosophical insights, that is refreshing for the ways in which it is different from standard economic theory. It addresses one of the major questions of our day-indeed, of the past two hundred years-and does so in a readable, thought-provoking way. -- Robert Axtell, George Mason UniversityTable of ContentsList of TablesList of FiguresPreface1. Extreme Inequality in Income and Wealth2. Foundational Principles of a Fair Capitalist Society3. Distributive Justice in a Hybrid Utopia4. Statistical Thermodynamics and Equilibrium Distribution5. Fairness in Income Distribution6. Global Trends in Income Inequality: Theory Versus Reality7. What Is Fair Pay for Executives?8. Final Synthesis and Future DirectionsNotesBibliographyIndex

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Book SynopsisHow Much Inequality Is Fair? synthesizes concepts from economics, political philosophy, game theory, information theory, statistical mechanics, and systems engineering into a mathematical framework for a fair free-market society. Venkat Venkatasubramanian compares his theory’s predictions to actual inequality data and discusses its implications.Trade ReviewVenkat Venkatasubramanian’s unusual argument, which draws on both mathematical and philosophical principles to propose a model of a fair society, is itself worthy of remark. Whether or not you agree with it, it is clearly and fairly presented. It’s one of the best books of its kind. -- Simon DeDeo, Carnegie Mellon UniversityA thoughtful book, with unique philosophical insights, that is refreshing for the ways in which it is different from standard economic theory. It addresses one of the major questions of our day—indeed, of the past two hundred years—and does so in a readable, thought-provoking way. -- Robert Axtell, George Mason UniversityStands out in originality, interdisciplinary focus, and crisp phrasing. * Journal of Philosophical Economics *Table of ContentsList of TablesList of FiguresPreface1. Extreme Inequality in Income and Wealth2. Foundational Principles of a Fair Capitalist Society3. Distributive Justice in a Hybrid Utopia4. Statistical Thermodynamics and Equilibrium Distribution5. Fairness in Income Distribution6. Global Trends in Income Inequality: Theory Versus Reality7. What Is Fair Pay for Executives?8. Final Synthesis and Future DirectionsNotesBibliographyIndex

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Book SynopsisThis book offers a lively exploration of the mathematics, physics, and neuroscience that underlie music. Written for musicians and music lovers with any level of science and math proficiency, including none, Music, Math, and Mind demystifies how music works while testifying to its beauty and wonder.Trade ReviewIt is rare that one finds a book where on opening any page, one is drawn to read on and . . . to read back. Every page has a story, every page a fascinating connection between the universal joy we find in music and some biological or mathematical fact. Here is the place to find out about the way crickets make music, and the McGurk effect! The science comes along gently, never intimidating. Only a neurobiologist who is a master composer and musician could have written this wonderful book! -- Roald Hoffmann, author and recipient of the Nobel Prize in ChemistryIf you ever suspected that musicians belonged to a secret society, this is the book that blows the mysteries wide open. Using a potent cocktail of math, physics, history, biology, and neurology, Dave Sulzer explains why music is the medicine most of us can’t live without. This is a book written for the initiate and the noninitiate about the universal way sound and music connect us, both human and nonhuman. -- Peter Gabriel, singer-songwriter, musician, and activistThis is an amazing book. Readers will come back to it again and again for its clear explanations, breadth of content, and “listening” advice. Importantly, it includes a chapter on animals, acknowledging that the sophisticated production and perception of music is not limited to humans. It is accessible to all readers but does not shy away from the direct presentation of science—it gives the reader things that anyone interested in this topic needs to begin to think about. It raises important philosophical questions while allowing the reader to gain the skills to explore these questions further and stops there—giving the reader the chance to pursue or ignore. -- Susan Savage-Rumbaugh, primatologist and psychologist, specialist in communication by bonobosDave Soldier’s excellent book turns into an encyclopedia of our tonal imagination as it catalogues the nefarious passion that gives our creativity its edge. -- John Cale, songwriter, composer, performerIf you think you love music as much as you possibly could, think again. Music, which is so hard to define, and which connects to everything, has yet to reveal every level of its joy to you. This book will help you experience music as an animal, a neural pathway, or a mathematical principle. -- Jaron Lanier, writer, computer scientist, and musicianWhen your band protests, “Whaddaya mean ‘dynamics’? I’m playing as loud as I can!”—turn them onto the solid matter in Music, Math, and Mind. As to Soldier’s confection? A ribald reality check on what makes music matter and why we should mind. I’ve waited seventy-six years in a musical immersion to put a buzz on Dave Soldier’s fly-leaf. -- Van Dyke Parks, performer, arranger, producer, composer, and lyricist, including with the Beach BoysPutting the worlds of science and music together is an ambitious, and potentially intimidating, endeavor. But David Sulzer had me at paragraph one, where he writes “no one needs this book!” No, I don’t need it—but I find I do want it. -- John Schaefer, host of New Sounds, WNYCMusicians shouldn’t be intimidated by the title Music, Math, and Mind: The Physics and Neuroscience of Music. This is a book that any musician or music fan will find both enjoyable and educational. The questions regarding the science, biology, and math related to music are made easily understandable, and the book is grounded in David’s passion for both creating and enjoying music. At the end, anyone reading this book will have a greater appreciation for the creative spirit and a way to understand music in even deeper ways. -- Bob Neuwirth, singer-songwriter and record producerWith his whimsical, philosophical deep dive into the musical interplay of science and mathematics, Sulzer draws on his dual roles – as professor of psychiatry, neurology, and pharmacology at Columbia University and as an experimental musician (under the name Dave Soldier). Each chapter unfolds with theory, history, mathematical notation, and riveting storytelling. * Library Journal *At last, the book for science nerds no musical home should be without. * Limelight Magazine *A jaunty, conversational manner...you barely realize that you're learning some rather heady stuff. * Memphis Flyer *[Music, Math, and Mind: the Physics and Neuroscience of Music] is exactly the sort of book that science written for a general audience should be—accessible on multiple levels from the neophyte to the expert, engagingly written, and informative in a way that stimulates curiosity and prompts further investigation. . . . Highly recommended. * Choice *Table of ContentsNota BeneIntroduction1. The Parameters of Sound2. The Math of Pitch, Scales, and Harmony3. Waves and Harmonics4. The Math of Sound and Resonance5. Math and Rhythmic StructureCenterpiece: The Sense of Hearing6. Brain Mechanisms of Rhythm7. Neural Mechanisms of Emotion8. Ear Physiology: How Air Waves Become Sound9. Deep Brain Physiology of Sound10. Sound Disorders, Illusions, and Hallucinations11. Animal Sound, Song, and MusicAcknowledgmentsAppendix 1: Musical Pitch to Frequency TableAppendix 2: Further ReadingBibliographyAuthor’s Selected Compositions and DiscographyIndex

