Geometry Books

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Book SynopsisSpecialized as it might be, continuum theory is one of the most intriguing areas in mathematics. However, despite being popular journal fare, few books have thoroughly explored this interesting aspect of topology. In Topics on Continua, Sergio Macías, one of the field's leading scholars, presents four of his favorite continuum topics: inverse limits, Jones's set function T, homogenous continua, and n-fold hyperspaces, and in doing so, presents the most complete set of theorems and proofs ever contained in a single topology volume. Many of the results presented have previously appeared only in research papers, and some appear here for the first time. After building the requisite background and exploring the inverse limits of continua, the discussions focus on Professor Jones''s set function T and continua for which T is continuous. An introduction to topological groups and group actions lead to a proof of Effros''s Theorem, followed by a presentTable of ContentsPreliminaries, including an introduction to Product Topology. Inverse Limits and Related Topics. Jones Set Function T. A Theorem of E.G. Effros. Decomposition Theorems. n-Fold Hyperspaces. Questions.

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Book Synopsis"Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems. Before the complete solution of every problem, a key idea is presented so that the reader will be able to provide the solution.Trade ReviewFrom the reviews:“Sotirios E. Louridas and Michael Th. Rassias, the authors of the book at hand, put together an excellent collection of problems for practice. They provide detailed solutions following the masters of that skill. … an active reader would greatly benefit from reading the book; while working out the problems is bound to sharpen his or her problem solving skills. … it’s a worthy addition to a library of a problem solver.” —Alex Bogomolny, MAA Reviews, December, 2013"The book is a wonderful presentation of the essential concepts, ideas and results of Euclidean Geometry useful in solving olympiad problems of various level of difficulties. The theoretical part is excellently illustrated by challenging olympiad problems. The complete solutions to these problems are carefully presented, most of them together with several interesting comments and remarks. ... All in all the text is a highly recommendable choice for any olympiad training program, and fills some gaps in the existing literature in Euclidean Geometry. The book is a very useful source of models and ideas for students, teachers, heads of national teams and authors of problems, as well as for people who are interested in mathematics and solving difficult problems."—Mihaly Bencze, EMS Newsletter, November 2013"A subject of high interest for problem-solving in Euclidean Geometry is the application of geometric transformations ... The authors have succeeded to study with great accuracy these transformations. Additionally, they have applied them in order to obtain very nice solutions for some quite challenging problems ... The book is full of new and challenging ideas that will provide guidance and inspiration for future study in the fundamental area of Euclidean Geometry. The large collection of problems in this book provides a valuable recourse for advanced high school students, university undergraduates, instructors, and Mathematics coaches preparing students to participate in mathematical Olympiads...."—Nicusor Minculete, Gazeta Matematică, Seria B., 10/2013"This book provides an essential presentation of concepts and ideas as well as problems with their solutions in Euclidean Geometry, a traditional and still challenging part of Geometry.—Dorian Andrica, Zentralblatt"The book is mainly devoted to several very interesting problems, some of which constructed by the authors, that have been presented in a rigorous and self-contained manner. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry. The book will be of particular interest to students and teachers who train them for Mathematical Olympiads and other Mathematical Contests. Additionally to everyone who enjoys studying some of the jewels of Euclidean Geometry and has some special love for good problems and beautiful ideas. ... The Foreword of the book has been written by Michael H. Freedman (Fields Medal in Mathematics, 1986) ... The authors deserve congratulations for their excellent effort and success to provide a high quality service in fundamental mathematics. " —Jose Luis Diaz Barrero, Octogon Mathematical Magazine, October 2013"Sixty-five problems and their solutions are arranged in three parts: problems based on basic theory, problems based on advancedtheory, and geometric inequalities. Some problems were included in International Mathematical Olympiads (IMOs) or proposed in short lists in IMOs ... the problem part of the book ... contains a collection of interesting problems. ... Chapter 4 seeks to "present some of the most essential theorems of Euclidean Geometry". Some of these theorems (Pythagoras', Ceva's, Menelaus') are important indeed and applicable to many problems."—Yury J. Ionin, Mathematical Reviews, January 2014"There are many excellent books on plane Euclidean geometry, exploring the subject at various levels. The book under review, which is foreworded by Michael H. Freedman (Fields Medal, 1986), adds yet another facet to this colorful subject. This delightful book presents a collection of problems in plane Euclidean geometry in the spirit of mathematical olympiads, along with their solutions. Additionally, it provides essential theory of plane Euclidean geometry, with proofs of some fundamental theorems. As such, this monograph is an excellent training manual to use in preparation for mathematical competitions and olympiads. Hence, this is a book that belongs in all academic libraries, from high school through graduate level." —Abraham A. Ungar, Acta Universitatis Apulensis, 40/2014.Table of ContentsForeword.- Preface.- Basic Concepts and Theorems of Euclidean Geometry.- Methods of Analysis, Synthesis, Construction and Proof.-Geometrical Constructions.- Geometrical Loci.- Problems of Olympiad Caliber.- Solutions of the Problems.- Bibliography.- Index.

