Royal Road to Topology, A: Convergence of Filters PDF Download
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Author: Szymon Dolecki
Publisher: World Scientific Publishing Company
ISBN: 9789811232107
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathematical landscapes and you see more.The book is addressed both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to review it from a different perspective, which goes well beyond the traditional knowledge.Usual topics of classic courses of set-theoretic topology are treated at an early stage of the book -- from a viewpoint of convergence of filters, but in a rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of convergence theory.The mentioned virtues of the approach stem from the fact that the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory complements topology like the field of complex numbers algebraically completes the field of real numbers.Convergence theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal.
Author: Szymon Dolecki
Publisher: World Scientific Publishing Company
ISBN: 9789811232107
Category : Mathematics
Languages : en
Pages : 0
Get Book Here
Book Description
Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathematical landscapes and you see more.The book is addressed both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to review it from a different perspective, which goes well beyond the traditional knowledge.Usual topics of classic courses of set-theoretic topology are treated at an early stage of the book -- from a viewpoint of convergence of filters, but in a rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of convergence theory.The mentioned virtues of the approach stem from the fact that the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory complements topology like the field of complex numbers algebraically completes the field of real numbers.Convergence theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal.
Author: Szymon Dolecki
Publisher: World Scientific
ISBN: 9811232121
Category : Mathematics
Languages : en
Pages : 733
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Book Description
Topological spaces are a special case of convergence spaces. This textbook introduces topology within a broader context of convergence theory. The title alludes to advantages of the present approach, which is more gratifying than many traditional ones: you travel more comfortably through mathematical landscapes and you see more.The book is addressed both to those who wish to learn topology and to those who, being already knowledgeable about topology, are curious to review it from a different perspective, which goes well beyond the traditional knowledge.Usual topics of classic courses of set-theoretic topology are treated at an early stage of the book — from a viewpoint of convergence of filters, but in a rather elementary way. Later on, most of these facts reappear as simple consequences of more advanced aspects of convergence theory.The mentioned virtues of the approach stem from the fact that the class of convergences is closed under several natural, essential operations, under which the class of topologies is not! Accordingly, convergence theory complements topology like the field of complex numbers algebraically completes the field of real numbers.Convergence theory is intuitive and operational because of appropriate level of its abstraction, general enough to grasp the underlying laws, but not too much in order not to lose intuitive appeal.
Author: Steve Y. Oudot
Publisher: American Mathematical Soc.
ISBN: 1470434431
Category : Mathematics
Languages : en
Pages : 229
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Book Description
Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.
Author: Peter Watts
Publisher: Macmillan
ISBN: 1429955198
Category : Fiction
Languages : en
Pages : 388
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Book Description
Hugo and Shirley Jackson award-winning Peter Watts stands on the cutting edge of hard SF with his acclaimed novel, Blindsight Two months since the stars fell... Two months of silence, while a world held its breath. Now some half-derelict space probe, sparking fitfully past Neptune's orbit, hears a whisper from the edge of the solar system: a faint signal sweeping the cosmos like a lighthouse beam. Whatever's out there isn't talking to us. It's talking to some distant star, perhaps. Or perhaps to something closer, something en route. So who do you send to force introductions with unknown and unknowable alien intellect that doesn't wish to be met? You send a linguist with multiple personalities, her brain surgically partitioned into separate, sentient processing cores. You send a biologist so radically interfaced with machinery that he sees x-rays and tastes ultrasound. You send a pacifist warrior in the faint hope she won't be needed. You send a monster to command them all, an extinct hominid predator once called vampire, recalled from the grave with the voodoo of recombinant genetics and the blood of sociopaths. And you send a synthesist—an informational topologist with half his mind gone—as an interface between here and there. Pray they can be trusted with the fate of a world. They may be more alien than the thing they've been sent to find. At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.
Author: Avi Wigderson
Publisher: Princeton University Press
ISBN: 0691189137
Category : Computers
Languages : en
Pages : 434
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Book Description
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Author: John D. Joannopoulos
Publisher: Princeton University Press
ISBN: 1400828244
Category : Science
Languages : en
Pages : 305
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Book Description
Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications. Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory. They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism. Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written, Photonic Crystals is an indispensable resource for students and researchers. Extensively revised and expanded Features improved graphics throughout Includes new chapters on photonic-crystal fibers and combined index-and band-gap-guiding Provides an introduction to coupled-mode theory as a powerful tool for device design Covers many new topics, including omnidirectional reflection, anomalous refraction and diffraction, computational photonics, and much more.
