Diagrammatic Algebra

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Diagrammatic Algebra

J. Scott Carter,Seiichi Kamada
Diagrammatic Algebra Book PDF

Author : J. Scott Carter,Seiichi Kamada
Publisher : American Mathematical Society
Page : 365 pages
File Size : 45,9 Mb
Release : 2021-12-15
Category : Mathematics
ISBN : 9781470466718

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Diagrammatic Algebra by J. Scott Carter,Seiichi Kamada Pdf

This book is an introduction to techniques and results in diagrammatic algebra. It starts with abstract tensors and their categorifications, presents diagrammatic methods for studying Frobenius and Hopf algebras, and discusses their relations with topological quantum field theory and knot theory. The text is replete with figures, diagrams, and suggestive typography that allows the reader a glimpse into many higher dimensional processes. The penultimate chapter summarizes the previous material by demonstrating how to braid 3- and 4- dimensional manifolds into 5- and 6-dimensional spaces. The book is accessible to post-qualifier graduate students, and will also be of interest to algebraists, topologists and algebraic topologists who would like to incorporate diagrammatic techniques into their research.

An Excursion in Diagrammatic Algebra

J. Scott Carter
An Excursion in Diagrammatic Algebra Book PDF

Author : J. Scott Carter
Publisher : World Scientific
Page : 294 pages
File Size : 45,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814374507

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An Excursion in Diagrammatic Algebra by J. Scott Carter Pdf

1. A sphere -- 2. Surfaces, folds, and cusps -- 3. The inside and outside -- 4. Dimensions -- 5. Immersed surfaces -- 6. Movies -- 7. Movie moves -- 8. Taxonomic summary -- 9. How not to turn the sphere inside-out -- 10. A physical metaphor -- 11. Sarah's thesis -- 12. The eversion -- 13. The double point and fold surfaces

Algebraic and Diagrammatic Methods in Many-Fermion Theory

Frank E. Harris,Hendrik J. Monkhorst,David L. Freeman
Algebraic and Diagrammatic Methods in Many Fermion Theory Book PDF

Author : Frank E. Harris,Hendrik J. Monkhorst,David L. Freeman
Publisher : Courier Dover Publications
Page : 418 pages
File Size : 42,5 Mb
Release : 2020-01-15
Category : Science
ISBN : 9780486837215

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Algebraic and Diagrammatic Methods in Many-Fermion Theory by Frank E. Harris,Hendrik J. Monkhorst,David L. Freeman Pdf

This text on the use of electron correlation effects in the description of the electronic structure of atoms, molecules, and crystals is intended for graduate students in physical chemistry and physics. Modern theories of electronic structure and methods of incorporating electron correlation contributions are developed using a diagrammatic and algebraic formulation, and the methods developed in the text are illustrated with examples from molecular and solid state quantum mechanics. A brief Introduction is followed by chapters on operator algebra, the independent-particle model, occupation-number formalism, and diagrams. Additional topics include the configuration-interaction method, the many-body perturbation theory, and the coupled-cluster method.

Diagrammatic Immanence

Rocco Gangle
Diagrammatic Immanence Book PDF

Author : Rocco Gangle
Publisher : Edinburgh University Press
Page : 264 pages
File Size : 41,6 Mb
Release : 2015-11-13
Category : Philosophy
ISBN : 9781474404181

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Diagrammatic Immanence by Rocco Gangle Pdf

Rocco Gangle addresses the methodological questions raised by a commitment to immanence in terms of how diagrams may be used both as tools and as objects of philosophical investigation. Gangle integrates insights from Spinoza, Pierce and Deleuze in conjunction with the formal operations of category theory.

Diagrammatic Morphisms and Applications

David E. Radford,Category Theory AMS Special Session on Diagrammatic Morphisms in Algebra,David N. Yetter
Diagrammatic Morphisms and Applications Book PDF

Author : David E. Radford,Category Theory AMS Special Session on Diagrammatic Morphisms in Algebra,David N. Yetter
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 52,5 Mb
Release : 2003
Category : Categories (Mathematics)
ISBN : 9780821827949

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Diagrammatic Morphisms and Applications by David E. Radford,Category Theory AMS Special Session on Diagrammatic Morphisms in Algebra,David N. Yetter Pdf

The technique of diagrammatic morphisms is an important ingredient in comprehending and visualizing certain types of categories with structure. It was widely used in this capacity in many areas of algebra, low-dimensional topology and physics. It was also applied to problems in classical and quantum information processing and logic. This volume contains articles based on talks at the Special Session, ``Diagrammatic Morphisms in Algebra, Category Theory, and Topology'', at the AMS Sectional Meeting in San Francisco. The articles describe recent achievements in several aspects of diagrammatic morphisms and their applications. Some of them contain detailed expositions on various diagrammatic techniques. The introductory article by D. Yetter is a thorough account of the subject in a historical perspective.

Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science

Janusz Czelakowski
Don Pigozzi on Abstract Algebraic Logic Universal Algebra and Computer Science Book PDF

Author : Janusz Czelakowski
Publisher : Springer
Page : 454 pages
File Size : 44,5 Mb
Release : 2018-03-20
Category : Philosophy
ISBN : 9783319747729

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Don Pigozzi on Abstract Algebraic Logic, Universal Algebra, and Computer Science by Janusz Czelakowski Pdf

This book celebrates the work of Don Pigozzi on the occasion of his 80th birthday. In addition to articles written by leading specialists and his disciples, it presents Pigozzi’s scientific output and discusses his impact on the development of science. The book both catalogues his works and offers an extensive profile of Pigozzi as a person, sketching the most important events, not only related to his scientific activity, but also from his personal life. It reflects Pigozzi's contribution to the rise and development of areas such as abstract algebraic logic (AAL), universal algebra and computer science, and introduces new scientific results. Some of the papers also present chronologically ordered facts relating to the development of the disciplines he contributed to, especially abstract algebraic logic. The book offers valuable source material for historians of science, especially those interested in history of mathematics and logic.

Topological Quantum

Steven H. Simon
Topological Quantum Book PDF

Author : Steven H. Simon
Publisher : Oxford University Press
Page : 641 pages
File Size : 54,8 Mb
Release : 2023-09-29
Category : Science
ISBN : 9780198886778

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Topological Quantum by Steven H. Simon Pdf

At the intersection of physics, mathematics, and computer science, an exciting new field of study has formed, known as “Topological Quantum.” This research field examines the deep connections between the theory of knots, special types of subatomic particles known as anyons, certain phases of matter, and quantum computation. This book elucidates this nexus, drawing in topics ranging from quantum gravity to topology to experimental condensed matter physics. Topological quantum has increasingly been a focus point in the fields of condensed matter physics and quantum information over the last few decades, and the forefront of research now builds on the basic ideas presented in this book. The material is presented in a down-to-earth and entertaining way that is far less abstract than most of what is in the literature. While introducing the crucial concepts and placing them in context, the subject is presented without resort to the highly mathematical category theory that underlies the field. Requiring only an elementary background in quantum mechanics, this book is appropriate for all readers, from advanced undergraduates to the professional practitioner. This book will be of interest to mathematicians and computer scientists as well as physicists working on a wide range of topics. Those interested in working in these field will find this book to be an invaluable introduction as well as a crucial reference.

Encyclopedia of Knot Theory

Colin Adams,Erica Flapan,Allison Henrich,Louis H. Kauffman,Lewis D. Ludwig,Sam Nelson
Encyclopedia of Knot Theory Book PDF

Author : Colin Adams,Erica Flapan,Allison Henrich,Louis H. Kauffman,Lewis D. Ludwig,Sam Nelson
Publisher : CRC Press
Page : 954 pages
File Size : 41,6 Mb
Release : 2021-02-10
Category : Education
ISBN : 9781000222388

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Encyclopedia of Knot Theory by Colin Adams,Erica Flapan,Allison Henrich,Louis H. Kauffman,Lewis D. Ludwig,Sam Nelson Pdf

"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Features Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees Edited and contributed by top researchers in the field of knot theory

Representations and Nilpotent Orbits of Lie Algebraic Systems

Maria Gorelik,Vladimir Hinich,Anna Melnikov
Representations and Nilpotent Orbits of Lie Algebraic Systems Book PDF

Author : Maria Gorelik,Vladimir Hinich,Anna Melnikov
Publisher : Springer Nature
Page : 553 pages
File Size : 47,5 Mb
Release : 2019-10-18
Category : Mathematics
ISBN : 9783030235314

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Representations and Nilpotent Orbits of Lie Algebraic Systems by Maria Gorelik,Vladimir Hinich,Anna Melnikov Pdf

This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,” the first of which was held from July 16-18 at the Weizmann Institute of Science and the second from July 19-23 at the University of Haifa. The chapters in this volume cover a range of topics, including: Primitive ideals Invariant theory Geometry of Lie group actions Quantum affine algebras Yangians Categorification Vertex algebras This volume is addressed to mathematicians who specialize in representation theory and Lie theory, and who wish to learn more about this fascinating subject.

