The author has a direct style. His book presents detailed and intensive explanations. Many diagrams and key examples are used to aid understanding, as well as the application of calculus to physics and engineering and economics. The text is well organized, and it covers single variable and multivariable calculus in depth. An instructor's manual and student guide are available online at http: //ocw.mit.edu/ans7870/resources/Strang/....

    It also explains the "why" of trigonometry, using real-world examples that illustrate the value of trigonometry in a variety of careers. Mary Jane Sterling (Peoria, IL) has taught mathematics at Bradley University in Peoria for more than 20 years. She is also the author of the highly successful Algebra For Dummies (0-7645-5325-9).

    Early beginnings in antiquity, medieval contributions, and a century of anticipation lead up to a consideration of Newton and Leibniz, the period of indecison that followed them, and the final rigorous formulation that we know today.

    This groundbreaking and powerful theory now forms the basis of computer science. In Turing's Vision, Chris Bernhardt explains the theory, Turing's most important contribution, for the general reader. Bernhardt argues that the strength of Turing's theory is its simplicity, and that, explained in a straightforward manner, it is eminently understandable by the nonspecialist. As Marvin Minsky writes, -The sheer simplicity of the theory's foundation and extraordinary short path from this foundation to its logical and surprising conclusions give the theory a mathematical beauty that alone guarantees it a permanent place in computer theory.- Bernhardt begins with the foundation and systematically builds to the surprising conclusions. He also views Turing's theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turing's later work, and the birth of the modern computer.In the paper, -On Computable Numbers, with an Application to the Entscheidungsproblem, - Turing thinks carefully about how humans perform computation, breaking it down into a sequence of steps, and then constructs theoretical machines capable of performing each step. Turing wanted to show that there were problems that were beyond any computer's ability to solve; in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turing's ideas, Bernhardt examines three well-known decision problems to explore the concept of undecidability; investigates theoretical computing machines, including Turing machines; explains universal machines; and proves that certain problems are undecidable, including Turing's problem concerning computable numbers.

    Holistic Anatomy presents an authoritative study of anatomy, physiology, and pathology but expands the discussion by connecting the science of the body to a variety of alternative modalities to explore how human beings exist within—and interact with—their environment, and how they experience existence in emotional and spiritual terms. Basic scientific terminology and detailed descriptions are interwoven with informal, sometimes humorous observations, facts, and ideas about life. The mechanisms, structure, and functions of the body are explored, along with how they relate to spiritual and energetic paradigms, emotions, and ecological principles. The first half of the book covers basic anatomy and physiology, describing each major system of the body and how they interrelate. This part includes a thoughtful discussion of aging and the dying process. The second half focuses on models of health and disease, both traditional and holistic. Topics include western pathology, emotional health, five element medicine, and the spiritual cause for disease.

    Julia Diggins masterfully recreates the atmosphere of ancient times, when men, using three simple tools, the string, the straightedge, and the shadow, discovered the basic principles and constructions of elementary geometry. Her book reveals how these discoveries related to the early civilizations of Mesopotamia, Egypt, and Greece.The fabric of the story is woven out of archeological and historical records and legends about the major men of mathematics. By reconstructing the events as they might have happened, Diggins enables the attentive reader to easily follow the pattern of reasoning that leads to an ingenious proof of the Pythagorean theorem, an appreciation of the significance of the Golden Mean in art and architecture, and the construction of the five regular solids.Out of print for 34 years, Julia Diggins' classic book is back and is a must-read for middle school students or for parents helping their children through their first geometry course. You will be fascinated with the graphic illustrations and written depiction of how the knowledge and wisdom of so many cultures helped shape our civilization today. This book is popular with teachers and parents who use Jamie York's Making Math Meaningful curriculum books.

