Clifford Algebras And Zeons: Geometry To Combinatorics And Beyond PDF Download

Author: George Stacey Staples
Publisher: World Scientific
ISBN: 9811202591
Category : Mathematics
Languages : en
Pages : 378

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Book Description
Clifford algebras have many well-known applications in physics, engineering, and computer graphics. Zeon algebras are subalgebras of Clifford algebras whose combinatorial properties lend them to graph-theoretic applications such as enumerating minimal cost paths in dynamic networks. This book provides a foundational working knowledge of zeon algebras, their properties, and their potential applications in an increasingly technological world.As a graduate-level or advanced undergraduate-level mathematics textbook, it is suitable for self-study by researchers interested in new approaches to existing combinatorial problems and applications (wireless networks, Boolean satisfiability, coding theory, etc.).As the first textbook to explore algebraic and combinatorial properties of zeon algebras in depth, it is suitable for interdisciplinary study in analysis, algebra, and combinatorics. The material is complemented by the CliffMath software package for Mathematica, which is freely available through the book's webpage.

Author: George Stacey Staples
Publisher: World Scientific
ISBN: 1908977574
Category : Mathematics
Languages : en
Pages : 428

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Book Description
This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science.Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with packages for performing symbolic computations.

Author: Alexey Stakhov
Publisher: World Scientific
ISBN: 9812775838
Category : Mathematics
Languages : en
Pages : 745

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Book Description
Assisted by Scott Olsen ( Central Florida Community College, USA ). This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the OC Mathematics of Harmony, OCO a new interdisciplinary direction of modern science. This direction has its origins in OC The ElementsOCO of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the OC goldenOCO algebraic equations, the generalized Binet formulas, Fibonacci and OC goldenOCO matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and OC goldenOCO matrices). The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science. Sample Chapter(s). Introduction (503k). Chapter 1: The Golden Section (2,459k). Contents: Classical Golden Mean, Fibonacci Numbers, and Platonic Solids: The Golden Section; Fibonacci and Lucas Numbers; Regular Polyhedrons; Mathematics of Harmony: Generalizations of Fibonacci Numbers and the Golden Mean; Hyperbolic Fibonacci and Lucas Functions; Fibonacci and Golden Matrices; Application in Computer Science: Algorithmic Measurement Theory; Fibonacci Computers; Codes of the Golden Proportion; Ternary Mirror-Symmetrical Arithmetic; A New Coding Theory Based on a Matrix Approach. Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science."

Author: Abraham Berman
Publisher: World Scientific
ISBN: 9789812795212
Category : Mathematics
Languages : en
Pages : 222

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Book Description
A real matrix is positive semidefinite if it can be decomposed as A = BBOC . In some applications the matrix B has to be elementwise nonnegative. If such a matrix exists, A is called completely positive. The smallest number of columns of a nonnegative matrix B such that A = BBOC is known as the cp- rank of A . This invaluable book focuses on necessary conditions and sufficient conditions for complete positivity, as well as bounds for the cp- rank. The methods are combinatorial, geometric and algebraic. The required background on nonnegative matrices, cones, graphs and Schur complements is outlined. Contents: Preliminaries: Matrix Theoretic Background; Positive Semidefinite Matrices; Nonnegative Matrices and M -Matrices; Schur Complements; Graphs; Convex Cones; The PSD Completion Problem; Complete Positivity: Definition and Basic Properties; Cones of Completely Positive Matrices; Small Matrices; Complete Positivity and the Comparison Matrix; Completely Positive Graphs; Completely Positive Matrices Whose Graphs are Not Completely Positive; Square Factorizations; Functions of Completely Positive Matrices; The CP Completion Problem; CP Rank: Definition and Basic Results; Completely Positive Matrices of a Given Rank; Completely Positive Matrices of a Given Order; When is the CP-Rank Equal to the Rank?. Readership: Upper level undergraduates, graduate students, academics and researchers interested in matrix theory."

Author: Hardy Yorick
Publisher: World Scientific
ISBN: 9811202532
Category : Mathematics
Languages : en
Pages : 388

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Book Description
Our self-contained volume provides an accessible introduction to linear and multilinear algebra as well as tensor calculus. Besides the standard techniques for linear algebra, multilinear algebra and tensor calculus, many advanced topics are included where emphasis is placed on the Kronecker product and tensor product. The Kronecker product has widespread applications in signal processing, discrete wavelets, statistical physics, Hopf algebra, Yang-Baxter relations, computer graphics, fractals, quantum mechanics, quantum computing, entanglement, teleportation and partial trace. All these fields are covered comprehensively.The volume contains many detailed worked-out examples. Each chapter includes useful exercises and supplementary problems. In the last chapter, software implementations are provided for different concepts. The volume is well suited for pure and applied mathematicians as well as theoretical physicists and engineers.New topics added to the third edition are: mutually unbiased bases, Cayley transform, spectral theorem, nonnormal matrices, Gâteaux derivatives and matrices, trace and partial trace, spin coherent states, Clebsch-Gordan series, entanglement, hyperdeterminant, tensor eigenvalue problem, Carleman matrix and Bell matrix, tensor fields and Ricci tensors, and software implementations.

Author: Zhaojun Bai
Publisher: World Scientific
ISBN: 9814675784
Category : Mathematics
Languages : en
Pages : 146

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Book Description
Matrix functions and matrix equations are widely used in science, engineering and social sciences due to the succinct and insightful way in which they allow problems to be formulated and solutions to be expressed. This book covers materials relevant to advanced undergraduate and graduate courses in numerical linear algebra and scientific computing. It is also well-suited for self-study. The broad content makes it convenient as a general reference to the subjects.

Author: L. P. Lebedev
Publisher: World Scientific
ISBN: 9789812564467
Category : Mathematics
Languages : en
Pages : 208

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Book Description
Tensor analysis is an essential tool in any science (e.g. engineering, physics, mathematical biology) that employs a continuumdescription. This concise text offers a straightforward treatment ofthe subject suitable for the student or practicing engineer

Author: Kuncham Syam Prasad
Publisher: World Scientific
ISBN: 981320737X
Category : Mathematics
Languages : en
Pages : 324

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Book Description
Recent developments in various algebraic structures and the applications of those in different areas play an important role in Science and Technology. One of the best tools to study the non-linear algebraic systems is the theory of Near-rings.The forward note by G

Author: Marco Grandis
Publisher: World Scientific
ISBN: 9811236100
Category : Mathematics
Languages : en
Pages : 390

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Book Description
Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.

Author: Ioannis Farmakis
Publisher: World Scientific Publishing Company
ISBN: 9789813142619
Category : Algebra
Languages : en
Pages : 0

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Book Description
'I like the authorsâ (TM) taste in footnotes, what with their frequent emphasis on history, i.e. the minutiae of the lives of many mathematicians appearing in these pages. Their remarks add a particular dimension of fun and pleasure to what I think is a very good book. Itâ (TM)s pitched at the right level, it does a lot of serious stuff in preparation for what is coming the studentsâ (TM) way in the future, and it does it well.'MAA ReviewsThis comprehensive two-volume book deals with algebra, broadly conceived. Volume 1 (Chapters 1-6) comprises material for a first year graduate course in algebra, offering the instructor a number of options in designing such a course. Volume 1, provides as well all essential material that students need to prepare for the qualifying exam in algebra at most American and European universities. Volume 2 (Chapters 7-13) forms the basis for a second year graduate course in topics in algebra. As the table of contents shows, that volume provides ample material accommodating a variety of topics that may be included in a second year course. To facilitate matters for the reader, there is a chart showing the interdependence of the chapters.