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Experiments In Topology
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Book Synopsis Experiments in Topology by : Stephen Barr
Download or read book Experiments in Topology written by Stephen Barr and published by Courier Corporation. This book was released on 2012-12-04 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.
Book Synopsis Experiments in Topology by : Stephen Barr
Download or read book Experiments in Topology written by Stephen Barr and published by Courier Corporation. This book was released on 1989-01-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A mathematician named Klein Thought the Moebius band was divine. Said he: 'If you glue The edges of two, You'll get a weird bottle like mine.' " — Stephen Barr In this lively book, the classic in its field, a master of recreational topology invites readers to venture into such tantalizing topological realms as continuity and connectedness via the Klein bottle and the Moebius strip. Beginning with a definition of topology and a discussion of Euler's theorem, Mr. Barr brings wit and clarity to these topics: New Surfaces (Orientability, Dimension, The Klein Bottle, etc.) The Shortest Moebius Strip The Conical Moebius Strip The Klein Bottle The Projective Plane (Symmetry) Map Coloring Networks (Koenigsberg Bridges, Betti Numbers, Knots) The Trial of the Punctured Torus Continuity and Discreteness ("Next Number," Continuity, Neighborhoods, Limit Points) Sets (Valid or Merely True? Venn Diagrams, Open and Closed Sets, Transformations, Mapping, Homotopy) With this book and a square sheet of paper, the reader can make paper Klein bottles, step by step; then, by intersecting or cutting the bottle, make Moebius strips. Conical Moebius strips, projective planes, the principle of map coloring, the classic problem of the Koenigsberg bridges, and many more aspects of topology are carefully and concisely illuminated by the author's informal and entertaining approach. Now in this inexpensive paperback edition, Experiments in Topology belongs in the library of any math enthusiast with a taste for brainteasing adventures
Book Synopsis Experimental Mathematics by : V. I. Arnold
Download or read book Experimental Mathematics written by V. I. Arnold and published by American Mathematical Soc.. This book was released on 2015-07-14 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. 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. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).
Book Synopsis Topological Phases of Matter by : Roderich Moessner
Download or read book Topological Phases of Matter written by Roderich Moessner and published by Cambridge University Press. This book was released on 2021-04-29 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important graduate level text unites the physical mechanisms behind the phenomena of topological matter within a theoretical framework.
Book Synopsis Topology for Computing by : Afra J. Zomorodian
Download or read book Topology for Computing written by Afra J. Zomorodian and published by Cambridge University Press. This book was released on 2005-01-10 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.
Book Synopsis Computational Topology for Data Analysis by : Tamal Krishna Dey
Download or read book Computational Topology for Data Analysis written by Tamal Krishna Dey and published by Cambridge University Press. This book was released on 2022-03-10 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
Book Synopsis Entertaining Science Experiments with Everyday Objects by : Martin Gardner
Download or read book Entertaining Science Experiments with Everyday Objects written by Martin Gardner and published by Courier Corporation. This book was released on 2013-06-10 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: A prominent popular science writer presents simple instructions for 100 illustrated experiments. Memorable, easily understood experiments illuminate principles related to astronomy, chemistry, physiology, psychology, mathematics, topology, probability, acoustics, other areas.
Book Synopsis Computational Topology by : Herbert Edelsbrunner
Download or read book Computational Topology written by Herbert Edelsbrunner and published by American Mathematical Society. This book was released on 2022-01-31 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.
Book Synopsis Rick Brant's Science Projects by : John Blaine
Download or read book Rick Brant's Science Projects written by John Blaine and published by Applewood Books. This book was released on 2005-12 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: A non-fiction companion volume to the popular Rick Brant Science-Adventure Series. This reprint of a very hard-to-find title includes easy-to-read chapters about codes and ciphers, slingshots and archery, microscopes and radios, tricks and games, and scientific experiments and how to plan a science project. Please Note: These experiments have not been written with the modern reader in mind. Some may be dangerous and should not be undertaken. The Rick Brant series was written pseudonymously under the name John Blaine from 1946-1968 . Many millions of the books were sold. Rick Brant was a high school boy who lived on an island off the coast of New Jersey. His father was a world-famous scientist. Rick's best friend was Donald "Scotty" Scott and together they have adventures all over the globe usually involving a secret science project of some kind. Originally published in 1960.
Book Synopsis Topology Control in Wireless Sensor Networks by : Miguel A. Labrador
Download or read book Topology Control in Wireless Sensor Networks written by Miguel A. Labrador and published by Springer Science & Business Media. This book was released on 2009-02-27 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The eld of wireless sensor networks continues to evolve and grow in both practical and research domains. More and more wireless sensor networks are being used to gather information in real life applications. It is common to see how this technology is being applied in irrigation systems, intelligent buildings, bridges, security mec- nisms,militaryoperations,transportation-relatedapplications,etc.Atthesametime, new developments in hardware, software, and communication technologies are - panding these possibilities. As in any other technology, research brings new dev- opments and re nements and continuous improvements of current approaches that push the technology even further. Looking toward the future, the technology seems even more promising in two directions. First, a few years from now more powerful wireless sensor devices will be available, and wireless sensor networks will have applicability in an endless number of scenarios, as they will be able to handle traf c loads not possible today, make more computations, store more data, and live longer because of better energy sources. Second,a few years from now, the opposite scenario might also be possible. The availability of very constrained, nanotechnology-made wireless sensor devices will bring a whole new world of applications, as they will be able to operate in - vironments and places unimaginable today. These two scenarios, at the same time, will both bring new research challenges that are always welcome to researchers.
