Two world-renowned scientists present an audacious new vision of the cosmos that “steals the thunder from the Big Bang theory.” — Wall Street JournalThe Big Bang theory—widely regarded as the leading explanation for the origin of the universe—posits that space and time sprang into being about 14 billion years ago in a hot, expanding fireball of nearly infinite density. Over the last three decades the theory has been repeatedly revised to address such issues as how galaxies and stars first formed and why the expansion of the universe is speeding up today. Furthermore, an explanation has yet to be found for what caused the Big Bang in the first place.In Endless Universe , Paul J. Steinhardt and Neil Turok, both distinguished theoretical physicists, present a bold new cosmology. Steinhardt and Turok “contend that what we think of as the moment of creation was simply part of an infinite cycle of titanic collisions between our universe and a parallel world” ( Discover ). They recount the remarkable developments in astronomy, particle physics, and superstring theory that form the basis for their groundbreaking “Cyclic Universe” theory. According to this theory, the Big Bang was not the beginning of time but the bridge to a past filled with endlessly repeating cycles of evolution, each accompanied by the creation of new matter and the formation of new galaxies, stars, and planets.Endless Universe provides answers to longstanding problems with the Big Bang model, while offering a provocative new view of both the past and the future of the cosmos. It is a “theory that could solve the cosmic mystery” ( USA Today ).

Elementary Methods in Number Theory begins with "a first course in number theory" for students with no previous knowledge of the subject. The main topics are divisibility, prime numbers, and congruences. There is also an introduction to Fourier analysis on finite abelian groups, and a discussion on the abc conjecture and its consequences in elementary number theory. In the second and third parts of the book, deep results in number theory are proved using only elementary methods. Part II is about multiplicative number theory, and includes two of the most famous results in mathematics: the Erdös-Selberg elementary proof of the prime number theorem, and Dirichlets theorem on primes in arithmetic progressions. Part III is an introduction to three classical topics in additive number theory: Warings problems for polynomials, Liouvilles method to determine the number of representations of an integer as the sum of an even number of squares, and the asymptotics of partition functions. Melvyn B. Nathanson is Professor of Mathematics at the City University of New York (Lehman College and the Graduate Center). He is the author of the two other graduate texts: Additive Number Theory: The Classical Bases and Additive Number Theory: Inverse Problems and the Geometry of Sumsets.

This easy-to-read handbook provides a comprehensive review of the current knowledge on lichens. The structure of lichens and their dual nature is explained, as well as the physiology of interaction of the symbionts. The way lichens reproduce and their ecology is included, with methods for cultivating them and their isolated symbionts. Extremely useful as a text of lichenology, this handbook will benefit students of lichenology and allied fields, those interested in symbiotic associations and ecology, and teachers of biology, botany, and ecology courses.

An introduction to computers giving a brief history of the machines in addition to the author's personal experiences while learning to work with them