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Book SynopsisThis book is an introduction to programming with Python for MBA students and others in business positions who need a crash course. Beginning with fundamentals such as variables, strings, lists, and functions, it builds up to data analytics and practical ways to derive value from large and complex datasets.Trade ReviewBusiness leaders everywhere increasingly need top technology and data skills to stay competitive. Mattan Griffel and Daniel Guetta bring Python to life through clear and compelling stories and case studies, showing you how to use the power of variables, strings, and lists to immediately help your business and analytics. -- Glenn Hubbard, dean emeritus and Russell L. Carson Professor of Finance and Economics, Columbia Business SchoolIn the data-driven economy, there is an enormous demand for hybrid professionals who are simultaneously broad and deep across business and technical fields. Mattan Griffel and Daniel Guetta have done a great job providing a practical, step-by-step guide for commercially minded individuals to upskill quickly in the technical arena. This will be required reading for all those in my team who need to rapidly learn fundamental data and analytical skills. -- Afsheen Afshar, founder and CEO, Pilot Wave Holdings ManagementBusiness education is changing to prepare MBA students for careers in the digital age and to provide an understanding of the technological capabilities and analytics tools driving this digital transformation. Griffel and Guetta are experts in Python and its use in business analytics. This book will be an incredible resource for teaching programming to students in MBA programs and for business practitioners and managers. -- Costis Maglaras, dean and David and Lyn Silfen Professor of Business, Columbia Business SchoolTable of ContentsIntroductionPart I1. Getting Started with Python2. Python Basics, Part 13. Python Basics, Part 24. Python Basics, Part 3Part II5. Introduction to Data in Python6. Exploring, Plotting, and Modifying Data in Python7. Bringing Together Datasets8. Aggregation9. PracticeWhat’s Next?NotesIndex

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Book SynopsisJames C. Zimring argues that many of the mistakes that the human mind consistently makes boil down to misperceiving fractions. Blending key scientific research in cognitive psychology with accessible real-life examples, Partial Truths helps readers spot the fallacies lurking in everyday information.Trade ReviewIn this brilliant follow up to What Science Is and How It Really Works, James Zimring engages the reader in a kind of detective story about the classic mistakes of human reasoning, due to our innumeracy. From bad social policy to pandemics to terrorism, he shows how human decision making often gets it so wrong. What I loved most about Partial Truths though is that he didn't just establish that we make errors, but why. This amounts to a handy, insightful, eminently readable guide to the intricate evolution of the human mind itself. If you enjoyed Daniel Kahneman's Thinking, Fast and Slow, you'll love this book. -- Lee McIntyre, author of How to Talk to a Science Denier: Conversations with Flat Earthers, Climate Deniers, and Others Who Defy ReasonUsing the simple notion of a fraction as a lens, James Zimring insightfully discusses a remarkable variety of issues from cognitive psychology to New Age beliefs to misunderstandings in politics. Thoughtful and wide-ranging. -- John Allen Paulos, Temple University, and author of A Mathematician Reads the Newspaper and InnumeracyIn Partial Truths, Zimring offers an entertaining and illuminating look at how we all misunderstand—and how the media and politicians misrepresent, and even scientists sometimes distort—the numbers and data that underlie so much of our conventional wisdom. -- David Zweig, author of Invisibles: The Power of Anonymous Work in an Age of Relentless Self-PromotionZimring’s book Partial Truths takes a walk through the various ways human cognition fails when dealing with numbers, probabilities, risk, and assessing evidence. Along the way, Zimring takes us through a bestiary of fascinating case studies both historical and modern. His clear prose illuminates the ways that politicians take advantage of our cognitive shortcomings, the ways that numbers mislead us in everyday life, and what this means for important social topics like racialized criminal justice, war mongering, and public belief in science. While Zimring follows previous authors in advocating for improved information literacy, he takes a more measured approach. Zimring is admirably aware of the ways that human cognition is hard to change, and recognizes that sometimes our reasoning biases actually benefit us, even as he helps the reader see these biases more clearly. A great book for those grappling with the confusion of our modern information environments. -- Cailin O'Connor, author of The Misinformation Age: How False Beliefs SpreadNumbers become far more than abstractions in the capable hands of James Zimring. I learned something fascinating and enlightening on nearly every page of Partial Truths­ – about politics, social policy, economics, cultural choices, criminal justice, and much more. -- Steven Lubet, author of Interrogating Ethnography: Why Evidence MattersZimring does a great job breaking down complex theories of statistics and mathematical equations into relatable stories and examples. His perception… is fascinating. * AIPT *Partial Truths is a book to read through very carefully and then keep next to your desk. . . . Let’s all keep help like [this] close at hand at least until the next time our prejudices are about to make us decide wrongly or vote stupidly. * Forbes *As mathematics (or mathematics adjacent) treatises go Partial Truths is as reader-friendly and interesting as they come. * Brain Drain Blog *The book is easy to read, has entertaining examples, and no math is required. This book should be required reading for all. * Choice *Table of ContentsAcknowledgmentsIntroductionPart I. The Problem of Misperception1. The Fraction Problem2. How Our Minds Fractionate the World3. Confirmation Bias: How Your Mind Filters Evidence Based on Preexisting Beliefs4. Bias with a Cherry on Top: Cherry-Picking the DataPart II. The Fraction Problem in Different Arenas5. The Criminal Justice System6. The March to War7. Patterns in the Static8. Alternative and New Age Beliefs9. The Appearance of Design in the Natural World10. The Hard SciencesPart III. Reversing Misperception11. How Misperceiving the Fraction Can Be Advantageous12. Can We Solve the Problems with Human Perception and Reasoning and Should We Even Try?NotesBibliographyIndex

