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Books > Science & Mathematics > Mathematics > Geometry

Elliptic Curves and Their Applications to Cryptography - An Introduction (Hardcover, 1999 ed.): Andreas Enge Elliptic Curves and Their Applications to Cryptography - An Introduction (Hardcover, 1999 ed.)
Andreas Enge
R6,416 Discovery Miles 64 160 Ships in 10 - 15 working days

Since their invention in the late seventies, public key cryptosystems have become an indispensable asset in establishing private and secure electronic communication, and this need, given the tremendous growth of the Internet, is likely to continue growing. Elliptic curve cryptosystems represent the state of the art for such systems. Elliptic Curves and Their Applications to Cryptography: An Introduction provides a comprehensive and self-contained introduction to elliptic curves and how they are employed to secure public key cryptosystems. Even though the elegant mathematical theory underlying cryptosystems is considerably more involved than for other systems, this text requires the reader to have only an elementary knowledge of basic algebra. The text nevertheless leads to problems at the forefront of current research, featuring chapters on point counting algorithms and security issues. The Adopted unifying approach treats with equal care elliptic curves over fields of even characteristic, which are especially suited for hardware implementations, and curves over fields of odd characteristic, which have traditionally received more attention. Elliptic Curves and Their Applications: An Introduction has been used successfully for teaching advanced undergraduate courses. It will be of greatest interest to mathematicians, computer scientists, and engineers who are curious about elliptic curve cryptography in practice, without losing the beauty of the underlying mathematics.

Mathematical Visualization - Algorithms, Applications and Numerics (Hardcover, 1998 ed.): H.C. Hege, K. Polthier Mathematical Visualization - Algorithms, Applications and Numerics (Hardcover, 1998 ed.)
H.C. Hege, K. Polthier
R2,954 Discovery Miles 29 540 Ships in 10 - 15 working days

Mathematical Visualization is a young new discipline. It offers efficient visualization tools to the classical subjects of mathematics, and applies mathematical techniques to problems in computer graphics and scientific visualization. Originally, it started in the interdisciplinary area of differential geometry, numerical mathematics, and computer graphics. In recent years, the methods developed have found important applications.
The current volume is the quintessence of an international workshop in September 1997 in Berlin, focusing on recent developments in this emerging area. Experts present selected research work on new algorithms for visualization problems, describe the application and experiments in geometry, and develop new numerical or computer graphical techniques.

The Foundations of Geometry and the Non-Euclidean Plane (Hardcover, 1st Corrected ed. 1975. Corr. 3rd printing 1997): G.E.... The Foundations of Geometry and the Non-Euclidean Plane (Hardcover, 1st Corrected ed. 1975. Corr. 3rd printing 1997)
G.E. Martin
R2,090 Discovery Miles 20 900 Ships in 12 - 19 working days

The Foundations of Geometry and the Non-Euclidean Plane is a self-contained text for junior, senior, and first-year graduate courses. Historical material is interwoven with a rigorous ruler- and protractor axiomatic development of the Euclidean and hyperbolic planes. Additional topics include the classical axiomatic systems of Euclid and Hilbert, axiom systems for three and four dimensional absolute geometry, and Pieri's system based on rigid motions. Models, such as Taxicab Geometry, are used extensively to illustrate theory.

The Sub-Laplacian Operators of Some Model Domains (Hardcover): Der-Chen Chang, Jingzhi Tie The Sub-Laplacian Operators of Some Model Domains (Hardcover)
Der-Chen Chang, Jingzhi Tie
R4,158 Discovery Miles 41 580 Ships in 12 - 19 working days

The book constructs explicitly the fundamental solution of the sub-Laplacian operator for a family of model domains in Cn+1. This type of domain is a good point-wise model for a Cauchy-Rieman (CR) manifold with diagonalizable Levi form. Qualitative results for such operators have been studied extensively, but exact formulas are difficult to derive. Exact formulas are closely related to the underlying geometry and lead to equations of classical types such as hypergeometric equations and Whittaker's equations.