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

One Infinite Series and Infinite Sequences.- 1 Operations with Power Series.- Additive Number Theory, Combinatorial Problems, and Applications.- Binomial Coefficients and Related Problems.- Differentiation of Power Series.- Functional Equations and Power Series.- Gaussian Binomial Coefficients.- Majorant Series.- 2 Linear Transformations of Series. A Theorem of Cesàro.- Triangular Transformations of Sequences into Sequences.- More General Transformations of Sequences into Sequences.- Transformations of Sequences into Functions. Theorem of Cesàro.- 3 The Structure of Real Sequences and Series.- The Structure of Infinite Sequences.- Convergence Exponent.- The Maximum Term of a Power Series.- Subseries.- Rearrangement of the Terms.- Distribution of the Signs of the Terms.- 4 Miscellaneous Problems.- Enveloping Series.- Various Propositions on Real Series and Sequences.- Partitions of Sets, Cycles in Permutations.- Two Integration.- 1 The Integral as the Limit of a Sum of Rectangles.- The Lower and the Upper Sum.- The Degree of Approximation.- Improper Integrals Between Finite Limits.- Improper Integrals Between Infinite Limits.- Applications to Number Theory.- Mean Values and Limits of Products.- Multiple Integrals.- 2 Inequalities.- Inequalities.- Some Applications of Inequalities.- 3 Some Properties of Real Functions.- Proper Integrals.- Improper Integrals.- Continuous, Differentiate, Convex Functions.- Singular Integrals. Weierstrass' Approximation Theorem.- 4 Various Types of Equidistribution.- Counting Function. Regular Sequences.- Criteria of Equidistribution.- Multiples of an Irrational Number.- Distribution of the Digits in a Table of Logarithms and Related Questions.- Other Types of Equidistribution.- 5 Functions of Large Numbers.- Laplace's Method.- Modifications of the Method.- Asymptotic Evaluation of Some Maxima.- Minimax and Maximin.- Three Functions of One Complex Variable. General Part.- 1 Complex Numbers and Number Sequences.- Regions and Curves. Working with Complex Variables.- Location of the Roots of Algebraic Equations.- Zeros of Polynomials, Continued. A Theorem of Gauss.- Sequences of Complex Numbers.- Sequences of Complex Numbers, Continued: Transformation of Sequences.- Rearrangement of Infinite Series.- 2 Mappings and Vector Fields.- The Cauchy-Riemann Differential Equations.- Some Particular Elementary Mappings.- Vector Fields.- 3 Some Geometrical Aspects of Complex Variables.- Mappings of the Circle. Curvature and Support Function.- Mean Values Along a Circle.- Mappings of the Disk. Area.- The Modular Graph. The Maximum Principle.- 4 Cauchy's Theorem • The Argument Principle.- Cauchy's Formula.- Poisson's and Jensen's Formulas.- The Argument Principle.- Rouche's Theorem.- 5 Sequences of Analytic Functions.- Lagrange's Series. Applications.- The Real Part of a Power Series.- Poles on the Circle of Convergence.- Identically Vanishing Power Series.- Propagation of Convergence.- Convergence in Separated Regions.- The Order of Growth of Certain Sequences of Polynomials.- 6 The Maximum Principle.- The Maximum Principle of Analytic Functions.- Schwarz's Lemma.- Hadamard's Three Circle Theorem.- Harmonic Functions.- The Phragmén-Lindelöf Method.- Author Index.

Numerical linear algebra, digital signal processing, and parallel algorithms are three disciplines with a great deal of activity in the last few years. The interaction between them has been growing to a level that merits an Advanced Study Institute dedicated to the three areas together. This volume gives an account of the main results in this interdisciplinary field. The following topics emerged as major themes of the - Singular value and eigenvalue decompositions, including applications, - Toeplitz matrices, including special algorithms and architectures, - Recursive least squares in linear algebra, digital signal processing and control, - Updating and downdating techniques in linear algebra and signal processing, - Stability and sensitivity analysis of special recursive least squares problems, - Special architectures for linear algebra and signal processing. This book contains tutorials on these topics given by leading scientists in each of the three areas. A consider- able number of new research results are presented in contributed papers. The tutorials and papers will be of value to anyone interested in the three disciplines.

The failures of “free-market” capitalism are perhaps nowhere more evident than in the production and distribution of food. Although modern human societies have attained unprecedented levels of wealth, a significant amount of the world’s population continues to suffer from hunger or food insecurity on a daily basis. In Agriculture and Food in Crisis , Fred Magdoff and Brian Tokar have assembled an exceptional collection of scholars from around the world to explore this frightening long-term trend in food production. While approaching the issue from many angles, the contributors to this volume share a focus on investigating how agricultural production is shaped by a system that is oriented around the creation of profit above all else, with food as nothing but an afterthought. As the authors make clear, it is technically possible to feed to world’s people, but it is not possible to do so as long as capitalism exists. Toward that end, they examine what can be, and is being, done to create a human-centered and ecologically sound system of food production, from sustainable agriculture and organic farming on a large scale to movements for radical land reform and national food sovereignty. This book will serve as an indispensible guide to the years ahead, in which world politics will no doubt come to be increasingly understood as food politics.