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Book SynopsisJames C. Zimring argues that many of the mistakes that the human mind consistently makes boil down to misperceiving fractions. Blending key scientific research in cognitive psychology with accessible real-life examples, Partial Truths helps readers spot the fallacies lurking in everyday information.Trade ReviewIn this brilliant follow up to What Science Is and How It Really Works, James Zimring engages the reader in a kind of detective story about the classic mistakes of human reasoning, due to our innumeracy. From bad social policy to pandemics to terrorism, he shows how human decision making often gets it so wrong. What I loved most about Partial Truths though is that he didn't just establish that we make errors, but why. This amounts to a handy, insightful, eminently readable guide to the intricate evolution of the human mind itself. If you enjoyed Daniel Kahneman's Thinking, Fast and Slow, you'll love this book. -- Lee McIntyre, author of How to Talk to a Science Denier: Conversations with Flat Earthers, Climate Deniers, and Others Who Defy ReasonUsing the simple notion of a fraction as a lens, James Zimring insightfully discusses a remarkable variety of issues from cognitive psychology to New Age beliefs to misunderstandings in politics. Thoughtful and wide-ranging. -- John Allen Paulos, Temple University, and author of A Mathematician Reads the Newspaper and InnumeracyIn Partial Truths, Zimring offers an entertaining and illuminating look at how we all misunderstand—and how the media and politicians misrepresent, and even scientists sometimes distort—the numbers and data that underlie so much of our conventional wisdom. -- David Zweig, author of Invisibles: The Power of Anonymous Work in an Age of Relentless Self-PromotionZimring’s book Partial Truths takes a walk through the various ways human cognition fails when dealing with numbers, probabilities, risk, and assessing evidence. Along the way, Zimring takes us through a bestiary of fascinating case studies both historical and modern. His clear prose illuminates the ways that politicians take advantage of our cognitive shortcomings, the ways that numbers mislead us in everyday life, and what this means for important social topics like racialized criminal justice, war mongering, and public belief in science. While Zimring follows previous authors in advocating for improved information literacy, he takes a more measured approach. Zimring is admirably aware of the ways that human cognition is hard to change, and recognizes that sometimes our reasoning biases actually benefit us, even as he helps the reader see these biases more clearly. A great book for those grappling with the confusion of our modern information environments. -- Cailin O'Connor, author of The Misinformation Age: How False Beliefs SpreadNumbers become far more than abstractions in the capable hands of James Zimring. I learned something fascinating and enlightening on nearly every page of Partial Truths­ – about politics, social policy, economics, cultural choices, criminal justice, and much more. -- Steven Lubet, author of Interrogating Ethnography: Why Evidence MattersZimring does a great job breaking down complex theories of statistics and mathematical equations into relatable stories and examples. His perception… is fascinating. * AIPT *Partial Truths is a book to read through very carefully and then keep next to your desk. . . . Let’s all keep help like [this] close at hand at least until the next time our prejudices are about to make us decide wrongly or vote stupidly. * Forbes *As mathematics (or mathematics adjacent) treatises go Partial Truths is as reader-friendly and interesting as they come. * Brain Drain Blog *The book is easy to read, has entertaining examples, and no math is required. This book should be required reading for all. * Choice *Table of ContentsAcknowledgmentsIntroductionPart I. The Problem of Misperception1. The Fraction Problem2. How Our Minds Fractionate the World3. Confirmation Bias: How Your Mind Filters Evidence Based on Preexisting Beliefs4. Bias with a Cherry on Top: Cherry-Picking the DataPart II. The Fraction Problem in Different Arenas5. The Criminal Justice System6. The March to War7. Patterns in the Static8. Alternative and New Age Beliefs9. The Appearance of Design in the Natural World10. The Hard SciencesPart III. Reversing Misperception11. How Misperceiving the Fraction Can Be Advantageous12. Can We Solve the Problems with Human Perception and Reasoning and Should We Even Try?NotesBibliographyIndex

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Book SynopsisThe role of gender in making and shaping mathematicians.Trade Review'Mathematicians do their best work in their youth'; 'mathematicians work in complete isolation'; 'mathematics and politics don't mix.'These and other myths are discussed and debunked—in both theoretical and concrete terms—in the particular context of the role of women in mathematics. Henrion studies the nature of the participation of women in mathematical research and surrounding issues of gender and race by weaving her narrative around detailed profiles of nine respected women mathematicians (including two African American women). The individual biographies themselves make for enthralling, often inspiring, reading; combined with Henrion's careful, generally evenhanded, and tightly conceived commentary, this volume should be compelling reading for women mathematics students and professionals. A fine addition to the literature on women in science and, as it is written by a mathematical 'insider,' it is all the more likely to receive attention by the mathematics community. Highly recommended. Undergraduates through faculty. -- S. J. Colley * Choice *

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Book SynopsisEnglish translation of standard mathematical work on theory of numbers, first published in Latin in 1801.

