Exploring The Infinite
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| Author | : Jennifer Brooks |
| Publisher | : CRC Press |
| Total Pages | : 226 |
| Release | : 2016-11-30 |
| Genre | : Mathematics |
| ISBN | : 1498704522 |
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 | : Maurits Cornelis Escher |
| Publisher | : |
| Total Pages | : 164 |
| Release | : 1989-03-25 |
| Genre | : Art |
| ISBN | : |
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 | : Shaughan Lavine |
| Publisher | : Harvard University Press |
| Total Pages | : 386 |
| Release | : 1998-01-13 |
| Genre | : Philosophy |
| ISBN | : 0674039998 |
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.
| Author | : Mike Dooley |
| Publisher | : Simon and Schuster |
| Total Pages | : 308 |
| Release | : 2009-09-08 |
| Genre | : Body, Mind & Spirit |
| ISBN | : 1439121478 |
Infinite Possibilities is the masterwork from teacher, author, and featured speaker Mike Dooley. As the next step beyond his immensely popular Notes from the Universe trilogy, and his follow up, Choose them Wisely, this book contains even more enriching wisdom for living an abundant, joyous life. Mike Dooley knows that we create our own reality, our own fate, and our own luck. We’re beings filled with infinite possibility—just ready to explore how powerful we truly are. Manifesting the magnificence of our dreams isn’t about hard work, but rather about belief and expectation. These principles transcend belief, realizing the truth about our human nature. Your dreams are not accidental, nor inconsequential. And if someone were tell the truth about life, reality, and the powers we all possessed, would it be recognized? Our lives are full of adventures—and not exactly the sky-diving, mountain-climbing variety—but something better. Readers will laugh, applaud, and be inspired by Mike Dooley’s wit and wisdom.
| Author | : Maria Coffey |
| Publisher | : Penguin |
| Total Pages | : 308 |
| Release | : 2008-05-29 |
| Genre | : Sports & Recreation |
| ISBN | : 1440631506 |
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 | : Richard Evan Schwartz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 178 |
| Release | : 2018 |
| Genre | : Juvenile Nonfiction |
| ISBN | : 1470447363 |
Mathematics professor from Brown University uses colorful illustrations and cartoons to display the concepts of infinity and large numbers.
| Author | : Geoffrey A. Moore |
| Publisher | : BenBella Books |
| Total Pages | : 233 |
| Release | : 2021-08-10 |
| Genre | : Philosophy |
| ISBN | : 1950665984 |
NAUTILUS BOOK AWARD GOLD MEDALIST — BODY, MIND, SPIRIT PRACTICES “Combining an extraordinary range of scholarship with an accessible and entertaining writing style, The Infinite Staircase . . . provides a coherent and unified platform for a full human life.” —Midwest Book Review In this bold new book, high-tech’s best-known strategist makes a seminal contribution to the search for meaning in a secular era. Two questions fundamental to human existence have always been the metaphysical “where do I fit in the grand scheme of things?” and the ethical “how should I behave?” Religion is no longer a source of answers for many people, and nothing has replaced it. Moore uses his signature framework-based approach to answer these questions, taking us on an intellectual roller coaster ride through physics, chemistry, biology, the social sciences and the humanities. Along the way, he builds a metaphorical ladder that leads from the big bang to the need for ethical action in our daily lives. Combining an extraordinary range of scholarship with an accessible and entertaining writing style, The Infinite Staircase: What the Universe Tells Us About Life, Ethics, and Mortality provides a coherent and unified platform for a full human life.
| Author | : Steven Strogatz |
| Publisher | : Mariner Books |
| Total Pages | : 389 |
| Release | : 2019 |
| Genre | : Biography & Autobiography |
| ISBN | : 1328879984 |
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.
| Author | : Jeremy Robinson |
| Publisher | : |
| Total Pages | : 398 |
| Release | : 2017-05-15 |
| Genre | : Fiction |
| ISBN | : 9781941539330 |
Robinson, the master of fast-paced stories blending horror, science fiction, and thrillers, tackles his most ambitious subject to date: reality itself. An amalgam of the works of J.J. Abrams and Ridley Scott, Infinite is a bold SF novel exploring the vastness of space and a man's desire to exist, find love, and alter the course of his life.
| Author | : Leonhard Euler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 341 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461210216 |
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..."
