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Author: Roger Penrose Publisher: Vintage ISBN: 0307596745 Category : Science Languages : en Pages : 307
Book Description
From Nobel prize-winner Roger Penrose, this groundbreaking book is for anyone "who is interested in the world, how it works, and how it got here" (New York Journal of Books). Penrose presents a new perspective on three of cosmology’s essential questions: What came before the Big Bang? What is the source of order in our universe? And what cosmic future awaits us? He shows how the expected fate of our ever-accelerating and expanding universe—heat death or ultimate entropy—can actually be reinterpreted as the conditions that will begin a new “Big Bang.” He details the basic principles beneath our universe, explaining various standard and non-standard cosmological models, the fundamental role of the cosmic microwave background, the paramount significance of black holes, and other basic building blocks of contemporary physics. Intellectually thrilling and widely accessible, Cycles of Time is a welcome new contribution to our understanding of the universe from one of our greatest mathematicians and thinkers.
Author: Stephen J. Puetz Publisher: ISBN: 9781432781330 Category : Science Languages : en Pages : 626
Book Description
These simple statements hold huge implications about how the universe must operate if it was truly infinite rather than finite, as is commonly thought. In one sense, this book, Universal Cycle Theory, may seem radical because it postulates that the universe operates in ways that are dramatically different from what we are taught. Yet, this new theory is conventional in the sense that it closely conforms to virtually all existing laws, equations, and observations. There are only two elements that make the Universal Cycle Theory radical cycles and infinity. Other than that, much of what you read in this book will seem familiar and conventional. Cycles are crucial because they are reflections of how matter behaves in an infinite universe: as vortices and waves. A vortex forms when matter rotates, producing circular cycles. A wave forms when colliding matter compresses and decompresses, producing linear cycles. Infinity is crucial because it explains the extent and structure of the universe. We assume that matter is infinitely divisible in the microscopic direction and infinitely integrable in the macroscopic direction. We assume that time was infinite in the past and will be infinite in the future. This concept of infinity is unique, having never been employed in a model of the universe before. It resolves many of the paradoxes and contradictions currently riddling physics and cosmology.
Author: Franz G. Riffert Publisher: Cambridge Scholars Press ISBN: 1904303579 Category : Education Languages : en Pages : 444
Book Description
"In this book a selection of 15 papers explores Whitehead's educational ideas which are based on his radical process approach. Following the Introduction which presents Whitehead's criticism of traditional education and the false psychology which it is based on, the book is divided into two major parts. The first part deals with Whitehead's philosophically inspired alternative theoretical framework for learning and education. Special focus is layed on the concept of the learning process which according to Whitehead is essentially cyclic in nature. In the second part it is shown how Whitehead's ideas can profitably be applied to different sub-domains within education: management education, college education and evaluation."--http://www.cambridgescholarspress.com.
Author: Arnaldo Garcia Publisher: Springer Science & Business Media ISBN: 1402053347 Category : Mathematics Languages : en Pages : 212
Book Description
The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory. This book presents survey articles on some of these new developments. The topics focus on material which has not yet been presented in other books or survey articles.
Author: Mirna Džamonja Publisher: Cambridge University Press ISBN: 1108351964 Category : Mathematics Languages : en Pages : 163
Book Description
This quick yet detailed introduction to set theory and forcing builds the reader's intuition about it as much as the mathematical detail. Intuition, rather absent from the existing literature on the subject, here plays a large role. The reader will not only learn the facts, but will understand why they are true and will be brought to ask: what else could be true? Having presented forcing in Part I, the second part of the book discusses contemporary issues in the theory of forcing. It includes known and some previously unpublished results as well as many open questions. This is ideal for those who want to start a research career in forcing but do not have a personal interlocutor. Obviously, not everything about forcing is in this book. Many references are included to help the reader further explore the vast amount of research literature available on the subject.
Author: Patrick Dehornoy Publisher: Cambridge University Press ISBN: 1108922880 Category : Mathematics Languages : en Pages : 260
Book Description
Everyone knows what braids are, whether they be made of hair, knitting wool, or electrical cables. However, it is not so evident that we can construct a theory about them, i.e. to elaborate a coherent and mathematically interesting corpus of results concerning them. This book demonstrates that there is a resoundingly positive response to this question: braids are fascinating objects, with a variety of rich mathematical properties and potential applications. A special emphasis is placed on the algorithmic aspects and on what can be called the 'calculus of braids', in particular the problem of isotopy. Prerequisites are kept to a minimum, with most results being established from scratch. An appendix at the end of each chapter gives a detailed introduction to the more advanced notions required, including monoids and group presentations. Also included is a range of carefully selected exercises to help the reader test their knowledge, with solutions available.
Author: Antonio Giorgilli Publisher: Cambridge University Press ISBN: 100917486X Category : Science Languages : en Pages : 474
Book Description
Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov–Arnold–Moser theorem, Nekhoroshev's theorem and superexponential stability. Its analytic approach allows students to learn about perturbation methods leading to advanced results. Key topics covered include Liouville's theorem, the proof of Poincaré's non-integrability theorem and the nonlinear dynamics in the neighbourhood of equilibria. The theorem of Kolmogorov on persistence of invariant tori and the theory of exponential stability of Nekhoroshev are proved via constructive algorithms based on the Lie series method. A final chapter is devoted to the discovery of chaos by Poincaré and its relations with integrability, also including recent results on superexponential stability. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students.
Author: Daniel G. Quillen
Author: Daniel G. Quillen
Author: Roger Penrose
Author: Stephen J. Puetz
Author: Caterina Consani
Author: Franz G. Riffert
Author: Arnaldo Garcia
Author: Raf Bocklandt
Author: Mirna Džamonja
Author: Patrick Dehornoy
Author: Antonio Giorgilli