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Book SynopsisDesigned for a one-semester course at the junior undergraduate level, Transformational Plane Geometry takes a hands-on, interactive approach to teaching plane geometry. The book is self-contained, defining basic concepts from linear and abstract algebra gradually as needed.The text adheres to the National Council of Teachers of Mathematics Principles and Standards for School Mathematics and the Common Core State Standards Initiative Standards for Mathematical Practice. Future teachers will acquire the skills needed to effectively apply these standards in their classrooms. Following Felix Klein's Erlangen Program, the book provides students in pure mathematics and students in teacher training programs with a concrete visual alternative to Euclid's purely axiomatic approach to plane geometry. It enables geometrical visualization in three ways: Key concepts are motivated with explorTrade Review"This book is designed for a one-semester course at the junior undergraduate level and turns especially to future educators in the USA. … The arrangement and clarity of the text meet the most demanding pedagogical and mathematical requirements. Highlights of the book are the classification of isometries and similarities of the Euclidean plane. … a wonderful first step into transformational plane geometry …"—Zentralblatt MATH 1311 Table of ContentsAxioms of Euclidean Plane Geometry. Theorems of Euclidean Plane Geometry. Introduction to Transformations, Isometries, and Similarities. Translations, Rotations, and Reflections. Compositions of Translations, Rotations, and Reflections. Classification of Isometries. Symmetry of Plane Figures. Similarity. Appendix. Bibliography. Index.

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Book SynopsisBlow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book first studies the particular self-similar singularity solutions (patterns) of the equations. This approach allows four different classes of nonlinear PDEs to be treated simultaneously to establish their striking common features. The book describes many properties of the equations and examines traditional questions of existence/nonexistence, uniqueness/nonuniqueness, global asymptotics, regularizations, shock-wave theory, and various blow-up singularities.Preparing readers for more advanced mathematical PDE analysis, the book demonstrates that quasilinear degenerate higher-order PDEs, even exoticTrade Review"This volume gives a collection of results on self-similar singular solutions for nonlinear partial differential equations (PDEs), with special emphasis on ‘exotic’ equations of higher order …"—Zentralblatt MATH 1320Table of ContentsIntroduction. Complicated Self-Similar Blow-Up, Compacton, and Standing Wave Patterns for Four Nonlinear PDEs: A Unified Variational Approach to Elliptic Equations. Classification of Global Sign-Changing Solutions of Semilinear Heat Equations in the Subcritical Fujita Range: Second- and Higher-Order Diffusion. Global and Blow-Up Solutions for Kuramoto–Sivashinsky, Navier–Stokes, and Burnett Equations. Regional, Single-Point, and Global Blow-Up for a Fourth-Order Porous Medium-Type Equation with Source. Semilinear Fourth-Order Hyperbolic Equation: Two Types of Blow-Up Patterns. Quasilinear Fourth-Order Hyperbolic Boussinesq Equation: Shock, Rarefaction, and Fundamental Solutions. Blow-Up and Global Solutions for Korteweg–de Vries-Type Equations. Higher-Order Nonlinear Dispersion PDEs: Shock, Rarefaction, and Blow-Up Waves. Higher-Order Schrödinger Equations: From "Blow-Up" Zero Structures to Quasilinear Operators. References.

