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Author: Yongju Bae Publisher: World Scientific ISBN: 9811292779 Category : Mathematics Languages : en Pages : 456
Book Description
This book studies dihedral groups, dicyclic groups, other finite subgroups of the 3-dimensional sphere, and the 2-fold extensions of the symmetric group on 4 letters from the point of view of decorated string diagrams of permutations. These are our metaphorical quipu. As you might expect, the book is replete with illustrations. In (almost) all cases, explicit diagrams for the elements of the group are given. The exception is the binary icosahedral group in which only the generators and relations are exhibited.
Author: Yongju Bae Publisher: World Scientific ISBN: 9811292779 Category : Mathematics Languages : en Pages : 456
Book Description
This book studies dihedral groups, dicyclic groups, other finite subgroups of the 3-dimensional sphere, and the 2-fold extensions of the symmetric group on 4 letters from the point of view of decorated string diagrams of permutations. These are our metaphorical quipu. As you might expect, the book is replete with illustrations. In (almost) all cases, explicit diagrams for the elements of the group are given. The exception is the binary icosahedral group in which only the generators and relations are exhibited.
Author: Dong-eog Kim Publisher: World Scientific ISBN: 9811209383 Category : Medical Languages : en Pages : 195
Book Description
The book provides updated knowledge on cerebrovascular imaging-related anatomy and topographic maps for neurologists, neurosurgeons, neuroradiologists, and neurovascular researchers as well as medical or neuroscience students. It includes not only high-resolution cerebrovascular images but also topographic brain maps.The topographic brain maps will provide (a) 'recently-updated' knowledge on cerebrovascular territories, which are of key clinical importance in patients with stroke; (b) age-specific WMH maps that allows a 'tailored patient-specific' interpretation in stroke- and vascular dementia-related clinical practice; and (c) easy-to-use 'reference maps' that allow prompt and reliable visual estimation of cerebral infarct volumes. This pocket book will serve as the best format for these image datasets to be looked up and referenced by the vast majority of readers.Apart from being a handy reference for neurovascular or neuroscience researchers, this book can also be used as a supplementary text book in medical schools.
Author: David Lippman Publisher: ISBN: 9781479276530 Category : Electronic books Languages : en Pages : 0
Book Description
Math in Society is a survey of contemporary mathematical topics, appropriate for a college-level topics course for liberal arts major, or as a general quantitative reasoning course.This book is an open textbook; it can be read free online at http://www.opentextbookstore.com/mathinsociety/. Editable versions of the chapters are available as well.
Author: Roland Barthes Publisher: Macmillan ISBN: 0809071940 Category : Literary Collections Languages : en Pages : 296
Book Description
"This new edition of MYTHOLOGIES is the first complete, authoritative English version of the French classic, Roland Barthes's most emblematic work"--
Author: Nataša Jonoska Publisher: Springer Science & Business Media ISBN: 3642401937 Category : Computers Languages : en Pages : 522
Book Description
Theoretical tools and insights from discrete mathematics, theoretical computer science, and topology now play essential roles in our understanding of vital biomolecular processes. The related methods are now employed in various fields of mathematical biology as instruments to "zoom in" on processes at a molecular level. This book contains expository chapters on how contemporary models from discrete mathematics – in domains such as algebra, combinatorics, and graph and knot theories – can provide perspective on biomolecular problems ranging from data analysis, molecular and gene arrangements and structures, and knotted DNA embeddings via spatial graph models to the dynamics and kinetics of molecular interactions. The contributing authors are among the leading scientists in this field and the book is a reference for researchers in mathematics and theoretical computer science who are engaged with modeling molecular and biological phenomena using discrete methods. It may also serve as a guide and supplement for graduate courses in mathematical biology or bioinformatics, introducing nontraditional aspects of mathematical biology.
Author: R.K. Owens Publisher: ISBN: 9780648794790 Category : Electronic books Languages : en Pages : 372
Book Description
The mystery of the Pyramids has been solved! For thousands of years the Pyramids have been enshrouded in mystery and their purpose for being built has been an enigma. This book solves the mystery of the Pyramids and presents the mathematical discoveries in a clear and rational way. The connection between the mathematics of the Pyramids and the Crop Circles is revealed!Mathematician, R.K. Owens, presents compelling findings about the geometry behind the Pyramids. Using the Golden Ratio, Vesica Piscis and Pi, new and exciting discoveries are presented mapping the precise geometry behind the Pyramids of Giza, the conical structures of Guachimontones and the Sun and Moon Pyramids of Teotihuacan. The mathematics that appears in natural organic growth is the same mathematics that unifies the Pyramid complexes.R.K. Owens demonstrates the interconnections between the height, slopes and base of the Pyramids. He shows how the same measurements that appear in the Pyramids of Giza are also the same mathematics and ratios of sunflowers and natural organic growth. The mathematics of the layout of the Pyramid complexes is mapped out, demonstrating the reason for the three Pyramids being lined up in the way that they are. The reason that the third, smaller Pyramid is offset by a number of degrees is mathematically explained. The same mathematics and ratios that appear in the layout of the Pyramids of Giza also occurs in the structures of Guachimontones and the Sun and Moon Pyramids of Teotihuacan. This is demonstrated in this book with clear mathematics. Most compellingly, R.K. Owens decodes the mathematics of Crop Circles that feature the same mathematics as the layout of the Pyramids. This presents questions as to the origin of the Pyramids and our own sacred origins as a human race.
