General Galois Geometries

Author: James Hirschfeld,Joseph A. Thas

Publisher: Springer

ISBN: 1447167902

Category: Mathematics

Page: 409

View: 6776

DOWNLOAD NOW »

This book is the second edition of the third and last volume of a treatise on projective spaces over a finite field, also known as Galois geometries. This volume completes the trilogy comprised of plane case (first volume) and three dimensions (second volume). This revised edition includes much updating and new material. It is a mostly self-contained study of classical varieties over a finite field, related incidence structures and particular point sets in finite n-dimensional projective spaces. General Galois Geometries is suitable for PhD students and researchers in combinatorics and geometry. The separate chapters can be used for courses at postgraduate level.

Arithmetic, Geometry, Cryptography and Coding Theory

Author: Alp Bassa,Alain Couvreur,David Kohel

Publisher: American Mathematical Soc.

ISBN: 1470428105

Category: Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Finite ground fields

Page: 199

View: 2672

DOWNLOAD NOW »

This volume contains the proceedings of the 15th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory (AGCT), held at the Centre International de Rencontres Mathématiques in Marseille, France, from May 18–22, 2015. Since the first meeting almost 30 years ago, the biennial AGCT meetings have been one of the main events bringing together researchers interested in explicit aspects of arithmetic geometry and applications to coding theory and cryptography. This volume contains original research articles reflecting recent developments in the field.

Codes, Cryptology and Curves with Computer Algebra

Author: Ruud Pellikaan,Stanislav Bulygin,Xin-Wen Wu,Relinde Jurrius

Publisher: Cambridge University Press

ISBN: 0521817110

Category: Language Arts & Disciplines

Page: 600

View: 6860

DOWNLOAD NOW »

Graduate-level introduction to error-correcting codes, which are used to protect digital data and applied in public key cryptosystems.

Foundations of Incidence Geometry

Projective and Polar Spaces

Author: Johannes Ueberberg

Publisher: Springer Science & Business Media

ISBN: 3642209726

Category: Mathematics

Page: 248

View: 310

DOWNLOAD NOW »

Incidence geometry is a central part of modern mathematics that has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polar spaces. Embedded into the modern view of diagram geometry, projective and affine geometry including the fundamental theorems, polar geometry including the Theorem of Buekenhout-Shult and the classification of quadratic sets are presented in this volume. Incidence geometry is developed along the lines of the fascinating work of Jacques Tits and Francis Buekenhout. The book is a clear and comprehensible introduction into a wonderful piece of mathematics. More than 200 figures make even complicated proofs accessible to the reader.

Brauer Groups, Hopf Algebras and Galois Theory

Author: Stefaan Caenepeel

Publisher: Springer Science & Business Media

ISBN: 9781402003462

Category: Mathematics

Page: 488

View: 2261

DOWNLOAD NOW »

This volume is devoted to the Brauer group of a commutative ring and related invariants. Part I presents a new self-contained exposition of the Brauer group of a commutative ring. Included is a systematic development of the theory of Grothendieck topologies and �tale cohomology, and discussion of topics such as Gabber's theorem and the theory of Taylor's big Brauer group of algebras without a unit. Part II presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois objects of a cocommutative Hopf algebra. The development of the theory is carried out in such a way that the connection to the theory of the Brauer group in Part I is made clear. Recent developments are considered and examples are included. The Brauer-Long group of a Hopf algebra over a commutative ring is discussed in Part III. This provides a link between the first two parts of the volume and is the first time this topic has been discussed in a monograph. Audience: Researchers whose work involves group theory. The first two parts, in particular, can be recommended for supplementary, graduate course use.

Handbook of Finite Translation Planes

Author: Norman Johnson,Vikram Jha,Mauro Biliotti

Publisher: Chapman and Hall/CRC

ISBN: 9781584886051

Category: Mathematics

Page: 888

View: 1130

DOWNLOAD NOW »

The Handbook of Finite Translation Planes provides a comprehensive listing of all translation planes derived from a fundamental construction technique, an explanation of the classes of translation planes using both descriptions and construction methods, and thorough sketches of the major relevant theorems. From the methods of André to coordinate and linear algebra, the book unifies the numerous diverse approaches for analyzing finite translation planes. It pays particular attention to the processes that are used to study translation planes, including ovoid and Klein quadric projection, multiple derivation, hyper-regulus replacement, subregular lifting, conical distortion, and Hermitian sequences. In addition, the book demonstrates how the collineation group can affect the structure of the plane and what information can be obtained by imposing group theoretic conditions on the plane. The authors also examine semifield and division ring planes and introduce the geometries of two-dimensional translation planes. As a compendium of examples, processes, construction techniques, and models, the Handbook of Finite Translation Planes equips readers with precise information for finding a particular plane. It presents the classification results for translation planes and the general outlines of their proofs, offers a full review of all recognized construction techniques for translation planes, and illustrates known examples.