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Book SynopsisIn this vibrant work, which is ideal for both teaching and learning, Apoorva Khare and Anna Lachowska explain the mathematics essential for understanding and appreciating our quantitative world. They show with examples that mathematics is a key tool in the creation and appreciation of art, music, and literature, not just science and technology. The book covers basic mathematical topics from logarithms to statistics, but the authors eschew mundane finance and probability problems. Instead, they explain how modular arithmetic helps keep our online transactions safe, how logarithms justify the twelve-tone scale commonly used in music, and how transmissions by deep space probes are similar to knights serving as messengers for their traveling prince. Ideal for coursework in introductory mathematics and requiring no knowledge of calculus, Khare and Lachowska's enlightening mathematics tour will appeal to a wide audience.Trade Review“A whirlwind tour through mathematics and its applications to the real world, laced with stimulating exercises and fascinating historical insights. Destined to become a classic of mathematical exposition.”—Eli Maor, author of e: the Story of a Number and Trigonometric Delights“Khare and Lachowska introduce bite-size pieces of important math by surrounding them with interesting context, from the Monty Hall problem for probability to a story by Dino Buzzati for velocity. Math treated with seriousness and fun.”—Michael Frame, co-author, with Benoit Mandelbrot, of Fractals, Graphics, and Mathematics Education“It is an excellent book, well-suited for a thoughtful, quantitatively-rigorous ‘Math for Humanists’ course.”—William Goldbloom Bloch, author of The Unimaginable Mathematics of Borges’ Library of Babel“The authors have assembled a fascinating group of very interesting topics.”—Richard Bedient, Hamilton College“A whirlwind tour through mathematics and its applications to the real world, laced with stimulating exercises and fascinating historical insights. Destined to become a classic of mathematical exposition.”—Eli Maor, author of e: the Story of a Number and Trigonometric Delights -- Eli Maor“Khare and Lachowska introduce bite-size pieces of important math by surrounding them with interesting context, from the Monty Hall problem for probability to a story by Dino Buzzati for velocity. Math treated with seriousness and fun.”—Michael Frame, co-author, with Benoit Mandelbrot, of Fractals, Graphics, and Mathematics Education -- Michael Frame“It is an excellent book, well-suited for a thoughtful, quantitatively-rigorous ‘Math for Humanists’ course.”—William Goldbloom Bloch, author of The Unimaginable Mathematics of Borges’ Library of Babel -- William Goldbloom Bloch“The authors have assembled a fascinating group of very interesting topics.”—Richard Bedient, Hamilton College -- Richard Bedient

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Book SynopsisA new approach to the foundations of single variable calculus, based on the introductory course taught at CaltechTrade Review"The author’s stress on repeatable techniques . . . and the real numbers treated as infinite decimals results in a distinctive excursion through familiar territory.”—Nick Lord, The Mathematical Gazette"A very useful and constructive way to teach the subject."—Dominic Thorrington, IMA“Every science and engineering student takes calculus, but few learn the subject with depth and rigor. Calculus for Cranks addresses this gap head-on, introducing fundamental concepts in analysis that are valuable for all students – not just math majors.”—Carina Curto, Professor of Mathematics, Pennsylvania State University “Nets Katz has written a calculus textbook for students who don’t like being lied to. It will be essential for those who are constantly harassing their teachers with questions beginning with ‘why’ and ‘how.’”—Deane Yang, Professor of Mathematics, New York University “Calculus for Cranks unspools like a good novel! Katz deftly weaves abstraction and computation into a single narrative, with an entertaining set of exercises along the way.”—Amie Wilkinson, Professor of Mathematics, University of Chicago “Blending formal and informal insights, Katz pulls back the curtain on calculus, revealing its foundations, especially for those who think they’ve seen it before.”—Francis Su, author of Mathematics for Human Flourishing “Calculus for Cranks is a beautiful, rigorous, intuitive, introduction to real and complex analysis starting from logical reasoning and the number system. I recommend it highly for serious students.”—Wilhelm Schlag, Professor of Mathematics, Yale University

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a huge range and FREE tracked UK delivery on ALL orders.

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Book Synopsis1 Integers.- 2 Congruences and Residue Class Rings.- 3 Encryption.- 4 Probability and Perfect Secrecy.- 5 DES.- 6 AES.- 7 Prime Number Generation.- 8 Public-Key Encryption.- 9 Factoring.- 10 Discrete Logarithms.- 11 Cryptographic Hash Functions.- 12 Digital Signatures.- 13 Other Systems.- 14 Identification.- 15 Secret Sharing.- 16 Public-Key Infrastructures.- Solutions of the exercises.- References.Trade ReviewFrom the reviews: Zentralblatt Math "[......] Of the three books under review, Buchmann's is by far the most sophisticated, complete and up-to-date. It was written for computer-science majors - German ones at that - and might be rough going for all but the best American undergraduates. It is amazing how much Buchmann is able to do in under 300 pages: self-contained explanations of the relevant mathematics (with proofs); a systematic introduction to symmetric cryptosystems, including a detailed description and discussion of DES; a good treatment of primality testing, integer factorization, and algorithms for discrete logarithms, clearly written sections describing most of the major types of cryptosystems, and explanations of basic concepts of practical cryptography such as hash functions, message authentication codes, signatures, passwords, certification authorities, and certificate chains. This book is an excellent reference, and I believe that it would also be a good textbook for a course for mathematics or computer science majors, provided that the instructor is prepared to supplement it with more leisurely treatments of some of the topics." N. Koblitz (Seattle, WA) - American Math. Society Monthly. J.A. Buchmann Introduction to Cryptography "It gives a clear and systematic introduction into the subject whose popularity is ever increasing, and can be recommended to all who would like to learn about cryptography. The book contains many exercises and examples. It can be used as a textbook and is likely to become popular among students. The necessary definitions and concepts from algebra, number theory and probability theory are formulated, illustrated by examples and applied to cryptography." —ZENTRALBLATT MATH "For those of use who wish to learn more about cryptography and/or to teach it, Johannes Buchmann has written this book. … The book is mathematically complete and a satisfying read. There are plenty of homework exercises … . This is a good book for upperclassmen, graduate students, and faculty. … This book makes a superior reference and a fine textbook." (Robert W. Vallin, MathDL, January, 2001) "Buchmann’s book is a text on cryptography intended to be used at the undergraduate level. … the intended audiences of this book are ‘readers who want to learn about modern cryptographic algorithms and their mathematical foundations … . I enjoy reading this book. … Readers will find a good exposition of the techniques used in developing and analyzing these algorithms. … These make Buchmann’s text an excellent choice for self study or as a text for students … in elementary number theory and algebra." (Andrew C. Lee, SIGACT News, Vol. 34 (4), 2003) From the reviews of the second edition: "This is the english translation of the second edition of the author’s prominent german textbook ‘Einführung in die Kryptographie’. The original text grew out of several courses on cryptography given by the author at the Technical University Darmstadt; it is aimed at readers who want to learn about modern cryptographic techniques and its mathematical foundations … . As compared with the first edition the number of exercises has almost been doubled and some material … has been added." (R. Steinbauer, Monatshefte für Mathematik, Vol. 150 (4), 2007)Table of ContentsIntegers.- Congruences and Residue Class Rings.- Encryption.- Probability and Perfect Secrecy.- DES.- AES.- Prime Number Generation.- Public-Key Encryption.- Factoring.- Discrete Logarithms.- Cryptographic Hash Functions.- Digital Signatures.- Other Systems.- Identification.- Public-Key Infrastructures.- Solutions of the Odd Exercises.- Subject Index.- Bibliography.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisThis book is an evolution from my book A First Course in Information Theory published in 2002 when network coding was still at its infancy.Trade ReviewFrom the reviews: "This book could serve as a reference in the general area of information theory and would be of interest to electrical engineers, computer engineers, or computer scientists with an interest in information theory. Each chapter has an appropriate problem set at the end and a brief paragraph that provides insight into the historical significance of the material covered therein. … Summing Up: Recommended. Upper-division undergraduate through professional collections." (J. Beidler, Choice, Vol. 46 (9), May, 2009) "The book consisting of 21 chapters is divided into two parts. Part I, Components of Information Theory … . Part II Fundamentals of Network Coding … . A comprehensive instructor’s manual is available. This is a well planned comprehensive book on the subject. The writing style of the author is quite reader friendly. … it is a welcome addition to the subject and will be very useful to students as well as to the researchers in the field." (Arjun K. Gupta, Zentralblatt MATH, Vol. 1154, 2009)Table of ContentsThe Science of Information.- The Science of Information.- Fundamentals of Network Coding.- Information Measures.- Information Measures.- Zero-Error Data Compression.- Weak Typicality.- Strong Typicality.- Discrete Memoryless Channels.- Rate-Distortion Theory.- The Blahut–Arimoto Algorithms.- Differential Entropy.- Continuous-Valued Channels.- Markov Structures.- Information Inequalities.- Shannon-Type Inequalities.- Beyond Shannon-Type Inequalities.- Entropy and Groups.- Fundamentals of Network Coding.- The Max-Flow Bound.- Single-Source Linear Network Coding: Acyclic Networks.- Single-Source Linear Network Coding: Cyclic Networks.- Multi-source Network Coding.