Computations with Modular Forms - Proceedings of a Summer School and Conference, Heidelberg, August/September 2011 (English,... Computations with Modular Forms - Proceedings of a Summer School and Conference, Heidelberg, August/September 2011 (English, French, Hardcover, 2014 ed.)
Gebhard Bockle, Gabor Wiese
R4,405 Discovery Miles 44 050 Ships in 10 - 15 working days

This volume contains original research articles, survey articles and lecture notes related to the Computations with Modular Forms 2011 Summer School and Conference, held at the University of Heidelberg. A key theme of the Conference and Summer School was the interplay between theory, algorithms and experiment. The 14 papers offer readers both, instructional courses on the latest algorithms for computing modular and automorphic forms, as well as original research articles reporting on the latest developments in the field. The three Summer School lectures provide an introduction to modern algorithms together with some theoretical background for computations of and with modular forms, including computing cohomology of arithmetic groups, algebraic automorphic forms, and overconvergent modular symbols. The 11 Conference papers cover a wide range of themes related to computations with modular forms, including lattice methods for algebraic modular forms on classical groups, a generalization of the Maeda conjecture, an efficient algorithm for special values of p-adic Rankin triple product L-functions, arithmetic aspects and experimental data of Bianchi groups, a theoretical study of the real Jacobian of modular curves, results on computing weight one modular forms, and more.

The Conformal Structure of Space-Times - Geometry, Analysis, Numerics (Hardcover, 2002 ed.): Joerg Frauendiener, Helmut... The Conformal Structure of Space-Times - Geometry, Analysis, Numerics (Hardcover, 2002 ed.)
Joerg Frauendiener, Helmut Friedrich
R3,099 Discovery Miles 30 990 Ships in 10 - 15 working days

Causal relations, and with them the underlying null cone or conformal structure, form a basic ingredient in all general analytical studies of asymptotically flat space-time. The present book reviews these aspects from the analytical, geometrical and numerical points of view. Care has been taken to present the material in a way that will also be accessible to postgraduate students and nonspecialist reseachers from related fields.

Geometric Fundamentals of Robotics (Hardcover, 2nd ed. 2005): J. M. Selig Geometric Fundamentals of Robotics (Hardcover, 2nd ed. 2005)
J. M. Selig
R3,114 Discovery Miles 31 140 Ships in 10 - 15 working days

* Provides an elegant introduction to the geometric concepts that are important to applications in robotics

* Includes significant state-of-the art material that reflects important advances, connecting robotics back to mathematical fundamentals in group theory and geometry

* An invaluable reference that serves a wide audience of grad students and researchers in mechanical engineering, computer science, and applied mathematics

Groups - Korea 98 - Proceedings of the International Conference held at Pusan National University, Pusan, Korea, August 10-16,... Groups - Korea 98 - Proceedings of the International Conference held at Pusan National University, Pusan, Korea, August 10-16, 1998 (Hardcover, Reprint 2016)
Young Gheel Baik, Johnson David L. Johnson, Ann Chi Kim
R6,064 Discovery Miles 60 640 Ships in 12 - 19 working days

These 25 papers from a conference held in August 1998 at Pusan National U. provide a broad overview of contemporary group theory, with a particular emphasis on geometric and topological methods. Topics covered include: deformations and rigidity, combinatorial group theory and wild metric complexes, generalized triangle groups, HNN extensions, Eilenberg-Ganea Conjecture, cyclically presented groups, Takahashi manifolds, wreath products, reduction formulae, group actions on graphs and designs, Grushko-Neumann theorem, and variations on a theme of Higman and Conder. Includes a list of the authors and participants with contact information. Conference sponsors included the Korea Science and Engineering Foundation and International Mathematical Union Commission on Development and Exchange. Lacks an index.

