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Author: Maurits Cornelis Escher
Publisher:
Published: 1989-03-25
Total Pages: 164
ISBN-13:
DOWNLOAD EBOOK →This book provides a solid image of Escher as he saw himself--not as an 'artist' but as an artisan, a graphic artist with heart and soul, obsessed by contrasts and possessed by a unique creativity.
Author: Jennifer Brooks
Publisher: CRC Press
Published: 2016-11-30
Total Pages: 280
ISBN-13: 1498704522
DOWNLOAD EBOOK →Exploring the Infinite addresses the trend toward a combined transition course and introduction to analysis course. It guides the reader through the processes of abstraction and log- ical argumentation, to make the transition from student of mathematics to practitioner of mathematics. This requires more than knowledge of the definitions of mathematical structures, elementary logic, and standard proof techniques. The student focused on only these will develop little more than the ability to identify a number of proof templates and to apply them in predictable ways to standard problems. This book aims to do something more; it aims to help readers learn to explore mathematical situations, to make conjectures, and only then to apply methods of proof. Practitioners of mathematics must do all of these things. The chapters of this text are divided into two parts. Part I serves as an introduction to proof and abstract mathematics and aims to prepare the reader for advanced course work in all areas of mathematics. It thus includes all the standard material from a transition to proof" course. Part II constitutes an introduction to the basic concepts of analysis, including limits of sequences of real numbers and of functions, infinite series, the structure of the real line, and continuous functions. Features Two part text for the combined transition and analysis course New approach focuses on exploration and creative thought Emphasizes the limit and sequences Introduces programming skills to explore concepts in analysis Emphasis in on developing mathematical thought Exploration problems expand more traditional exercise sets
Author: Jennifer Kacmarcik Brooks
Publisher:
Published: 2017
Total Pages:
ISBN-13: 9781315371719
DOWNLOAD EBOOK →Author: Leonhard Euler
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 341
ISBN-13: 1461210216
DOWNLOAD EBOOK →From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..."
Author: Shaughan Lavine
Publisher: Harvard University Press
Published: 2009-06-30
Total Pages: 262
ISBN-13: 0674265335
DOWNLOAD EBOOK →An accessible history and philosophical commentary on our notion of infinity. How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge. Praise for Understanding the Infinite “Understanding the Infinite is a remarkable blend of mathematics, modern history, philosophy, and logic, laced with refreshing doses of common sense. It is a potted history of, and a philosophical commentary on, the modern notion of infinity as formalized in axiomatic set theory . . . An amazingly readable [book] given the difficult subject matter. Most of all, it is an eminently sensible book. Anyone who wants to explore the deep issues surrounding the concept of infinity . . . will get a great deal of pleasure from it.” —Ian Stewart, New Scientist “How, in a finite world, does one obtain any knowledge about the infinite? Lavine argues that intuitions about the infinite derive from facts about the finite mathematics of indefinitely large size . . . The issues are delicate, but the writing is crisp and exciting, the arguments original. This book should interest readers whether philosophically, historically, or mathematically inclined, and large parts are within the grasp of the general reader. Highly recommended.” —D. V. Feldman, Choice
Author: Maria Coffey
Publisher: Penguin
Published: 2008-05-29
Total Pages: 308
ISBN-13: 1440631506
DOWNLOAD EBOOK →Real-life psychic, near-death, and paranormal experiences are combined with cutting-edge science and vivid adventure stories in this energetic look at why extreme athletes and mountaineers take the risks that allow them to push the limits of consciousness, and what they encounter there. In the life-or-death world of extreme adventure sports, there is one thing that athletes often keep quiet about: the “forbidden” territory of paranormal experiences. Ranging from fleeting moments of transcendence to full-blown encounters with ghosts and everything in between—visions, near-death experiences, psychic communication—many extreme athletes have experienced these moments of connection with the beyond, but have been reluctant to talk about them. In Explorers of the Infinite, award-winning outdoors journalist and lifelong adventure sports devotee Maria Coffey probes the mystical and paranormal experiences of mountaineers, snowboarders, surfers, and more. She reviews cutting-edge science, and consults the history of philosophy and spirituality to answer the question: Could the state of intense “aliveness” that is the allure of extreme sports for so many actually be a route to a connection with the beyond? Coffey investigates the scientific explanations for mystical phenomena, ranging from simple explanations to theories from consciousness studies and quantum physics, and leaves us wondering where science ends and spirituality begins. An energetic, you-are-there look at the spiritual lives of extreme athletes, Explorers of the Infinite asks why extreme athletes take the risks that allow them to push the limits of consciousness, what they encounter there, and what we can learn from them.
