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Author: Fred Van Oystaeyen
Publisher: CRC Press
ISBN: 1420060570
Category : Mathematics
Languages : en
Pages : 170
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Book Description
Intrinsically noncommutative spaces today are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. From this point of view, it is ideal to devise a concept of space and its geometry that is fundamentally noncommutative. Providing a clear introduction to noncommutat
Author: Fred Van Oystaeyen
Publisher: CRC Press
ISBN: 1420060570
Category : Mathematics
Languages : en
Pages : 170
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Book Description
Intrinsically noncommutative spaces today are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. From this point of view, it is ideal to devise a concept of space and its geometry that is fundamentally noncommutative. Providing a clear introduction to noncommutat
Author: Piero Pagliani
Publisher: Springer Science & Business Media
ISBN: 1402086229
Category : Philosophy
Languages : en
Pages : 771
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Book Description
'A Geometry of Approximation' addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focuses mainly on its logic-algebraic interpretation. The theory is embedded in a broader perspective that includes logical and mathematical methodologies pertaining to the theory, as well as related epistemological issues. Any mathematical technique that is introduced in the book is preceded by logical and epistemological explanations. Intuitive justifications are also provided, insofar as possible, so that the general perspective is not lost. Such an approach endows the present treatise with a unique character. Due to this uniqueness in the treatment of the subject, the book will be useful to researchers, graduate and pre-graduate students from various disciplines, such as computer science, mathematics and philosophy. It features an impressive number of examples supported by about 40 tables and 230 figures. The comprehensive index of concepts turns the book into a sort of encyclopaedia for researchers from a number of fields. 'A Geometry of Approximation' links many areas of academic pursuit without losing track of its focal point, Rough Sets.
Author: Frederik Caenepeel
Publisher: CRC Press
ISBN: 1000731561
Category : Mathematics
Languages : en
Pages : 283
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Book Description
Glider Representations offer several applications across different fields within Mathematics, thereby motivating the introduction of this new glider theory and opening numerous doors for future research, particularly with respect to more complex filtration chains. Features • Introduces new concepts in the Theory of Rings and Modules • Suitable for researchers and graduate students working in this area, and as supplementary reading for courses in Group Theory, Ring Theory, Lie Algebras and Sheaf Theory • The first book to explicitly outline this new approach to gliders and fragments and associated concepts
Author: Peter Falb
Publisher: Springer
ISBN: 3319980262
Category : Mathematics
Languages : en
Pages : 211
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Book Description
"An introduction to the ideas of algebraic geometry in the motivated context of system theory." Thus the author describes his textbook that has been specifically written to serve the needs of students of systems and control. Without sacrificing mathematical care, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than abstraction. The student will find here a clear presentation with an applied flavor, of the core ideas in the algebra-geometric treatment of scalar linear system theory. The author introduces the four representations of a scalar linear system and establishes the major results of a similar theory for multivariable systems appearing in a succeeding volume (Part II: Multivariable Linear Systems and Projective Algebraic Geometry). Prerequisites are the basics of linear algebra, some simple notions from topology and the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises are an integral part of the treatment and are used where relevant in the main body of the text. The present, softcover reprint is designed to make this classic textbook available to a wider audience. "This book is a concise development of affine algebraic geometry together with very explicit links to the applications...[and] should address a wide community of readers, among pure and applied mathematicians." —Monatshefte für Mathematik
Author: P.A. Grillet
Publisher: Springer Science & Business Media
ISBN: 1475733895
Category : Mathematics
Languages : en
Pages : 443
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Book Description
This is the first book about commutative semigroups in general. Emphasis is on structure but the other parts of the theory are at least surveyed and a full set of about 850 references is included. The book is intended for mathematicians who do research on semigroups or who encounter commutative semigroups in their research.
Author: John von Neumann
Publisher: Princeton University Press
ISBN: 1400883954
Category : Mathematics
Languages : en
Pages : 312
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Book Description
In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Neumann founded the field of continuous geometry. This book, based on von Neumann's lecture notes, begins with the development of the axioms of continuous geometry, dimension theory, and--for the irreducible case--the function D(a). The properties of regular rings are then discussed, and a variety of results are presented for lattices that are continuous geometries, for which irreducibility is not assumed. For students and researchers interested in ring theory or projective geometries, this book is required reading.
Author: James Der Derian
Publisher: Oxford University Press
ISBN: 0197568203
Category : Political Science
Languages : en
Pages : 417
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Book Description
The contributors to this volume are motivated by a common apprehension and a common hope. The apprehension was first voiced by Einstein, who lamented the inability of humanity, at the individual and social level, to keep up with the increased speed of technological change brought about by the quantum revolution. As quantum science and technology fast forward into the 21st century, the social sciences remain stuck in classical, 19th century ways of thinking. Can such a mechanistic model of the mind and society possibly help us manage the fully realized technological potential of the quantum? That's where the hope appears: that perhaps quantum is not just a physical science, but a human science too. In Quantum International Relations, James Der Derian and Alexander Wendt gather rising scholars and leading experts to make the case for quantum approaches to world politics. As a fundamental theory of reality and enabler of new technologies, quantum now touches everything, with the potential to revolutionize how we conduct diplomacy, wage war, and make wealth. Contributors present the core principles of quantum mechanics--entanglement, uncertainty, superposition, and the wave function--as significant catalysts and superior heuristics for an accelerating quantum future. Facing a reality which no longer corresponds to an outdated Newtonian worldview of states as billiard balls, individuals as rational actors or power as objective interest, Der Derian and Wendt issue an urgent call for a new human science of quantum International Relations. At the centenary of the first quantum thought experiment in the 1920s, this book offers a diversity of explorations, speculations and approaches for understanding geopolitics in the 21st century.
Author: Michael Gil'
Publisher: CRC Press
ISBN: 1439800332
Category : Mathematics
Languages : en
Pages : 318
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Book Description
One of the most important problems in the theory of entire functions is the distribution of the zeros of entire functions. Localization and Perturbation of Zeros of Entire Functions is the first book to provide a systematic exposition of the bounds for the zeros of entire functions and variations of zeros under perturbations. It also offers a new a
Author: Sandor Szabo
Publisher: CRC Press
ISBN: 142009047X
Category : Mathematics
Languages : en
Pages : 282
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Book Description
Decomposing an abelian group into a direct sum of its subsets leads to results that can be applied to a variety of areas, such as number theory, geometry of tilings, coding theory, cryptography, graph theory, and Fourier analysis. Focusing mainly on cyclic groups, Factoring Groups into Subsets explores the factorization theory of abelian groups. Th
Author: Hal Schenck
Publisher: Cambridge University Press
ISBN: 9780521536509
Category : Computers
Languages : en
Pages : 212
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Book Description
The interplay between algebra and geometry is a beautiful (and fun!) area of mathematical investigation. Advances in computing and algorithms make it possible to tackle many classical problems in a down-to-earth and concrete fashion. This opens wonderful new vistas and allows us to pose, study and solve problems that were previously out of reach. Suitable for graduate students, the objective of this 2003 book is to bring advanced algebra to life with lots of examples. The first chapters provide an introduction to commutative algebra and connections to geometry. The rest of the book focuses on three active areas of contemporary algebra: Homological Algebra (the snake lemma, long exact sequence inhomology, functors and derived functors (Tor and Ext), and double complexes); Algebraic Combinatorics and Algebraic Topology (simplicial complexes and simplicial homology, Stanley-Reisner rings, upper bound theorem and polytopes); and Algebraic Geometry (points and curves in projective space, Riemann-Roch, Cech cohomology, regularity).