Formal Methods: Foundations and Applications

Gustavo Carvalho,Volker Stolz
Formal Methods Foundations and Applications Book PDF

Author : Gustavo Carvalho,Volker Stolz
Publisher : Springer Nature
Page : 234 pages
File Size : 50,6 Mb
Release : 2020-11-19
Category : Computers
ISBN : 9783030638825

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Formal Methods: Foundations and Applications by Gustavo Carvalho,Volker Stolz Pdf

This book constitutes the refereed proceedings of the 23rd Brazilian Symposium on Formal Methods, SBMF 2020, which was supposed to take place in Ouro Preto, Brazil, in November 2020. Instead the symposium took place virtually due to the COVID-19 pandemic. The 10 regular papers presented together with 3 invited talks in this book were carefully reviewed and selected from 17 submissions. The papers are organized in topical sections such as: experience reports; models, languages and semantics; and software product lines. Chapter ‘Safety Assurance of a High Voltage Controller for an Industrial Robotic System’ is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

The Road to Reality

Roger Penrose
The Road to Reality Book PDF

Author : Roger Penrose
Publisher : Vintage
Page : 1136 pages
File Size : 51,5 Mb
Release : 2021-06-09
Category : Science
ISBN : 9780593315309

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The Road to Reality by Roger Penrose Pdf

**WINNER OF THE 2020 NOBEL PRIZE IN PHYSICS** The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader, so that, for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book. Roger Penrose's purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections. The Road to Reality is rarely less than challenging, but the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams. In a single work of colossal scope one of the world's greatest scientists has given us a complete and unrivalled guide to the glories of the universe that we all inhabit. 'Roger Penrose is the most important physicist to work in relativity theory except for Einstein. He is one of the very few people I've met in my life who, without reservation, I call a genius' Lee Smolin

Categorification in Geometry, Topology, and Physics

Anna Beliakova,Aaron D. Lauda
Categorification in Geometry Topology and Physics Book PDF

Author : Anna Beliakova,Aaron D. Lauda
Publisher : American Mathematical Soc.
Page : 267 pages
File Size : 51,7 Mb
Release : 2017-02-21
Category : Categories (Mathematics)
ISBN : 9781470428211

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Categorification in Geometry, Topology, and Physics by Anna Beliakova,Aaron D. Lauda Pdf

The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorification is a powerful tool for relating various branches of mathematics and exploiting the commonalities between fields. It provides a language emphasizing essential features and allowing precise relationships between vastly different fields. This volume focuses on the role categorification plays in geometry, topology, and physics. These articles illustrate many important trends for the field including geometric representation theory, homotopical methods in link homology, interactions between higher representation theory and gauge theory, and double affine Hecke algebra approaches to link homology. The companion volume (Contemporary Mathematics, Volume 683) is devoted to categorification and higher representation theory.

Quantum Physics and Linguistics

Chris Heunen,Mehrnoosh Sadrzadeh,Edward Grefenstette
Quantum Physics and Linguistics Book PDF

Author : Chris Heunen,Mehrnoosh Sadrzadeh,Edward Grefenstette
Publisher : Oxford University Press
Page : 430 pages
File Size : 48,9 Mb
Release : 2013-02-21
Category : Computers
ISBN : 9780199646296

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Quantum Physics and Linguistics by Chris Heunen,Mehrnoosh Sadrzadeh,Edward Grefenstette Pdf

An interdisciplinary attempt to bring together physicists and linguists who use the same compositional mathematical methods. Although seemingly unrelated, due to the complexity and dynamics of the compound phenomena they aim to model, and also advances in their high level methods, these fields have come to share a common mathematical structure.

Residuated Structures in Algebra and Logic

George Metcalfe,Francesco Paoli,Constantine Tsinakis
Residuated Structures in Algebra and Logic Book PDF

Author : George Metcalfe,Francesco Paoli,Constantine Tsinakis
Publisher : American Mathematical Society
Page : 282 pages
File Size : 41,5 Mb
Release : 2023-11-06
Category : Mathematics
ISBN : 9781470469856

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Residuated Structures in Algebra and Logic by George Metcalfe,Francesco Paoli,Constantine Tsinakis Pdf

This book is an introduction to residuated structures, viewed as a common thread binding together algebra and logic. The framework includes well-studied structures from classical abstract algebra such as lattice-ordered groups and ideals of rings, as well as structures serving as algebraic semantics for substructural and other non-classical logics. Crucially, classes of these structures are studied both algebraically, yielding a rich structure theory along the lines of Conrad's program for lattice-ordered groups, and algorithmically, via analytic sequent or hypersequent calculi. These perspectives are related using a natural notion of equivalence for consequence relations that provides a bridge offering benefits to both sides. Algorithmic methods are used to establish properties like decidability, amalgamation, and generation by subclasses, while new insights into logical systems are obtained by studying associated classes of structures. The book is designed to serve the purposes of novices and experts alike. The first three chapters provide a gentle introduction to the subject, while subsequent chapters provide a state-of-the-art account of recent developments in the field.

Algebra and Number Theory

Rajat Tandon
Algebra and Number Theory Book PDF

Author : Rajat Tandon
Publisher : Springer
Page : 411 pages
File Size : 43,8 Mb
Release : 2005-05-01
Category : Mathematics
ISBN : 9789386279231

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Algebra and Number Theory by Rajat Tandon Pdf

Contributed articles presented at the Conference.