Lectures in Real Geometry (Hardcover, Reprint 2011): Fabrizio Broglia Lectures in Real Geometry (Hardcover, Reprint 2011)
Fabrizio Broglia
R5,428 Discovery Miles 54 280 Ships in 12 - 19 working days

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Topological Spaces - From Distance to Neighborhood (Hardcover, 1997 ed.): Gerard Buskes, Arnoud Van Rooij Topological Spaces - From Distance to Neighborhood (Hardcover, 1997 ed.)
Gerard Buskes, Arnoud Van Rooij
R1,957 Discovery Miles 19 570 Ships in 10 - 15 working days

gentle introduction to the subject, leading the reader to understand the notion of what is important in topology with regard to geometry. Divided into three sections - The line and the plane, Metric spaces and Topological spaces -, the book eases the move into higher levels of abstraction. Students are thereby informally assisted in learning new ideas while remaining on familiar territory. The authors do not assume previous knowledge of axiomatic approach or set theory. Similarly, they have restricted the mathematical vocabulary in the book so as to avoid overwhelming the reader, and the concept of convergence is employed to allow students to focus on a central theme while moving to a natural understanding of the notion of topology. The pace of the book is relaxed with gradual acceleration: the first nine sections form a balanced course in metric spaces for undergraduates while also containing ample material for a two-semester graduate course. Finally, the book illustrates the many connections between topology and other subjects, such as analysis and set theory, via the inclusion of "Extras" at the end of each chapter presenting a brief foray outside topology.

General Topology III - Paracompactness, Function Spaces, Descriptive Theory (Hardcover, 1995 ed.): A.V. Arhangel'skii General Topology III - Paracompactness, Function Spaces, Descriptive Theory (Hardcover, 1995 ed.)
A.V. Arhangel'skii
R3,010 Discovery Miles 30 100 Ships in 10 - 15 working days

This reference work deals with important topics in general topology and their role in functional analysis and axiomatic set theory, for graduate students and researchers working in topology, functional analysis, set theory and probability theory. It provides a guide to recent research findings, with three contributions by Arhangel'skii and Choban.

Singular Semi-Riemannian Geometry (Hardcover, 1996 ed.): D.N. Kupeli Singular Semi-Riemannian Geometry (Hardcover, 1996 ed.)
D.N. Kupeli
R2,981 Discovery Miles 29 810 Ships in 10 - 15 working days

This book is an exposition of "Singular Semi-Riemannian Geometry"- the study of a smooth manifold furnished with a degenerate (singular) metric tensor of arbitrary signature. The main topic of interest is those cases where the metric tensor is assumed to be nondegenerate. In the literature, manifolds with degenerate metric tensors have been studied extrinsically as degenerate submanifolds of semi Riemannian manifolds. One major aspect of this book is first to study the intrinsic structure of a manifold with a degenerate metric tensor and then to study it extrinsically by considering it as a degenerate submanifold of a semi-Riemannian manifold. This book is divided into three parts. Part I deals with singular semi Riemannian manifolds in four chapters. In Chapter I, the linear algebra of indefinite real inner product spaces is reviewed. In general, properties of certain geometric tensor fields are obtained purely from the algebraic point of view without referring to their geometric origin. Chapter II is devoted to a review of covariant derivative operators in real vector bundles. Chapter III is the main part of this book where, intrinsically, the Koszul connection is introduced and its curvature identities are obtained. In Chapter IV, an application of Chapter III is made to degenerate submanifolds of semi-Riemannian manifolds and Gauss, Codazzi and Ricci equations are obtained. Part II deals with singular Kahler manifolds in four chapters parallel to Part I."

The Geometry of Infinite-Dimensional Groups (Hardcover, 2009 ed.): Boris Khesin, Robert Wendt The Geometry of Infinite-Dimensional Groups (Hardcover, 2009 ed.)
Boris Khesin, Robert Wendt
R5,676 Discovery Miles 56 760 Ships in 12 - 19 working days