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Book SynopsisFundamental Fixed-Point Principles.- 1 The Banach Fixed-Point Theorem and Iterative Methods.- 2 The Schauder Fixed-Point Theorem and Compactness.- Applications of the Fundamental Fixed-Point Principles.- 3 Ordinary Differential Equations in B-spaces.- 4 Differential Calculus and the Implicit Function Theorem.- 5 Newton's Method.- 6 Continuation with Respect to a Parameter.- 7 Positive Operators.- 8 Analytic Bifurcation Theory.- 9 Fixed Points of Multivalued Maps.- 10 Nonexpansive Operators and Iterative Methods.- 11 Condensing Maps and the BourbakiKneser Fixed-Point Theorem.- The Mapping Degree and the Fixed-Point Index.- 12 The Leray-Schauder Fixed-Point Index.- 13 Applications of the Fixed-Point Index.- 14 The Fixed-Point Index of Differentiable and Analytic Maps.- 15 Topological Bifurcation Theory.- 16 Essential Mappings and the Borsuk Antipodal Theorem.- 17 Asymptotic Fixed-Point Theorems.- References.- Additional References to the Second Printing.- List of Symbols.- List of TheoreTable of ContentsFundamental Fixed-Point Principles.- 1 The Banach Fixed-Point Theorem and Iterative Methods.- §1.1. The Banach Fixed-Point Theorem.- §1.2. Continuous Dependence on a Parameter.- §1.3. The Significance of the Banach Fixed-Point Theorem.- §1.4. Applications to Nonlinear Equations.- §1.5. Accelerated Convergence and Newton’s Method.- § 1.6. The Picard-Lindelof Theorem.- §1.7. The Main Theorem for Iterative Methods for Linear Operator Equations.- §1.8. Applications to Systems of Linear Equations.- §1.9. Applications to Linear Integral Equations.- 2 The Schauder Fixed-Point Theorem and Compactness.- §2.1. Extension Theorem.- §2.2. Retracts.- §2.3. The Brouwer Fixed-Point Theorem.- §2.4. Existence Principle for Systems of Equations.- §2.5. Compact Operators.- §2.6. The Schauder Fixed-Point Theorem.- §2.7. Peano’s Theorem.- §2.8. Integral Equations with Small Parameters.- §2.9. Systems of Integral Equations and Semilinear Differential Equations.- §2.10. A General Strategy.- §2.11. Existence Principle for Systems of Inequalities.- Applications of the Fundamental Fixed-Point Principles.- 3 Ordinary Differential Equations in B-spaces.- §3.1. Integration of Vector Functions of One Real Variable t.- §3.2. Differentiation of Vector Functions of One Real Variable t.- §3.3. Generalized Picard-Lindelöf Theorem.- §3.4. Generalized Peano Theorem.- §3.5. Gronwall’s Lemma.- §3.6. Stability of Solutions and Existence of Periodic Solutions.- §3.7. Stability Theory and Plane Vector Fields, Electrical Circuits, Limit Cycles.- §3.8. Perspectives.- 4 Differential Calculus and the Implicit Function Theorem.- §4.1. Formal Differential Calculus.- §4.2. The Derivatives of Fréchet and Gâteaux.- §4.3. Sum Rule, Chain Rule, and Product Rule.- §4.4. Partial Derivatives.- §4.5. Higher Differentials and Higher Derivatives.- §4.6. Generalized Taylor’s Theorem.- §4.7. The Implicit Function Theorem.- §4.8. Applications of the Implicit Function Theorem.- §4.9. Attracting and Repelling Fixed Points and Stability.- §4.10. Applications to Biological Equilibria.- §4.11. The Continuously Differentiable Dependence of the Solutions of Ordinary Differential Equations in B-spaces on the Initial Values and on the Parameters.- §4.12. The Generalized Frobenius Theorem and Total Differential Equations.- §4.13. Diffeomorphisms and the Local Inverse Mapping Theorem.- §4.14. Proper Maps and the Global Inverse Mapping Theorem.- §4.15. The Suijective Implicit Function Theorem.- §4.16. Nonlinear Systems of Equations, Subimmersions, and the Rank Theorem.- §4.17. A Look at Manifolds.- §4.18. Submersions and a Look at the Sard-Smale Theorem.- §4.19. The Parametrized Sard Theorem and Constructive Fixed-Point Theory.- 5 Newton’s Method.- §5.1. A Theorem on Local Convergence.- §5.2. The Kantorovi? Semi-Local Convergence Theorem.- 6 Continuation with Respect to a Parameter.- §6.1. The Continuation Method for Linear Operators.- §6.2. B-spaces of Hölder Continuous Functions.- §6.3. Applications to Linear Partial Differential Equations.- §6.4. Functional-Analytic Interpretation of the Existence Theorem and its Generalizations.- §6.5. Applications to Semi-linear Differential Equations.- §6.6. The Implicit Function Theorem and the Continuation Method.- §6.7. Ordinary Differential Equations in B-spaces and the Continuation Method.- §6.8. The Leray—Schauder Principle.- §6.9. Applications to Quasi-linear Elliptic Differential Equations.- 7 Positive Operators.- §7.1. Ordered B-spaces.- §7.2. Monotone Increasing Operators.- §7.3. The Abstract Gronwall Lemma and its Applications to Integral Inequalities.- §7.4. Supersolutions, Subsolutions, Iterative Methods, and Stability.- §7.5. Applications.- §7.6. Minorant Methods and Positive Eigensolutions.- §7.7. Applications.- §7.8. The Krein-Rutman Theorem and its Applications.- §7.9. Asymptotic Linear Operators.- §7.10. Main Theorem for Operators of Monotone Type.- §7.11. Application to a Heat Conduction Problem.- §7.12. Existence of Three Solutions.- §7.13. Main Theorem for Abstract Hammerstein Equations in Ordered B-spaces.- §7.14. Eigensolutions of Abstract Hammerstein Equations, Bifurcation, Stability, and the Nonlinear Krein-Rutman Theorem.- §7.15. Applications to Hammerstein Integral Equations.- §7.16. Applications to Semi-linear Elliptic Boundary-Value Problems.- §7.17. Application to Elliptic Equations with Nonlinear Boundary Conditions.- §7.18. Applications to Boundary Initial-Value Problems for Parabolic Differential Equations and Stability.- 8 Analytic Bifurcation Theory.