Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    Providing a concise introduction to abstract algebra, this work unfolds some of the fundamental systems with the aim of reaching applicable, significant results.

    Verification that algorithms work is emphasized more than their complexity. An effective use of examples, and huge number of interesting exercises, demonstrate the topics of trees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs. For those who need to learn to make coherent arguments in the fields of mathematics and computer science.

    In the Fourth Edition CALCULUS, EARLY TRANSCENDENTALS these functions are introduced in the first chapter and their limits and derivatives are found in Chapters 2 and 3 at the same time as polynomials and other elementary functions. In this Fourth Edition, Stewart retains the focus on problem solving, the meticulous accuracy, the patient explanations, and the carefully graded problems that have made these texts word so well for a wide range of students. All new and unique features in CALCULUS, FOURTH EDITION have been incorporated into these revisions also.

    Throughout the book, the authors show how the study of learning helps solve practical problems, such as improving study skills, improving relationships, raising children, and effectively stopping smoking. This book is both solidly based in research and engaging for the student. To help ensure that students understand the materials, the authors strategically include multiple opportunities for review and self-testing within the text.

    Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications. An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

    In-depth explorations of the derivative, the differentiation and integration of the powers of x, and theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Clear-cut explanations, numerous drills, illustrative examples. 1967 edition. Solution guide available upon request.

    The book's hallmark values-accuracy, currency, and passion for teaching and learning-have made Campbell/Reece the most successful book for readers for seven consecutive editions. More than 6 million readers have benefited from "BIOLOGY's"clear explanations, carefully crafted artwork, and student-friendly narrative style.Introduction: Themes in the Study of Life, The Chemical Context of Life, Water and the Fitness of the Environment, Carbon and the Molecular Diversity of Life, The Structure and Function of Large Biological Molecules, A Tour of the Cell, Membrane Structure and Function, An Introduction to Metabolism, Cellular Respiration: Harvesting Chemical Energy, Photosynthesis, Cell Communication, The Cell Cycle, Meiosis and Sexual Life Cycles, Mendel and the Gene Idea, The Chromosomal Basis of Inheritance, The Molecular Basis of Inheritance, From Gene to Protein, Control of Gene Expression, Viruses, Biotechnology, Genomes and Their Evolution, Descent with Modification: A Darwinian View of Life, The Evolution of Populations, The Origin of Species, The History of Life on Earth, Phylogeny and the Tree of Life, Bacteria and Archaea, Protists, Plant Diversity I: How Plants Colonized Land, Plant Diversity II: The Evolution of Seed Plants, Fungi, An Introduction to Animal Diversity, Invertebrates, Vertebrates, Plant Structure, Growth, and Development, Transport in Vascular Plants, Soil and Plant Nutrition, Angiosperm Reproduction and Biotechnology, Plant Responses to Internal and External Signals, Basic Principles of Animal Form and Function, Animal Nutrition, Circulation and Gas Exchange, The Immune System, Osmoregulation and Excretion, Hormones and the Endocrine System, Animal Reproduction, Animal Development, Neurons, Synapses, and Signaling, Nervous Systems, Sensory and Motor Mechanisms, Animal Behavior, An Introduction to Ecology and the Biosphere, Population Ecology, Community Ecology, Ecosystems, Conservation Biology and Restoration Ecology.For readers interested in learning the basics of Biology.

    His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

    It has an algebra and trigonometry prerequisite, but calculus is preferred.

    While the text is descriptive (largely conceptual) it does provide quantitative material, including worked examples in optional boxed sections.

    These singularities are places where space-time begins or ends, and the presently known laws of physics break down. They will occur inside black holes, and in the past are what might be construed as the beginning of the universe. To show how these predictions arise, the authors discuss the General Theory of Relativity in the large. Starting with a precise formulation of the theory and an account of the necessary background of differential geometry, the significance of space-time curvature is discussed and the global properties of a number of exact solutions of Einstein's field equations are examined. The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions. A discussion of the Cauchy problem for General Relativity is also included in this 1973 book.

    It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

    Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

    For the calculus-based General Physics course primarily taken by engineers and scientists.