The aim of this monograph is to give an overview of various classes of in?ni- dimensional Lie groups and their applications, mostly in Hamiltonian - chanics, ?uid dynamics, integrable systems, and complex geometry. We have chosen to present the unifying ideas of the theory by concentrating on speci?c typesandexamplesofin?nite-dimensionalLiegroups. Ofcourse, theselection of the topics is largely in?uenced by the taste of the authors, but we hope thatthisselectioniswideenoughtodescribevariousphenomenaarisinginthe geometry of in?nite-dimensional Lie groups and to convince the reader that they are appealing objects to study from both purely mathematical and more applied points of view. This book can be thought of as complementary to the existing more algebraic treatments, in particular, those covering the str- ture and representation theory of in?nite-dimensional Lie algebras, as well as to more analytic ones developing calculus on in?nite-dimensional manifolds. This monograph originated from advanced graduate courses and mi- courses on in?nite-dimensional groups and gauge theory given by the ?rst author at the University of Toronto, at the CIRM in Marseille, and at the Ecole Polytechnique in Paris in 2001-2004. It is based on various classical and recentresultsthathaveshapedthisnewlyemergedpartofin?nite-dimensional geometry and group theory. Our intention was to make the book concise, relatively self-contained, and useful in a graduate course. For this reason, throughout the text, we have included a large number of problems, ranging from simple exercises to open questions

Algorithmic Algebraic Combinatorics and Groebner Bases (Hardcover, 2009 ed.): Mikhail Klin, Gareth A. Jones, Aleksandar... Algorithmic Algebraic Combinatorics and Groebner Bases (Hardcover, 2009 ed.)
Mikhail Klin, Gareth A. Jones, Aleksandar Jurisic, Mikhail Muzychuk, Ilia Ponomarenko
R5,245 Discovery Miles 52 450 Ships in 10 - 15 working days

In 2006 a special semester on Gr] obner bases and related methods was or- nized by RICAM and RISC, directed by Bruno Buchberger and Heinz Engl. The main focus of the semester were the development of the formal theory of Gr] obner bases (brie?y GB), the e?cient implementation of all algorithms related to this theory, and the promotion of recent and new applications of GB. The workshop D1 "Gr] obner bases in cryptography, coding theory and - gebraic combinatorics," Linz, May 1-6, 2006 (chairmen M. Klin, L. Perret, M. Sala) was one of the main ingredients of the semester. The last two days of this workshop, devoted to combinatorics, made it possible to bring together experts in algorithmic problems related to coherent con?gurations and as- ciation schemes with a community of people working in the area of GB. Each side was interested in understanding the computational problems and current algorithmicpossibilitiesoftheother, withaparticularobjectiveofintroducing the practical use of GB in algebraic combinatorics. Materials (mainly slides of lectures and posters) available from the site http: //www.ricam.oeaw.ac.at/specsem/srs/groeb/schedule D1.htmlprovidea helpful and vivid picture of the successful exchange of scienti?c information during the workshop D1. Asafollow-uptothespecialsemester,10volumesofproceedingsarebeing published by di?erent publishers. The current collection of papers re?ects diverse investigations in the area of algebraic combinatorics (with or without explicit use of GB), but with a de?nite emphasis on algorithmic approaches."

Integrable Systems and Foliations - Feuilletages et Systemes Integrables (Hardcover, 1997 ed.): Claude Albert, Robert Brouzet,... Integrable Systems and Foliations - Feuilletages et Systemes Integrables (Hardcover, 1997 ed.)
Claude Albert, Robert Brouzet, Jean P. Dufour
R3,000 Discovery Miles 30 000 Ships in 10 - 15 working days

The articles in this volume are an outgrowth of a colloquium "Systemes Integrables et Feuilletages," which was held in honor of the sixtieth birthday of Pierre Molino.
The topics cover the broad range of mathematical areas which were of keen interest to Molino, namely, integral systems and more generally symplectic geometry and Poisson structures, foliations and Lie transverse structures, transitive structures, and classification problems.
Contributors to the volume include: Y. Benoist, G. Cairns, V. Cavalier, H. Flaschka, E. Ghys, A. Haefliger, B. Jessup, A. Lichnerowicz, G. Meigniez, I. Moerdijk, J. Pitkethly, T. Ratiu, J. Turiel, I. Vaisman, and P. Vanhaechke.