    Never before in history have we been able to acquire, record, communicate, and use information in so many different forms. Never before have we had access to such vast quantities of data of every kind. This revolution goes far beyond the limitless content that fills our lives, because information also underlies our understanding of ourselves, the natural world, and the universe. It is the key that unites fields as different as linguistics, cryptography, neuroscience, genetics, economics, and quantum mechanics. And the fact that information bears no necessary connection to meaning makes it a profound puzzle that people with a passion for philosophy have pondered for centuries.Table of ContentsLECTURE 1The Transformability of Information 4LECTURE 2Computation and Logic Gates 17LECTURE 3Measuring Information 26LECTURE 4Entropy and the Average Surprise 34LECTURE 5Data Compression and Prefix-Free Codes 44LECTURE 6Encoding Images and Sounds 57LECTURE 7Noise and Channel Capacity 69LECTURE 8Error-Correcting Codes 82LECTURE 9Signals and Bandwidth 94LECTURE 10Cryptography and Key Entropy 110LECTURE 11Cryptanalysis and Unraveling the Enigma 119LECTURE 12Unbreakable Codes and Public Keys 130LECTURE 13What Genetic Information Can Do 140LECTURE 14Life’s Origins and DNA Computing 152LECTURE 15Neural Codes in the Brain 169LECTURE 16Entropy and Microstate Information 185LECTURE 17Erasure Cost and Reversible Computing 198LECTURE 18Horse Races and Stock Markets 213LECTURE 19Turing Machines and Algorithmic Information 226LECTURE 20Uncomputable Functions and Incompleteness 239LECTURE 21Qubits and Quantum Information 253LECTURE 22Quantum Cryptography via Entanglement 266LECTURE 23It from Bit: Physics from Information 281LECTURE 24The Meaning of Information 293

    W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.

    40 illustrations throughout.

    Concise and original, this engaging book is an antidote to the behemoth art history textbooks from which we were all taught. As he demonstrates so persuasively, there can never be one story of art. Cultures have their own stories - about themselves, about other cultures - and to hear them all is one way to hear the multiple stories that art tells. But each of us also has our own story of art, a kind of private art history made up of the pieces we have seen, and loved or hated, the effects they had on us, and the connections that might be drawn among them.Elkins opens up the questions that traditional art history usually avoids. What about all the art not produced in Western Europe or in the Europeanized Americas? Is it possible to include Asian art and Indian art in 'the story?' What happens when one does? To help us find answers, he uses both Western and non-Western artworks, tables of contents from art histories written in cultures outside the centre of Western European tradition, and strangely wonderful diagrams of how artworks might connect through a single individual. True multiculturalism may be an impossibility, but art lovers can each create a 'story of art' that is right for themselves.

    In this beautiful book, we hear the full story of the meteoric rise of Heston Blumenthal and The Fat Duck, birthplace of snail porridge and bacon-and-egg ice cream, and encounter the passion, perfection and weird science behind the man and the restaurant.

    But not everyone accepts the same religious premises or recognizes the same spiritual authorities. Are there public arguments--reasons that can be given that do not presuppose agreement on religious grounds or common religious commitments--that can guide our thoughts and actions, as well as our laws and public policies?In Ten Universal Principles: A Brief Philosophy of the Life Issues, Jesuit Father Robert Spitzer sets out, in a brief, yet highly-readable and lucid style, ten basic principles that must govern the reasonable person's thinking and acting about life issues. A highly-regarded philosopher, Father Spitzer provides an intelligent outline for thinking and talking about human life. This book is a powerful tool for persuasively articulating and effectively inculturating a prolife philosophy.

    A timeless introduction to the field and a landmark in symbolic logic, showing that classical logic can be treated algebraically.

    There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again for the classroom or for self-study.Principles of Statistics was created primarily for the student of natural sciences, the social scientist, the undergraduate mathematics student, or anyone familiar with the basics of mathematical language. It assumes no previous knowledge of statistics or probability; nor is extensive mathematical knowledge necessary beyond a familiarity with the fundamentals of differential and integral calculus. (The calculus is used primarily for ease of notation; skill in the techniques of integration is not necessary in order to understand the text.)Professor Bulmer devotes the first chapters to a concise, admirably clear description of basic terminology and fundamental statistical theory: abstract concepts of probability and their applications in dice games, Mendelian heredity, etc.; definitions and examples of discrete and continuous random variables; multivariate distributions and the descriptive tools used to delineate them; expected values; etc. The book then moves quickly to more advanced levels, as Professor Bulmer describes important distributions (binomial, Poisson, exponential, normal, etc.), tests of significance, statistical inference, point estimation, regression, and correlation. Dozens of exercises and problems appear at the end of various chapters, with answers provided at the back of the book. Also included are a number of statistical tables and selected references.

    Drawing on more than two decades of firsthand research and experience, Bruce reports that our minds are subject to influences from many unseen spiritual sources. Some of these can influence how we think, feel, act, and even how our bodies function. They can make us unhappy, irritable, confused, sick, unstable, even crazy. This is why we need practical tools and countermeasures for psychic self-defense, all of which Bruce provides. This is the ultimate guide to combating the influences of earthbound spirits, deranged ghosts, astral snakes and spiders, demonic spirits, and poltergeists. This is a highly anecdotal and comprehensive practical guide to the dark side of the psychic universe.