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Author: Vladimir I. Arnold Publisher: Springer Science & Business Media ISBN: 9783540206149 Category : Mathematics Languages : en Pages : 664
Book Description
Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research
Author: Vladimir I. Arnold Publisher: Springer Science & Business Media ISBN: 9783540206149 Category : Mathematics Languages : en Pages : 664
Book Description
Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research
Author: V. I. Arnold Publisher: American Mathematical Soc. ISBN: 147042259X Category : Education Languages : en Pages : 176
Book Description
Vladimir Arnold (1937-2010) was one of the great mathematical minds of the late 20th century. He did significant work in many areas of the field. On another level, he was keeping with a strong tradition in Russian mathematics to write for and to directly teach younger students interested in mathematics. This book contains some examples of Arnold's contributions to the genre. "Continued Fractions" takes a common enrichment topic in high school math and pulls it in directions that only a master of mathematics could envision. "Euler Groups" treats a similar enrichment topic, but it is rarely treated with the depth and imagination lavished on it in Arnold's text. He sets it in a mathematical context, bringing to bear numerous tools of the trade and expanding the topic way beyond its usual treatment. In "Complex Numbers" the context is physics, yet Arnold artfully extracts the mathematical aspects of the discussion in a way that students can understand long before they master the field of quantum mechanics. "Problems for Children 5 to 15 Years Old" must be read as a collection of the author's favorite intellectual morsels. Many are not original, but all are worth thinking about, and each requires the solver to think out of his or her box. Dmitry Fuchs, a long-term friend and collaborator of Arnold, provided solutions to some of the problems. Readers are of course invited to select their own favorites and construct their own favorite solutions. In reading these essays, one has the sensation of walking along a path that is found to ascend a mountain peak and then being shown a vista whose existence one could never suspect from the ground. Arnold's style of exposition is unforgiving. The reader--even a professional mathematician--will find paragraphs that require hours of thought to unscramble, and he or she must have patience with the ellipses of thought and the leaps of reason. These are all part of Arnold's intent. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Author: V.B. Alekseev Publisher: Springer Science & Business Media ISBN: 1402021879 Category : Mathematics Languages : en Pages : 278
Book Description
Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals. A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable. This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii. As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.
Author: V.I. Arnol'd Publisher: Springer Science & Business Media ISBN: 1475720637 Category : Mathematics Languages : en Pages : 530
Book Description
This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Author: Vladimir I. Arnold Publisher: Springer Science & Business Media ISBN: 3662054418 Category : Mathematics Languages : en Pages : 168
Book Description
Choice Outstanding Title! (January 2006) This richly illustrated text covers the Cauchy and Neumann problems for the classical linear equations of mathematical physics. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging! What makes the book unique is Arnold's particular talent at holding a topic up for examination from a new and fresh perspective. He likes to blow away the fog of generality that obscures so much mathematical writing and reveal the essentially simple intuitive ideas underlying the subject. No other mathematical writer does this quite so well as Arnold.
Author: I. G. Petrovsky Publisher: Courier Corporation ISBN: 0486155080 Category : Mathematics Languages : en Pages : 261
Book Description
Graduate-level exposition by noted Russian mathematician offers rigorous, readable coverage of classification of equations, hyperbolic equations, elliptic equations, and parabolic equations. Translated from the Russian by A. Shenitzer.
Author: Katie Arnold Publisher: Random House Trade Paperbacks ISBN: 0425284670 Category : Biography & Autobiography Languages : en Pages : 402
Book Description
In the tradition of Wild and H Is for Hawk, an Outside magazine writer tells her story—of fathers and daughters, grief and renewal, adventure and obsession, and the power of running to change your life. NAMED ONE OF THE BEST BOOKS OF THE YEAR BY REAL SIMPLE I’m running to forget, and to remember. For more than a decade, Katie Arnold chased adventure around the world, reporting on extreme athletes who performed outlandish feats—walking high lines a thousand feet off the ground without a harness, or running one hundred miles through the night. She wrote her stories by living them, until eventually life on the thin edge of risk began to seem normal. After she married, Katie and her husband vowed to raise their daughters to be adventurous, too, in the mountains and canyons of New Mexico. But when her father died of cancer, she was forced to confront her own mortality. His death was cataclysmic, unleashing a perfect storm of grief and anxiety. She and her father, an enigmatic photographer for National Geographic, had always been kindred spirits. He introduced her to the outdoors and took her camping and on bicycle trips and down rivers, and taught her to find solace and courage in the natural world. And it was he who encouraged her to run her first race when she was seven years old. Now nearly paralyzed by fear and terrified she was dying, too, she turned to the thing that had always made her feel most alive: running. Over the course of three tumultuous years, she ran alone through the wilderness, logging longer and longer distances, first a 50-kilometer ultramarathon, then 50 miles, then 100 kilometers. She ran to heal her grief, to outpace her worry that she wouldn’t live to raise her own daughters. She ran to find strength in her weakness. She ran to remember and to forget. She ran to live. Ultrarunning tests the limits of human endurance over seemingly inhuman distances, and as she clocked miles across mesas and mountains, Katie learned to tolerate pain and discomfort, and face her fears of uncertainty, vulnerability, and even death itself. As she ran, she found herself peeling back the layers of her relationship with her father, discovering that much of what she thought she knew about him, and her own past, was wrong. Running Home is a memoir about the stories we tell ourselves to make sense of our world—the stories that hold us back, and the ones that set us free. Mesmerizing, transcendent, and deeply exhilarating, it is a book for anyone who has been knocked over by life, or feels the pull of something bigger and wilder within themselves. “A beautiful work of searching remembrance and searing honesty . . . Katie Arnold is as gifted on the page as she is on the trail. Running Home will soon join such classics as Born to Run and Ultramarathon Man as quintessential reading of the genre.”—Hampton Sides, author of On Desperate Ground and Ghost Soldiers
Author: Vadim Kaloshin Publisher: Princeton University Press ISBN: 0691202524 Category : Mathematics Languages : en Pages : 218
Book Description
The first complete proof of Arnold diffusion—one of the most important problems in dynamical systems and mathematical physics Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. Kaloshin and Zhang follow Mather's strategy but emphasize a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, this book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.
Author: Vladimir I. Arnold
Author: Vladimir I. Arnold
Author: V. I. Arnold
Author: V.B. Alekseev
Author: V.I. Arnol'd
Author: Vladimir I. Arnold
Author: Vladimir Igorevich Arnolʹd
Author: I. G. Petrovsky
Author: Katie Arnold
Author: Vadim Kaloshin
Author: Arnold Rivkin