Geometric Algebra Applications Vol. I - Computer Vision, Graphics and Neurocomputing (Hardcover, 1st ed. 2019): Eduardo Bayro... Geometric Algebra Applications Vol. I - Computer Vision, Graphics and Neurocomputing (Hardcover, 1st ed. 2019)
Eduardo Bayro Corrochano
R6,359 Discovery Miles 63 590 Ships in 12 - 19 working days

The goal of the Volume I Geometric Algebra for Computer Vision, Graphics and Neural Computing is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra.Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra for instance: multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras and conformal geometry. By treating a wide spectrum of problems in a common language, this Volume I offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with the development and building of intelligent machines. Each chapter is written in accessible terms accompanied by numerous examples, figures and a complementary appendix on Clifford algebras, all to clarify the theory and the crucial aspects of the application of geometric algebra to problems in graphics engineering, image processing, pattern recognition, computer vision, machine learning, neural computing and cognitive systems.

Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds - Classical and Quantum Aspects (Hardcover, 1998 ed.): A.... Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds - Classical and Quantum Aspects (Hardcover, 1998 ed.)
A. K. Prykarpatsky, I. V. Mykytiuk
R3,201 Discovery Miles 32 010 Ships in 10 - 15 working days

In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e., characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation)."

High School Geometry (Hardcover): A H (Alexander Hiram) 1 McDougall High School Geometry (Hardcover)
A H (Alexander Hiram) 1 McDougall
R936 Discovery Miles 9 360 Ships in 12 - 19 working days
Fractal Geometry in Architecture and Design (Hardcover, 1996 ed.): Carl Bovill Fractal Geometry in Architecture and Design (Hardcover, 1996 ed.)
Carl Bovill
R3,056 Discovery Miles 30 560 Ships in 10 - 15 working days

na broad sense Design Science is the grammar of a language of images Irather than of words. Modern communication techniques enable us to transmit and reconstitute images without needing to know a specific verbal sequence language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multi dimensional. Architectural renderings commonly show projections onto three mutual ly perpendicular planes, or consist of cross sections at different altitudes capa ble of being stacked and representing different floor plans. Such renderings make it difficult to imagine buildings comprising ramps and other features which disguise the separation between floors, and consequently limit the cre ative process of the architect. Analogously, we tend to analyze natural struc tures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures. Perception is a complex process. Our senses record; they are analogous to audio or video devices. We cannot, however, claim that such devices perceive."

Lie Theory and Its Applications in Physics - Varna, Bulgaria, June 2015 (Hardcover, 1st ed. 2016): Vladimir Dobrev Lie Theory and Its Applications in Physics - Varna, Bulgaria, June 2015 (Hardcover, 1st ed. 2016)
Vladimir Dobrev
R5,762 Discovery Miles 57 620 Ships in 10 - 15 working days

This volume presents modern trends in the area of symmetries and their applications based on contributions from the workshop "Lie Theory and Its Applications in Physics", held near Varna, Bulgaria, in June 2015. Traditionally, Lie theory is a tool to build mathematical models for physical systems.Recently, the trend has been towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are employed in their widest sense, embracing representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators (PDO), special functions, and others. Furthermore, the necessary tools from functional analysis are included.

Geometry from the Pacific Rim - Proceedings of the Pacific Rim Geometry Conference held at National University of Singapore,... Geometry from the Pacific Rim - Proceedings of the Pacific Rim Geometry Conference held at National University of Singapore, Republic of Singapore, December 12-17, 1994 (Hardcover, Reprint 2011)
A. Jon Berrick, Bonaventure Loo, Hongyu Wang
R6,067 Discovery Miles 60 670 Ships in 12 - 19 working days

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Digital Sound Synthesis by Physical Modeling Using the Functional Transformation Method (Hardcover, 2003 ed.): Lutz Trautmann,... Digital Sound Synthesis by Physical Modeling Using the Functional Transformation Method (Hardcover, 2003 ed.)
Lutz Trautmann, Rudolf Rabenstein
R3,018 Discovery Miles 30 180 Ships in 10 - 15 working days

