Kategoria BISAC: Mathematics >> Algebra - General

C* tensor categories are a point of contact where Operator Algebras and Quantum Field Theory meet. They are the underlying unifying concept for homomorphisms of (properly infinite) von Neumann algebras and representations of quantum observables.

The present introductory text reviews the basic notions and their cross-relations in different contexts. The focus is on Q-systems that serve as complete invariants, both for subfactors and for extensions of quantum field theory models.

It proceeds with various operations on Q-systems (several decompositions, the mirror Q-system,...

The book focuses on the educational perspective of Riemann-Roch spaces and the computation of algebraic structures connected to the Riemann-Roch theorem, which is a useful tool in fields of complex analysis and algebraic geometry. On one hand, the theorem connects the Riemann surface with its topological genus, and on the other it allows us to compute the algebraic function field spaces. In the first part of this book, algebraic structures and some of their properties are presented. The second part shows efficient algorithms and examples connected to Riemann-Roch spaces. What is important,...

Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life.

This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition,...

Dieses Buch vermittelt die so genannte hohere Mathematik, also die uber das einfache Rechnen hinausgehende Mathematik, deren Lehre gewohnlich in den letzten Schuljahren begonnen und in den ersten Studiensemestern erweitert und vertieft wird. Es beginnt mit einer Einfuhrung in die mathematische Sprache und behandelt anschliessend die Themen Arithmetik, Algebra, Geometrie und Infinitesimalrechnung.

The topic of this book sits at the interface of the theory of higher categories (in the guise of (∞,1)-categories) and the theory of properads. Properads are devices more general than operads and enable one to encode bialgebraic, rather than just (co)algebraic, structures.

The text extends both the Joyal-Lurie approach to higher categories and the Cisinski-Moerdijk-Weiss approach to higher operads, and provides a foundation for a broad study of the homotopy theory of properads. This work also serves as a complete guide to the generalised graphs which are pervasive in the study...

Konrad Schobel aims to lay the foundations for a consequent algebraic geometric treatment of variable Separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together a great range of mathematics and mathematical physics, from the late 19th century theory of separation of variables to modern moduli space theory, Stasheff polytopes and operads.

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Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases. It also provides a solution of Hartshorne's Conjecture on Complete Intersections for the class of quadratic manifolds and new short proofs of previously known results, using the modern...

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Each year, test-takers report that the Mathematical Reasoning test is the toughest of all the GED(R) tests. That's why REA offers the most complete guide to success on the GED(R) Math test.

Written by Sandra Rush, a GED(R) Math tutor and test expert - This revised second edition of our best-selling test prep is completely aligned with the content and format of the current GED(R) test. A comprehensive review...

This textbook provides an introduction to the mathematics on which modern cryptology is based. It covers not only public key cryptography, the glamorous component of modern cryptology, but also pays considerable attention to secret key cryptography, its workhorse in practice.

Modern cryptology has been described as the science of the integrity of information, covering all aspects like confidentiality, authenticity and non-repudiation and also including the protocols required for achieving these aims. In both theory and practice it requires notions and constructions from three major...

IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of advanced textbooks for teacher education which aims to advance the teaching of mathematics by integrating mathematics content teaching with the broader research and theoretical base of mathematics education.

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The Learning and Teaching of Algebra" is a primer for teachers and researchers that provides a pedagogical framework for the teaching and learning of algebra grounded in theory and research.

Areas covered include:

Algebra: Setting the Scene

Some Lessons From History

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