Author: James Carse
Publisher: Simon and Schuster
Published: 2011-10-11
Total Pages: 256
ISBN-13: 1451657293
DOWNLOAD EBOOK →“There are at least two kinds of games,” states James Carse as he begins this extraordinary book. “One could be called finite; the other infinite.” Finite games are the familiar contests of everyday life; they are played in order to be won, which is when they end. But infinite games are more mysterious. Their object is not winning, but ensuring the continuation of play. The rules may change, the boundaries may change, even the participants may change—as long as the game is never allowed to come to an end. What are infinite games? How do they affect the ways we play our finite games? What are we doing when we play—finitely or infinitely? And how can infinite games affect the ways in which we live our lives? Carse explores these questions with stunning elegance, teasing out of his distinctions a universe of observation and insight, noting where and why and how we play, finitely and infinitely. He surveys our world—from the finite games of the playing field and playing board to the infinite games found in culture and religion—leaving all we think we know illuminated and transformed. Along the way, Carse finds new ways of understanding everything from how an actress portrays a role, to how we engage in sex, from the nature of evil, to the nature of science. Finite games, he shows, may offer wealth and status, power and glory. But infinite games offer something far more subtle and far grander. Carse has written a book rich in insight and aphorism. Already an international literary event, Finite and Infinite Games is certain to be argued about and celebrated for years to come. Reading it is the first step in learning to play the infinite game.
Author: Robert Kaplan
Publisher: Bloomsbury Publishing USA
Published: 2014-02-04
Total Pages: 417
ISBN-13: 1608198693
DOWNLOAD EBOOK →Traces the development of mathematical thinking and describes the characteristics of the "republic of numbers" in terms of humankind's fascination with, and growing knowledge of, infinity.
Author: David Deutsch
Publisher: Penguin UK
Published: 2011-03-31
Total Pages: 571
ISBN-13: 0141969695
DOWNLOAD EBOOK →'Science has never had an advocate quite like David Deutsch ... A computational physicist on a par with his touchstones Alan Turing and Richard Feynman, and a philosopher in the line of his greatest hero, Karl Popper. His arguments are so clear that to read him is to experience the thrill of the highest level of discourse available on this planet and to understand it' Peter Forbes, Independent In our search for truth, how far have we advanced? This uniquely human quest for good explanations has driven amazing improvements in everything from scientific understanding and technology to politics, moral values and human welfare. But will progress end, either in catastrophe or completion - or will it continue infinitely? In this profound and seminal book, David Deutsch explores the furthest reaches of our current understanding, taking in the Infinity Hotel, supernovae and the nature of optimism, to instill in all of us a wonder at what we have achieved - and the fact that this is only the beginning of humanity's infinite possibility. 'This is Deutsch at his most ambitious, seeking to understand the implications of our scientific explanations of the world ... I enthusiastically recommend this rich, wide-ranging and elegantly written exposition of the unique insights of one of our most original intellectuals' Michael Berry, Times Higher Education Supplement 'Bold ... profound ... provocative and persuasive' Economist 'David Deutsch may well go down in history as one of the great scientists of our age' Scotsman
Author: Jennifer Kacmarcik Brooks
Publisher: Chapman & Hall/CRC
Published: 2017
Total Pages: 0
ISBN-13: 9781498704496
DOWNLOAD EBOOK →This is a textbook for an introductory course in analysis, combining topics from a transition course. At some schools, a transition course is combined over one or two semesters to introduce topics from real analysis. This allows students a more gradual approach to the difficult topics of analysis. Beginning with logic and sets, this text gradually raises the sophistication level of students coming out of calculus and proceeds into analysis topics.