Book Synopsis Advanced Topological Insulators by : Huixia Luo
Download or read book Advanced Topological Insulators written by Huixia Luo and published by John Wiley & Sons. This book was released on 2019-03-12 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for researchers and graduate students preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with the fundamental description on the topological phases of matter such as one, two- and three-dimensional topological insulators, and methods and tools for topological material's investigations, topological insulators for advanced optoelectronic devices, topological superconductors, saturable absorber and in plasmonic devices. Advanced Topological Insulators provides researchers and graduate students with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.
Book Synopsis Principles of Topological Psychology by : Kurt Lewin
Download or read book Principles of Topological Psychology written by Kurt Lewin and published by Read Books Ltd. This book was released on 2013-04-16 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This antiquarian text contains a comprehensive treatise on topological psychology, being a detailed exposition of its principles written by Kurt Lewin. Written in clear, plain language and full of information fundamental to understanding this branch of psychology, this text will be of considerable utility to the student, and it would make for a great addition to collections of allied literature. The chapters of this book include: 'The Present State of Psychology', 'Formulation of Laws and Representations of General Situations', 'Considerations About Representing Life Space', 'Context and Extent of the Psychological Life Space', 'Causal Interconnections in Psychology', etcetera. We are republishing this vintage book now complete with a specially commissioned new biography of the author.
Book Synopsis Calculating the Secrets of Life by : National Research Council
Download or read book Calculating the Secrets of Life written by National Research Council and published by National Academies Press. This book was released on 1995-04-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: As researchers have pursued biology's secrets to the molecular level, mathematical and computer sciences have played an increasingly important roleâ€"in genome mapping, population genetics, and even the controversial search for "Eve," hypothetical mother of the human race. In this first-ever survey of the partnership between the two fields, leading experts look at how mathematical research and methods have made possible important discoveries in biology. The volume explores how differential geometry, topology, and differential mechanics have allowed researchers to "wind" and "unwind" DNA's double helix to understand the phenomenon of supercoiling. It explains how mathematical tools are revealing the workings of enzymes and proteins. And it describes how mathematicians are detecting echoes from the origin of life by applying stochastic and statistical theory to the study of DNA sequences. This informative and motivational book will be of interest to researchers, research administrators, and educators and students in mathematics, computer sciences, and biology.
Book Synopsis Electrons in Solids by : Hendrik Bluhm
Download or read book Electrons in Solids written by Hendrik Bluhm and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-04-01 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a continuation of classical condensed matter physics texts, this graduate textbook introduces advanced topics of correlated electron systems, mesoscopic transport,quantum computing, optical excitations and topological insulators. The book is focusing on an intuitive understanding of the basic concepts of these rather complex subjects.
Book Synopsis Topological Aspects of the Dynamics of Fluids and Plasmas by : H.K. Moffatt
Download or read book Topological Aspects of the Dynamics of Fluids and Plasmas written by H.K. Moffatt and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers arising out of the program of the Institute for Theoretical Physics (ITP) of the University of California at Santa Bar bara, August-December 1991, on the subject "Topological Fluid Dynamics". The first group of papers cover the lectures on Knot Theory, Relaxation un der Topological Constraints, Kinematics of Stretching, and Fast Dynamo Theory presented at the initial Pedagogical Workshop of the program. The remaining papers were presented at the subsequent NATO Advanced Re search Workshop or were written during the course of the program. We wish to acknowledge the support of the NATO Science Committee in making this workshop possible. The scope of "Topological Fluid Dynamics" was defined by an earlier Symposium of the International Union of Theoretical and Applied Mechan ics (IUTAM) held in Cambridge, England in August, 1989, the Proceedings of which were published (Eds. H.K. Moffatt and A. Tsinober) by Cambridge University Press in 1990. The proposal to hold an ITP program on this sub ject emerged from that Symposium, and we are grateful to John Greene and Charlie Kennel at whose encouragement the original proposal was formu lated. Topological fluid dynamics covers a range of problems, particularly those involving vortex tubes and/or magnetic flux tubes in nearly ideal fluids, for which topological structures can be identified and to some extent quantified.
Book Synopsis Performability in Internet of Things by : Fadi Al-Turjman
Download or read book Performability in Internet of Things written by Fadi Al-Turjman and published by Springer. This book was released on 2018-08-22 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the challenges in the convergence of technologies as the Internet of Things (IoT) evolves. These include sensing, computing, information processing, networking, and controlling intelligent technologies. The contributors first provide a survey of various assessment and evaluation approaches available for successful convergence. They then go on to cover several operational ideas to apply. The contributors then discuss the challenges involved bridging gaps in computation and the communication process, hidden networks, intelligent decision making, human-to-machine perception and large-scale IoT environments. The contributors aim to provide the reader an overview of trends in IoT in terms of performability and traffic modeling and efforts that can be spent in assessing the graceful degradation in IoT paradigms. Provides a survey of IoT assessment and evaluation approaches; Covers new and innovative operational ideas that apply to the IoT industry and the industries it affects; Includes chapters from researchers and industry leaders in IoT from around the world.
Download or read book Topologies of Power written by John Allen and published by Routledge. This book was released on 2016-01-13 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topologies of Power amounts to a radical departure in the way that power and space have been understood. It calls into question the very idea that power is simply extended across a given territory or network, and argues that power today has a new found ‘reach’. Topological shifts have subtly altered the reach of power, enabling governments, corporations and NGOs alike to register their presence through quieter, less brash forms of power than domination or overt control. In a world in which proximity and distance increasingly play across one another, topology offers an insight into how power remains continuous under transformation: the same but different in its ability to shape peoples’ lives. Drawing upon a range of political, economic and cultural illustrations, the book sets out a clear and accessible account of the topological workings of power in the contemporary moment. It will be invaluable for both students and academics in human geography, politics, sociology, and cultural studies.