- §8.1. A Necessary Condition for Existence of a Bifurcation Point.- §8.2. Analytic Operators.- §8.3. An Analytic Majorant Method.- §8.4. Fredholm Operators.- §8.5. The Spectrum of Compact Linear Operators (Riesz—Schauder Theory).- §8.6. The Branching Equations of Ljapunov—Schmidt.- §8.7. The Main Theorem on the Generic Bifurcation From Simple Zeros.- §8.8. Applications to Eigenvalue Problems.- §8.9. Applications to Integral Equations.- §8.10. Application to Differential Equations.- §8.11. The Main Theorem on Generic Bifurcation for Multiparametric Operator Equations—The Bunch Theorem.- §8.12. Main Theorem for Regular Semi-linear Equations.- §8.13. Parameter-Induced Oscillation.- §8.14. Self-Induced Oscillations and Limit Cycles.- §8.15. Hopf Bifurcation.- §8.16. The Main Theorem on Generic Bifurcation from Multiple Zeros.- §8.17. Stability of Bifurcation Solutions.- §8.18. Generic Point Bifurcation.- 9 Fixed Points of Multivalued Maps.- §9.1. Generalized Banach Fixed-Point Theorem.- §9.2. Upper and Lower Semi-continuity of Multivalued Maps.- §9.3. Generalized Schauder Fixed-Point Theorem.- §9.4. Variational Inequalities and the Browder Fixed-Point Theorem.- §9.5. An Extremal Principle.- §9.6. The Minimax Theorem and Saddle Points.- §9.7. Applications in Game Theory.- §9.8. Selections and the Marriage Theorem.- §9.9. Michael’s Selection Theorem.- §9.10. Application to the Generalized Peano Theorem for Differential Inclusions.- 10 Nonexpansive Operators and Iterative Methods.- §10.1. Uniformly Convex B-spaces.- §10.2. Demiclosed Operators.- §10.3. The Fixed-Point Theorem of Browder, Göhde, and Kirk.- §10.4. Demicompact Operators.- §10.5. Convergence Principles in B-spaces.- §10.6. Modified Successive Approximations.- §10.7. Application to Periodic Solutions.- 11 Condensing Maps and the Bourbaki—Kneser Fixed-Point Theorem.- §11.1. A Noncompactness Measure.- §11.2. Applications to Generalized Interval Nesting.- §11.3. Condensing Maps.- §11.4. Operators with Closed Range and an Approximation Technique for Constructing Fixed Points.- §11.5. Sadovskii’s Fixed-Point Theorem for Condensing Maps.- §11.6. Fixed-Point Theorems for Perturbed Operators.- §11.7. Application to Differential Equations in B-spaces.- §11.8. The Bourbaki-Kneser Fixed-Point Theorem.- § 11.9. The Fixed-Point Theorems of Amann and Tarski.- §11.10. Application to Interval Arithmetic.- §11.11. Application to Formal Languages.- The Mapping Degree and the Fixed-Point Index.- 12 The Leray-Schauder Fixed-Point Index.- §12.1. Intuitive Background and Basic Concepts.- §12.2. Homotopy.- §12.3. The System of Axioms.- §12.4. An Approximation Theorem.- §12.5. Existence and Uniqueness of the Fixed-Point Index in ?N.- §12.6. Proof of Theorem 12.A..- §12.7. Existence and Uniqueness of the Fixed-Point Index in B-spaces.- §12.8. Product Theorem and Reduction Theorem.- 13 Applications of the Fixed-Point Index.- §13.1. A General Fixed-Point Principle.- §13.2. A General Eigenvalue Principle.- §13.3. Existence of Multiple Solutions.- §13.4. A Continuum of Fixed Points.- §13.5. Applications to Differential Equations.- §13.6. Properties of the Mapping Degree.- §13.7. The Leray Product Theorem and Homeomorphisms.- §13.8. The Jordan-Brouwer Separation Theorem and Brouwer’s Invariance of Dimension Theorem.- §13.9. A Brief Glance at the History of Mathematics.- §13.10. Topology and Intuition.- §13.11. Generalization of the Mapping Degree.- 14 The Fixed-Point Index of Differentiable and Analytic Maps.- §14.1. The Fixed-Point Index of Classical Analytic Functions.- §14.2. The Leray—Schauder Index Theorem.- §14.3. The Fixed-Point Index of Analytic Mappings on Complex B-spaces.- §14.4. The Schauder Fixed-Point Theorem with Uniqueness.- §14.5. Solution of Analytic Operator Equations.- §14.6. The Global Continuation Principle of Leray—Schauder.- §14.7. Unbounded Solution Components.- §14.8. Applications to Systems of Equations.- §14.9. Applications to Integral Equations.- §14.10. Applications to Boundary-Value Problems.- §14.11. Applications to Integral Power Series.- 15 Topological Bifurcation Theory.- §15.1. The Index Jump Principle.- §15.2. Applications to Systems of Equations.- §15.3. Duality Between the Index Jump Principle and the Leray—Schauder Continuation Principle.- §15.4. The Geometric Heart of the Continuation Method.- §15.5. Stability Change and Bifurcation.- §15.6. Local Bifurcation.- §15.7. Global Bifurcation.- §15.8. Application to Systems of Equations.- §15.9. Application to Integral Equations.- §15.10. Application to Differential Equations.- §15.11. Application to Bifurcation at Infinity.- §15.12. Proof of the Main Theorem.- §15.13. Preventing Secondary Bifurcation.- 16 Essential Mappings and the Borsuk Antipodal Theorem.- §16.1. Intuitive Introduction.- §16.2. Essential Mappings and their Homotopy Invariance.- §16.3. The Antipodal Theorem.- §16.4. The Invariance of Domain Theorem and Global Homeomorphisms.- §16.5. The Borsuk—Ulam Theorem and its Applications.- §16.6. The Mapping Degree and Essential Maps.- §16.7. The Hopf Theorem.- §16.8. A Glance at Homotopy Theory.- 17 Asymptotic Fixed-Point Theorems.- §17.1. The Generalized Banach Fixed-Point Theorem.- §17.2. The Fixed-Point Index of Iterated Mappings.- §17.3. The Generalized Schauder Fixed-Point Theorem.- §17.4. Application to Dissipati ve Dynamical Systems.- §17.5. Perspectives.- References.- Additional References to the Second Printing.- List of Symbols.- List of Theorems.- List of the Most Important Definitions.- Schematic Overviews.- General References to the Literature.- List of Important Principles.- of the Other Parts.