This book considers signal processing and physical modeling meth ods for sound synthesis. Such methods are useful for example in mu sic synthesizers, computer sound cards, and computer games. Physical modeling synthesis has been commercialized for the first time about 10 years ago. Recently, it has been one of the most active research topics in musical acoustics and computer music. The authors of this book, Dr. Lutz Trautmann and Dr. Rudolf Rabenstein, are active researchers and inventors in the field of sound synthesis. Together they have developed a new synthesis technique, called the functional transformation method, which can be used for pro ducing musical sound in real time. Before this book, they have published over 20 papers on the topic in journals and conference proceedings. In this excellent textbook, the results are combined in a single volume. I believe that this will be considered an important step forward for the whole community."

Perspectives on the Teaching of Geometry for the 21st Century - An ICMI Study (Hardcover, 1998 ed.): Carmelo Mammana, V. Villani Perspectives on the Teaching of Geometry for the 21st Century - An ICMI Study (Hardcover, 1998 ed.)
Carmelo Mammana, V. Villani
R4,560 Discovery Miles 45 600 Ships in 10 - 15 working days

In recent years geometry seems to have lost large parts of its former central position in mathematics teaching in most countries. However, new trends have begun to counteract this tendency. There is an increasing awareness that geometry plays a key role in mathematics and learning mathematics. Although geometry has been eclipsed in the mathematics curriculum, research in geometry has blossomed as new ideas have arisen from inside mathematics and other disciplines, including computer science. Due to reassessment of the role of geometry, mathematics educators and mathematicians face new challenges. In the present ICMI study, the whole spectrum of teaching and learning of geometry is analysed. Experts from all over the world took part in this study, which was conducted on the basis of recent international research, case studies, and reports on actual school practice. This book will be of particular interest to mathematics educators and mathematicians who are involved in the teaching of geometry at all educational levels, as well as to researchers in mathematics education.

The Geometry of Higher-Order Lagrange Spaces - Applications to Mechanics and Physics (Hardcover, 1997 ed.): R. Miron The Geometry of Higher-Order Lagrange Spaces - Applications to Mechanics and Physics (Hardcover, 1997 ed.)
R. Miron
R4,552 Discovery Miles 45 520 Ships in 10 - 15 working days

This monograph is mostly devoted to the problem of the geome- trizing of Lagrangians which depend on higher order accelerations. It naturally prolongs the theme of the monograph "The Geometry of La- grange spaces: Theory and Applications", written together with M. Anastasiei and published by Kluwer Academic Publishers in 1994. The existence of Lagrangians of order k > 1 has been contemplated by mechanicists and physicists for a long time. Einstein had grasped their presence in connection with the Brownian motion. They are also present in relativistic theories based on metrics which depend on speeds and accelerations of particles or in the Hamiltonian formulation of non- linear systems given by Korteweg-de Vries equations. There resulted from here the methods to be adopted in their theoretical treatment. One is based on the variational problem involving the integral action of the Lagrangian. A second one is derived from the axioms of Analytical Mechanics involving the Poincare-Cartan forms. The geometrical methods based on the study of the geometries of higher order could invigorate the whole theory. This is the way adopted by us in defining and studying the Lagrange spaces of higher order. The problems raised by the geometrization of Lagrangians of order k > 1 investigated by many scholars: Ch. Ehresmann, P. Libermann, J. Pommaret; J.T. Synge, M. Crampin, P. Saunders; G.S. Asanov, P.Aringazin; I. Kolar, D. Krupka; M. de Leon, W. Sarlet, P. Cantrjin, H. Rund, W.M. Tulczyjew, A. Kawaguchi, K. Yano, K. Kondo, D.

Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change (Hardcover, 2012 ed.): Jayce Getz,... Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change (Hardcover, 2012 ed.)
Jayce Getz, Mark Goresky
R1,566 Discovery Miles 15 660 Ships in 10 - 15 working days

In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface. They then computed the Fourier coefficients of these forms in terms of period integrals and L-functions. In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adelic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.

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