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Book SynopsisThe first part of this book introduces the Schubert Cells and varieties of the general linear group Gl (k^(r+1)) over a field k according to Ehresmann geometric way. Smooth resolutions for these varieties are constructed in terms of Flag Configurations in k^(r+1) given by linear graphs called Minimal Galleries. In the second part, Schubert Schemes, the Universal Schubert Scheme and their Canonical Smooth Resolution, in terms of the incidence relation in a Tits relative building are constructed for a Reductive Group Scheme as in Grothendieck''s SGAIII. This is a topic where algebra and algebraic geometry, combinatorics, and group theory interact in unusual and deep ways.Table of ContentsGrassmannians and Flag Varieties. Schubert Cell Decomposition of Grassmannians and Flag Varieties. Resolution of Singularities of a Schubert Variety. The Singular Locus of a Schubert Variety. The Flag Complex. Configurations and Galleries Varieties. Configurations Varieties as Galleries Varieties. The Coxeter Complex. Minimal Generalized Galleries in a Coxeter Complex. Minimal Generalized Galleries in a Reductive Group Building. Parabolic Subgroups in a Reductive Group Scheme. Associated Schemes to the Relative Building. Incidence Type Schemes of the Relative Building. Smooth Resolutions of Schubert Schemes. Contracted Products and Galleries Configurations Schemes. Functoriality of Schubert Schemes Smooth Resolutions and Base Changes. About the Coxeter Complex. Generators and Relations and the Building of a Reductive Group.

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Book SynopsisThis volume records the proceedings of an international conference that explored recent developments and the interaction between mathematical theory and physical phenomena.Table of ContentsNON-COMMUTATIVE SPHERES and NUMERICAL QUANTUM MECHANICS; Matricial and Ultramatricial Topology; Remarks on the Three-Manifold Invariants ? p; The Crossed Product of the Irrational Rotation Algebra by the Flip; Quadratic and Exchange Algebras, and Modified Yang-Baxter Relations for the Selfdual Yang-Mills System and the WZNW Model; Regular Actions of Hopf Algebras on the C*-Algebra Generated by a Hilbert Space; Operator Algebras, Group Actions and Abstract Duals; A Classification of Certain Simple C*-Algebras; On Two Quantized Tensor Products 1; Geometry of Differential Equations and Projective Representations of the witt Algebra; Spin Model on Knot Projections; Towards Extracting Physical Predictions from Alain Connes' Version of the Standard Model (The New Grand Unification?); A Commutator Inequality; Duals of Compact Groups Realized by Semigroups of Non-Unital Endomorphisms of C *-Algebras; A New Index for Continuous Semigroups of *-Endomorphisms of B(H); Topological Orbit Equivalence; Toeplitz C *-Alegras on Pseudoconvex Domains with Transverse Symmetries; Normal Subgroups of the Automorphism Group of a Factor; Subfactors and Invariants of 3-Manifolds

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Book SynopsisThis volume documents the results and presentations, related to aspects of geometric design, of the Second International Conference on Curves and Surfaces, held in Chamonix in 1993. The papers represent directions for future research and development in many areas of application. From the table of contents: - Object Oriented Spline Software - An Introduction to Pade Approximations - Zonoidal Surfaces - Projective Blossoms and Derivatives - Piecewise Polynomial Approximation of Spheres - A Geometrical Approach to Interpolation on Quadric Surfaces

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Book SynopsisComprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress. This lively and very successful event drew the attendance of many top researchers, who offered both individual lectures and coordinated courses on specific research topics within this fast growing subject.Harmonic Analysis and Integral Geometry presents important recent advances in the fields of Radon transforms, integral geometry, and harmonic analysis on Lie groups and symmetric spaces. Several articles are devoted to the new theory of Radon transforms on trees.With its related presentations addressing recent developments in various aspects of these intriguing areas of study, Harmonic Analysis and Integral Geometry becomes an important addition not only to the Research Notes in Mathematics series, but to the general mathematics literature.Table of ContentsJohn's Equation and the Plane to Line Transform on R3. Radon Transforms on Compact Grassmann Manifolds and Invariant Differential Operators of Determinantal Type. Invariant Berezin Transforms. Integral Geometry on Hyperbolic Spaces. On Laguerre Polynomials of Two Variables. A Topological Obstruction for the Real Radon Transform. Integral Geometry in the Sphere Sd. The Distribution-Valued Horocyclic Radon Transform on Trees. The Geodesic Radon Transform on Trees. Integral Geometry on Affine Buildings. Poisson Transform on H3. Realization of a Holomorphic Discete-Series of the Lie Group SU(1,2) as Star-Representation. q-Analogue of Watanabe Unitary Transform Associated to the q-Continuous Gegenbauer Polynomials.