Author: Victor M. Buchstaber Publisher: American Mathematical Soc. ISBN: 147042214X Category : Mathematics Languages : en Pages : 534
Book Description
This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on moment-angle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and non-Kaehler complex geometry. A related categorical construction of moment-angle complexes and polyhedral products provides for a universal framework for many fundamental constructions of homotopical topology. The study of polyhedral products is now evolving into a separate subject of homotopy theory. A new perspective on torus actions has also contributed to the development of classical areas of algebraic topology, such as complex cobordism. This book includes many open problems and is addressed to experts interested in new ideas linking all the subjects involved, as well as to graduate students and young researchers ready to enter this beautiful new area.
Author: Jong Chul Ye Publisher: Springer Nature ISBN: 9811660468 Category : Mathematics Languages : en Pages : 338
Book Description
The focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective. Rather than describing deep learning as an implementation technique, as is usually the case in many existing deep learning books, here, deep learning is explained as an ultimate form of signal processing techniques that can be imagined. To support this claim, an overview of classical kernel machine learning approaches is presented, and their advantages and limitations are explained. Following a detailed explanation of the basic building blocks of deep neural networks from a biological and algorithmic point of view, the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and others are described. Here, too, the focus is on the fact that in these heuristic approaches, there is an important, beautiful geometric structure behind the intuition that enables a systematic understanding. A unified geometric analysis to understand the working mechanism of deep learning from high-dimensional geometry is offered. Then, different forms of generative models like GAN, VAE, normalizing flows, optimal transport, and so on are described from a unified geometric perspective, showing that they actually come from statistical distance-minimization problems. Because this book contains up-to-date information from both a practical and theoretical point of view, it can be used as an advanced deep learning textbook in universities or as a reference source for researchers interested in acquiring the latest deep learning algorithms and their underlying principles. In addition, the book has been prepared for a codeshare course for both engineering and mathematics students, thus much of the content is interdisciplinary and will appeal to students from both disciplines.
Author: Sarah Ann Wells Publisher: Northwestern University Press ISBN: 081013456X Category : Literary Criticism Languages : en Pages : 357
Book Description
Winner, LASA Best Book Published in 2017, Southern Cone Section, Humanities category Media Laboratories explores a pivotal time for South American literature of the 1930s and ’40s. Cinema, radio, and the typewriter, once seen as promising catalysts for new kinds of writing, began to be challenged by authors, workers, and the public. What happens when media no longer seem novel and potentially democratic but rather consolidated and dominant? Moving among authors from Brazil, Argentina, and Uruguay, and among the genres of fiction, the essay, popular journalism, and experimental little magazines, Sarah Ann Wells shows how writers on the periphery of global modernity were fashioning alternative approaches to these media. Analyzing authors such as Clarice Lispector, Jorge Luis Borges, and Felisberto Hernández, along with their lesser-known contemporaries, Media Laboratories casts a wide net: from spectators of Hollywood and Soviet montage films, to inventors of imaginary media, to proletarian typists who embodied the machine-human encounters of the period. The text navigates contemporary scholarly and popular debates about the relationship of literature to technological innovation, media archaeology, sound studies, populism, and global modernisms. Ultimately, Wells underscores a question that remains relevant: what possibilities emerge when the enthusiasm for new media has been replaced by anxiety over their potentially pernicious effects in a globalizing, yet vastly unequal, world?
Author: Louis H. Kauffman Publisher: Princeton University Press ISBN: 9780691084350 Category : Mathematics Languages : en Pages : 500
Book Description
On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory. This paves the way for later discussion of the recently discovered Jones and generalized polynomials. The central chapter, Chapter Six, is a miscellany of topics and recreations. Here the reader will find the quaternions and the belt trick, a devilish rope trick, Alhambra mosaics, Fibonacci trees, the topology of DNA, and the author's geometric interpretation of the generalized Jones Polynomial. Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized polynomials.
Author: Yongju Bae
Author: Yongju Bae
Author: Dong-eog Kim
Author: David Lippman
Author: Roland Barthes
Author: Nataša Jonoska
Author: R.K. Owens
Author: Victor M. Buchstaber
Author: Jong Chul Ye
Author: Sarah Ann Wells
Author: Louis H. Kauffman