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Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review
Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review
The acclaimed author of A Tour of the Calculus and The Infinite Ascent offers an enlightening and enthralling tour of the basics of mathematics, and reveals a world of fascination in fundamental mathematical ideas. One, Two, Three is David Berlinski’s captivating exploration of the foundation of mathematics, its fundamental ideas, and why they matter. By unraveling the complex answers to these most elementary questions—What is a number? How do addition, subtraction, and other functions actually work? What are geometry and logic?—Berlinski reveals the intricacy behind their seemingly simple exteriors. Peppered with enlightening historical anecdotes and asides on some of history’s most fascinating mathematicians, One, Two, Three, revels in the beauty of numbers as Berlinski shows us how and why these often slippery concepts are as essential to the field of mathematics as to who we are.
A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the "New York Times."
"[Acheson] introduces the fundamental ideas of calculus through the story of how the subject developed, from approximating π to imaginary numbers, and from Newton's falling apple to the vibrations of an electric guitar."--Back cover
This is the captivating story of mathematics' greatest ever idea: calculus. Without it, there would be no computers, no microwave ovens, no GPS, and no space travel. But before it gave modern man almost infinite powers, calculus was behind centuries of controversy, competition, and even death. Taking us on a thrilling journey through three millennia, professor Steven Strogatz charts the development of this seminal achievement from the days of Aristotle to today's million-dollar reward that awaits whoever cracks Reimann's hypothesis. Filled with idiosyncratic characters from Pythagoras to Euler, Infinite Powers is a compelling human drama that reveals the legacy of calculus on nearly every aspect of modern civilization, including science, politics, ethics, philosophy, and much besides.
This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.
A Tour Through Mathematical Logic provides a tour through the main branches of the foundations of mathematics. It contains chapters covering elementary logic, basic set theory, recursion theory, Gödel's (and others') incompleteness theorems, model theory, independence results in set theory, nonstandard analysis, and constructive mathematics. In addition, this monograph discusses several topics not normally found in books of this type, such as fuzzy logic, nonmonotonic logic, and complexity theory.
This unprecedented collection of 27,000 quotations is the most comprehensive and carefully researched of its kind, covering all fields of science and mathematics. With this vast compendium you can readily conceptualize and embrace the written images of scientists, laymen, politicians, novelists, playwrights, and poets about humankind's scientific achievements. Approximately 9000 high-quality entries have been added to this new edition to provide a rich selection of quotations for the student, the educator, and the scientist who would like to introduce a presentation with a relevant quotation that provides perspective and historical background on his subject. Gaither's Dictionary of Scientific Quotations, Second Edition, provides the finest reference source of science quotations for all audiences. The new edition adds greater depth to the number of quotations in the various thematic arrangements and also provides new thematic categories.