Mathematische Physik: Klassische Mechanik

Author: Andreas Knauf

Publisher: Springer-Verlag

ISBN: 3662557762

Category: Science

Page: 652

View: 6604

DOWNLOAD NOW »

Als Grenztheorie der Quantenmechanik besitzt die klassische Dynamik einen großen Formenreichtum – vom gut berechenbaren bis zum chaotischen Verhalten. Ausgehend von interessanten Beispielen wird in dem Band nicht nur eine gelungene Auswahl grundlegender Themen vermittelt, sondern auch der Einstieg in viele aktuelle Forschungsgebiete im Bereich der klassischen Mechanik. Didaktisch geschickt aufgebaut und mit hilfreichen Anhängen versehen, werden lediglich Kenntnisse der Grundvorlesungen in Mathematik vorausgesetzt. Mit über 100 Aufgaben und Lösungen.

Valued Fields

Author: Antonio J. Engler,Alexander Prestel

Publisher: Springer Science & Business Media

ISBN: 354030035X

Category: Mathematics

Page: 208

View: 2312

DOWNLOAD NOW »

Absolute values and their completions – such as the p-adic number fields – play an important role in number theory. Krull's generalization of absolute values to valuations made possible applications in other branches of mathematics. In valuation theory, the notion of completion must be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the skills of a standard graduate course in algebra.

Modern Projective Geometry

Author: Claude-Alain Faure,Alfred Frölicher

Publisher: Springer Science & Business Media

ISBN: 9401595909

Category: Mathematics

Page: 363

View: 7988

DOWNLOAD NOW »

This monograph develops projective geometries and provides a systematic treatment of morphisms. It introduces a new fundamental theorem and its applications describing morphisms of projective geometries in homogeneous coordinates by semilinear maps. Other topics treated include three equivalent definitions of projective geometries and their correspondence with certain lattices; quotients of projective geometries and isomorphism theorems; and recent results in dimension theory.

Bernhard Riemann 1826–1866

Wendepunkte in der Auffassung der Mathematik

Author: Detlef Laugwitz

Publisher: Springer-Verlag

ISBN: 3034889836

Category: Mathematics

Page: 348

View: 9317

DOWNLOAD NOW »

Das Riemannsche Integral lernen schon die Schüler kennen, die Theorien der reellen und der komplexen Funktionen bauen auf wichtigen Begriffsbildungen und Sätzen Riemanns auf, die Riemannsche Geometrie ist für Einsteins Gravitationstheorie und ihre Erweiterungen unentbehrlich, und in der Zahlentheorie ist die berühmte Riemannsche Vermutung noch immer offen. Riemann und sein um fünf Jahre jüngerer Freund Richard Dedekind sahen sich als Schüler von Gauss und Dirichlet. Um die Mitte des 19. Jahrhunderts leiteten sie den Übergang zur "modernen Mathematik" ein, der eine in Analysis und Geometrie, der andere in der Algebra mit der Hinwendung zu Mengen und Strukturen. Dieses Buch ist der erste Versuch, Riemanns wissenschaftliches Werk unter einem einheitlichen Gesichtspunkt zusammenzufassend darzustellen. Riemann gilt als einer der Philosophen unter den Mathematikern. Er stellte das Denken in Begriffen neben die zuvor vorherrschende algorithmische Auffassung von der Mathematik, welche die Gegenstände der Untersuchung, in Formeln und Figuren, in Termumformungen und regelhaften Konstruktionen als die allein legitimen Methoden sah. David Hilbert hat als Riemanns Grundsatz herausgestellt, die Beweise nicht durch Rechnung, sondern lediglich durch Gedanken zu zwingen. Hermann Weyl sah als das Prinzip Riemanns in Mathematik und Physik, "die Welt als das erkenntnistheoretische Motiv..., die Welt aus ihrem Verhalten im un- endlich kleinen zu verstehen."

Mathematical Tools for Physicists

Author: Michael Grinfeld

Publisher: John Wiley & Sons

ISBN: 3527684271

Category: Science

Page: 632

View: 2153

DOWNLOAD NOW »

The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.