1 Real Functions 2 Sequences and Series 3 Continuous Functions on Intervals 4 Differentiation 5 The Riemann Integral 6 Topology 7 Function Spaces 8 Differentiable Maps 9 Measures 10 Integration 11 Manifolds 12 Multilinear Algebra 13 Differential Forms 14 Integration on Manifolds

One of The New York Times Critics' Picks of the Year From acclaimed psychoanalyst Adam Phillips, a meditation on what we must give up to feel more alive. To give up or not to give up? The question can feel inescapable but the answer is never simple. Giving up our supposed vices is one thing; giving up on life itself is quite another. One form of self-sacrifice feels positive, something to admire and aspire to, while the other is profoundly unsettling, if not actively undesirable. There are always, it turns out, both good and bad sacrifices, but it is not always clear beforehand which is which. We give something up because we believe we can no longer go on as we are. In this sense, giving up is a critical moment—an attempt to make a different future. In On Giving Up , the acclaimed psychoanalyst Adam Phillips illuminates both the gaps and the connections between the many ways of giving up and helps us to address the central question: What must we give up in order to feel more alive?

In this work the distinguished physical chemist and philosopher, Michael Polanyi, demonstrates that the scientist's personal participation in his knowledge, in both its discovery and its validation, is an indispensable part of science itself. Even in the exact sciences, "knowing" is an art, of which the skill of the knower, guided by his personal committment and his passionate sense of increasing contact with reality, is a logically necessary part. In the biological and social sciences this becomes even more evident. The tendency to make knowledge impersonal in our culture has split fact from value, science from humanity. Polanyi wishes to substitute for the objective, impersonal ideal of scientific detachment an alternative ideal which gives attention to the personal involvement of the knower in all acts of understanding. His book should help to restore science to its rightful place in an integrated culture, as part of the whole person's continuing endeavor to make sense of the totality of his experience. In honor of this work and his The Study of Man Polanyi was presented with the Lecomte de Noüy Award for 1959.

Examines the schools that have won the Westinghouse Science Talent Search, a prestigious national academic contest, and chronicles how these schools have created phenomenal science programs.

"A pathbreaking book on an important subject which, surprisingly, has been paid little attention by social scientists. Zerubavel writes with both learning and lucidity. His book is a pleasure to read." -Peter Berger "Others have written about the structuring of time, but few so insightfully and compellingly as Zerubavel." -Neil J. Smelser "This is a jewel of a book, one of the most important contributions to cultural sociology in recent years. Professor Zerubavel's easy blend of history, religion, science, politics, and social values makes this a study a delightful voyage of unexpected discovery and new awareness. It hink the title has misled some people into thinking this is a book on music or something of the sort. All the more reason to rejoice at this reissue in paperback." -David S. Landes "Hidden Rhythms is an exciting study of a subject that has net yet gained the attention it deserves among sociologists and other social scientists . . . Zerubavel's book has the distinctive merit to discuss earlier approaches to the study of schedules and calendars and to add a series of extremely shrewd observations and calendars to add a series of extremely shrewd observations of his own on the sociology of time. His work seems indispensable for all those social scientists who have become conscious of the central position of the temporal dimension in the life of people and their society." -Lewis A. Coser "Eviatar Zerubavel's Hidden Rhythms is an original and highly imaginative analysis of the role time schedule plays in social life. Continuing the distinctive focus on social time Zerubavel develops in Patterns of Time in Hospital life, he provides in Hidden Rhythms more penetrating and profound analysis of the subtle and diverse significance of time in organizing our social relationships and lives. A joy to read." -Peter M. Blau

An Introduction to Harmonic Analysis

Describes how to interpret pets' bad behavior to determine the underlying problems, and offers techniques for helping the animals to act properly

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In this pioneering work, Robert M. Fano presents a comprehensive study of information theory as the basis for communication with computers. The book examines the methods and limits of transmitting and receiving information, with practical applications in digital technology and communication engineering. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Slight shelf wear. Marker mark fore edge. Pages are clean. Binding is tight.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.