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Book SynopsisFirst Part.- I The Complex Plane and Elementary Functions.- II Analytic Functions.- III Line Integrals and Harmonic Functions.- IV Complex Integration and Analyticity.- V Power Series.- VI Laurent Series and Isolated Singularities.- VII The Residue Calculus.- Second Part.- VIII The Logarithmic Integral.- IX The Schwarz Lemma and Hyperbolic Geometry.- X Harmonic Functions and the Reflection Principle.- XI Conformal Mapping.- Third Part.- XII Compact Families of Meromorphic Functions.- XIII Approximation Theorems.- XIV Some Special Functions.- XV The Dirichlet Problem.- XVI Riemann Surfaces.- Hints and Solutions for Selected Exercises.- References.- List of Symbols.Table of Contents* The Complex Plane and Elementary Functions * Analytic Functions * Line Integrals and Harmonic Functions * Complex Integration and Analyticity * Power Series * Laurent Series and Isolated Singularities * The Residue Calculus * The Logarithmic Integral * The Schwarz Lemma and Hyperbolic Geometry * Harmonic Functions and the Reflection Principle * Conformal Mapping * Compact Families of Meromorphic Functions * Approximation Theorems * Some Special Functions * The Dirichlet Problem * Riemann Surfaces

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Book SynopsisThe first part of this introduction to ergodic theory addresses measure-preserving transformations of probability spaces and covers such topics as recurrence properties and the Birkhoff ergodic theorem. The second part focuses on the ergodic theory of continuous transformations of compact metrizable spaces.Table of Contents0 Preliminaries.- §0.1 Introduction.- §0.2 Measure Spaces.- §0.3 Integration.- §0.4 Absolutely Continuous Measures and Conditional Expectations.- §0.5 Function Spaces.- §0.6 Haar Measure.- §0.7 Character Theory.- §0.8 Endomorphisms of Tori.- §0.9 Perron—Frobenius Theory.- §0.10 Topology.- 1 Measure-Preserving Transformations.- §1.1 Definition and Examples.- §1.2 Problems in Ergodic Theory.- §1.3 Associated Isometries.- §1.4 Recurrence.- §1.5 Ergodicity.- §1.6 The Ergodic Theorem.- §1.7 Mixing.- 2 Isomorphism, Conjugacy, and Spectral Isomorphism.- §2.1 Point Maps and Set Maps.- §2.2 Isomorphism of Measure-Preserving Transformations.- §2.3 Conjugacy of Measure-Preserving Transformations.- §2.4 The Isomorphism Problem.- §2.5 Spectral Isomorphism.- §2.6 Spectral Invariants.- 3 Measure-Preserving Transformations with Discrete Spectrum.- §3.1 Eigenvalues and Eigenfunctions.- §3.2 Discrete Spectrum.- §3.3 Group Rotations.- 4 Entropy.- §4.1 Partitions and Subalgebras.- §4.2 Entropy of a Partition.- §4.3 Conditional Entropy.- §4.4 Entropy of a Measure-Preserving Transformation.- §4.5 Properties of h (T, A) and h (T).- §4.6 Some Methods for Calculating h (T).- §4.7 Examples.- §4.8 How Good an Invariant is Entropy?.- §4.9 Bernoulli Automorphisms and Kolmogorov Automorphisms.- §4.10 The Pinsker ?-Algebra of a Measure-Preserving Transformation.- §4.11 Sequence Entropy.- §4.12 Non-invertible Transformations.- §4.13 Comments.- 5 Topological Dynamics.- §5.1 Examples.- §5.2 Minimality.- §5.3 The Non-wandering Set.- §5.4 Topological Transitivity.- §5.5 Topological Conjugacy and Discrete Spectrum.- §5.6 Expansive Homeomorphisms.- 6 Invariant Measures for Continuous Transformations.- §6.1 Measures on Metric Spaces.- §6.2 Invariant Measures for Continuous Transformations.- §6.3 Interpretation of Ergodicity and Mixing.- §6.4 Relation of Invariant Measures to Non-wandering Sets, Periodic Points and Topological Transitivity.- §6.5 Unique Ergodicity.- §6.6 Examples.- 7 Topological Entropy.- §7.1 Definition Using Open Covers.- §7.2 Bowen’s Definition.- §7.3 Calculation of Topological Entropy.- 8 Relationship Between Topological Entropy and Measure-Theoretic Entropy.- §8.1 The Entropy Map.- §8.2 The Variational Principle.- §8.3 Measures with Maximal Entropy.- §8.4 Entropy of Affine Transformations.- §8.5 The Distribution of Periodic Points.- §8.6 Definition of Measure-Theoretic Entropy Using the Metrics dn.- 9 Topological Pressure and Its Relationship with Invariant Measures.- §9.1 Topological Pressure.- §9.2 Properties of Pressure.- §9.3 The Variational Principle.- §9.4 Pressure Determines M(X, T).- §9.5 Equilibrium States.- 10 Applications and Other Topics.- §10.1 The Qualitative Behaviour of Diffeomorphisms.- §10.2 The Subadditive Ergodic Theorem and the Multiplicative Ergodic Theorem.- §10.3 Quasi-invariant Measures.- §10.4 Other Types of Isomorphism.- §10.5 Transformations of Intervals.- §10.6 Further Reading.- References.