Author: Bernhard Siegert
Publisher: Fordham Univ Press
ISBN: 0823263770
Category : Social Science
Languages : en
Pages : 287
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Book Description
In a crucial shift within posthumanistic media studies, Bernhard Siegert dissolves the concept of media into a network of operations that reproduce, displace, process, and reflect the distinctions fundamental for a given culture. Cultural Techniques aims to forget our traditional understanding of media so as to redefine the concept through something more fundamental than the empiricist study of a medium’s individual or collective uses or of its cultural semantics or aesthetics. Rather, Siegert seeks to relocate media and culture on a level where the distinctions between object and performance, matter and form, human and nonhuman, sign and channel, the symbolic and the real are still in the process of becoming. The result is to turn ontology into a domain of all that is meant in German by the word Kultur. Cultural techniques comprise not only self-referential symbolic practices like reading, writing, counting, or image-making. The analysis of artifacts as cultural techniques emphasizes their ontological status as “in-betweens,” shifting from firstorder to second-order techniques, from the technical to the artistic, from object to sign, from the natural to the cultural, from the operational to the representational. Cultural Techniques ranges from seafaring, drafting, and eating to the production of the sign-signaldistinction in old and new media, to the reproduction of anthropological difference, to the study of trompe-l’oeils, grids, registers, and doors. Throughout, Siegert addresses fundamental questions of how ontological distinctions can be replaced by chains of operations that process those alleged ontological distinctions within the ontic. Grounding posthumanist theory both historically and technically, this book opens up a crucial dialogue between new German media theory and American postcybernetic discourses.
Author: Thomas Metzinger
Publisher: ReadHowYouWant.com
ISBN: 1458759164
Category : Philosophy
Languages : en
Pages : 442
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Book Description
We're used to thinking about the self as an independent entity, something that we either have or are. In The Ego Tunnel, philosopher Thomas Metzinger claims otherwise: No such thing as a self exists. The conscious self is the content of a model created by our brain - an internal image, but one we cannot experience as an image. Everything we experience is ''a virtual self in a virtual reality.'' But if the self is not ''real,'' why and how did it evolve? How does the brain construct it? Do we still have souls, free will, personal autonomy, or moral accountability? In a time when the science of cognition is becoming as controversial as evolution, The Ego Tunnel provides a stunningly original take on the mystery of the mind.
Author: Alexander M. Wyglinski
Publisher: Artech House
ISBN: 1630814598
Category : Technology & Engineering
Languages : en
Pages : 375
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Book Description
Based on the popular Artech House classic, Digital Communication Systems Engineering with Software-Defined Radio, this book provides a practical approach to quickly learning the software-defined radio (SDR) concepts needed for work in the field. This up-to-date volume guides readers on how to quickly prototype wireless designs using SDR for real-world testing and experimentation. This book explores advanced wireless communication techniques such as OFDM, LTE, WLA, and hardware targeting. Readers will gain an understanding of the core concepts behind wireless hardware, such as the radio frequency front-end, analog-to-digital and digital-to-analog converters, as well as various processing technologies. Moreover, this volume includes chapters on timing estimation, matched filtering, frame synchronization message decoding, and source coding. The orthogonal frequency division multiplexing is explained and details about HDL code generation and deployment are provided. The book concludes with coverage of the WLAN toolbox with OFDM beacon reception and the LTE toolbox with downlink reception. Multiple case studies are provided throughout the book. Both MATLAB and Simulink source code are included to assist readers with their projects in the field.
Author: José L. Pons
Publisher: John Wiley & Sons
ISBN: 0470987650
Category : Technology & Engineering
Languages : en
Pages : 358
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Book Description
A wearable robot is a mechatronic system that is designed around the shape and function of the human body, with segments and joints corresponding to those of the person it is externally coupled with. Teleoperation and power amplification were the first applications, but after recent technological advances the range of application fields has widened. Increasing recognition from the scientific community means that this technology is now employed in telemanipulation, man-amplification, neuromotor control research and rehabilitation, and to assist with impaired human motor control. Logical in structure and original in its global orientation, this volume gives a full overview of wearable robotics, providing the reader with a complete understanding of the key applications and technologies suitable for its development. The main topics are demonstrated through two detailed case studies; one on a lower limb active orthosis for a human leg, and one on a wearable robot that suppresses upper limb tremor. These examples highlight the difficulties and potentialities in this area of technology, illustrating how design decisions should be made based on these. As well as discussing the cognitive interaction between human and robot, this comprehensive text also covers: the mechanics of the wearable robot and it’s biomechanical interaction with the user, including state-of-the-art technologies that enable sensory and motor interaction between human (biological) and wearable artificial (mechatronic) systems; the basis for bioinspiration and biomimetism, general rules for the development of biologically-inspired designs, and how these could serve recursively as biological models to explain biological systems; the study on the development of networks for wearable robotics. Wearable Robotics: Biomechatronic Exoskeletons will appeal to lecturers, senior undergraduate students, postgraduates and other researchers of medical, electrical and bio engineering who are interested in the area of assistive robotics. Active system developers in this sector of the engineering industry will also find it an informative and welcome resource.