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Book Synopsis1. Divisibility, the Fundamental Theorem of Number Theory.- 2. Congruences.- 3. Rational and Irrational Numbers. Approximation of Numbers by Rational Numbers (Diophantine Approximation).- 4. Geometric Methods in Number Theory.- 5. Properties of Prime Numbers.- 6. Sequences of Integers.- 7. Diophantine Problems.- 8. Arithmetic Functions.- Hints to the More Difficult Exercises.Trade ReviewFrom the reviews: "Read this book just for Erdös’s (Erdos’s) characteristic turn of thought, or for results hard to find elsewhere, such as a finiteness theorem concerning odd perfect numbers with a fixed number of factors. Summing Up: Recommended. Lower-division undergraduates through professionals." (D.V. Feldman, CHOICE, December, 2003) "This is an English translation of the second edition of a book originally published over 40 years ago … . The contents should be accessible to, and inspire and challenge, keen pre-university students as well as giving the experienced mathematician food for thought. The proofs are elementary and largely self-contained, and the problems and results well motivated. … This translation makes a very clearly and nicely written book available to many more readers who should benefit and gain much pleasure from studying it." (Eira J. Scourfield, Zentralblatt MATH, Issue 1018, 2003) "This rather unique book is a guided tour through number theory. While most introductions to number theory provide a systematic and exhaustive treatment of the subject, the authors have chosen instead to illustrate the many varied subjects by associating recent discoveries, interesting methods, and unsolved problems. … János Surányi’s vast teaching experience successfully complements Paul Erdös’s ability to initiate new directions of research by suggesting new problems and approaches." (L’Enseignement Mathematique, Vol. 49 (1-2), 2003) "This is a somewhat enlarged translation of the Hungarian book … . It goes without saying that the text is masterly written. It contains on comparatively few lines the fundamental ideas of not only elementary Number Theory: it contains also irrationality proofs ... . The book is hence by far not an n-th version of always the same matter. The style reminds me on the celebrated book of Pólya … . It is desirable that the book under discussion should have a similar success." (J. Schoissengeier, Monatshefte für Mathematik, Vol. 143 (2), 2004) "This an introduction to elementary number theory in which the authors present the main notions of that theory and ‘try to give glimpses into the deeper related mathematics’, as they write in the preface. There are 8 chapters … . Each of them brings not only the notions and theorems (sometimes with unconventional proofs) which usually appear in introductory texts, but discusses also topics found rarely … . One also finds several interesting historical comments." (W. Narkiewicz, Mathematical Reviews, 2003j)Table of Contents* Preface * Facts Used Without Proof in the Book * Divisibility, the Fundamental Theorem of Number Theory * Congruences * Rational and irrational numbers. Approximation of numbers by rational numbers. (Diophantine approximation.) * Geometric methods in number theory * Properties of prime numbers * Sequences of integers * Diophantine Problems * Arithmetic Functions * Hints to the more difficult exercises * Bibliography * Index

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Book SynopsisIn particu­ lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ­ ential equations.Table of ContentsI Elementary Local Properties of Holomorphic Functions.- II Domains of Holomorphy and Pseudoconvexity.- III Differential Forms and Hermitian Geometry.- IV Integral Representations in ?n.- V The Levi Problem and the Solution of ?? on Strictly Pseudoconvex Domains.- VI Function Theory on Domains of Holomorphy in ?n.- VII Topics in Function Theory on Strictly Pseudoconvex Domains.- Appendix A.- Appendix B.- Appendix C.- Glossary of Symbols and Notations.

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