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Book SynopsisThis book is a collection of research papers and surveys on algebra that were presented at the Conference on Groups, Rings, and Group Rings held in Ubatuba, Brazil. This text familiarizes researchers with the latest topics, techniques, and methodologies in several branches of contemporary algebra. With extensive coverage, it examines broad themes from group theory and ring theory, exploring their relationship with other branches of algebra including actions of Hopf algebras, groups of units of group rings, combinatorics of Young diagrams, polynomial identities, growth of algebras, and more. Featuring international contributions, this book is ideal for mathematicians specializing in these areas.Table of Contents1. On fine gradings on central simple algebras 2. On observable module categories 3. Group gradings on integral group rings 4. Profinite graphs – comparing notions 5. Lie identities in symmetric elements in group rings: A survey 6. Irreducible morphisms in subcategories 7. Bol loops with a unique nonidentity commutator/associator 8. Weil representations of symplectic groups 9. Gradings and graded identities for the upper triangular matrices over an infinite field 10. Structure of some classes of repeated-root constacyclic codes over integers modulo 2m 11. Units in noncommutative orders 12. Idempotents in group algebras and coding theory 13. Finitely generated constants of free algebras 14. Partial actions of groups on semiprime rings 15. Representations of affine Lie superalgebras 16. On algebras and superalgebras with linear codimension growth 17. On spectra of group rings of finite abelian groups 18. Wedderburn decomposition of small rational group algebras 19. Some questions on skewfields 20. On the role of rings and modules in algebraic coding theory 21. Semiperfect rings with T-nilpotent prime radical 22. The structure of the baric algebras 23. On torsion units of integral group rings of groups of small order 24. On a conjecture of Zassenhaus for metacyclic groups 25. Nilpotent blocks revisited 26. Decomposition of central units of integral group rings 27. Generic units in ZC 28. On quasi-Frobenius semigroup algebras 29. Twisted loop algebras and Galois cohomology 30. Presentation of the group of units of ZD 31. Engel theorem for Jordan rational group algebras.

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Book SynopsisAn examination of Neolithic timber circles in the east of England with reference to Alexander Thom's work on the geometrical setting out and astronomical alignments of stone circles in the west of Britain

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Book SynopsisWhile the architecture of present-day parallel supercomputers is largely based on the concept of a shared memory, with its attendant limitations of common access, advances in semicoductor technology have led to the development of highly parellel computer architectures with decentralized storage and limited connections in which each processor possesses high bandwidth local memory connected to a small number of such architectures, enabling cost-effective high-speed parallel processing for large volumes of data, with ultra-high throughput rates. Algorithms suitable for implementation on systolic arrays find applications in areas such as signal and image processing, pattern matching, linear algebra, recurrence algorithms and graph problems. This book provides an insight into the implementation of systolic arrays and gives a comprehensive overview of the techniques and theories contributing to the design of systolic algorithms.Table of ContentsPREFACE 1. INTRODUCTION Systolic Algorithms 2. POLYNOMIAL AND ROOT FINDING METHODS 3. SYSTOLIC MATRIX OPERATIONS 4. QUADRATURE AND DIFFERENTIAL EQUATIONS 5 . SOLUTION OF LINEAR SYSTEMS 6. EIGENV ALOE-EIGENVECTOR COMPUTATIONS 7. LINEAR AND DYNAMIC PROGRAMMING

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Book SynopsisThe 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.

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Table of ContentsI. Analytischer Aufbau der Geometrie.- 1. Geometrie als Analysis.- 2. Kongruenz und Bewegungen.- 3. Transitivität der Kongruenz und Gruppeneigenschaft der Bewegungen...- 4. Überblick.- 1. Gruppen von Transformationen.- 1. Eineindeutige Transformationen.- 2. Das assoziative Gesetz.- 3. Gruppen.- 4. Untergruppen, Isomorphismen.- 5. Kongruenz.- 6. Bezugsmengen.- 7. Grundmenge und Koordinatenvektor.- 8. Natürliche Koordinaten.- 9. Transitive, asystatische Gruppen von Transformationen.- 10. Einfach transitive Transformationsgruppen.- 11. Kongruenz nach Untergruppen.- 12. Lineare Transformationen und euklidische Geometrie.- 13. Affine Transformationen. Lineare Abhängigkeit.- 14. Bezugsmengen.- 15. Grundmenge. Koordinatenvektoren.- 16. Projektive Transformationen. Lineare Abhängigkeit.- 17. Affine und projektive Transformationen.- 18. Der Begriff des Punktes.- 2. Grundlagen der Algebra.- 1. Körper.- 2. Automorphismen. Zentrum. Rationale Zahlen.- 3. Geordnete Körper. Geordnete Gruppen.- 4. Reelle Zahlen als geordnete Gruppe.- 5. Kommutatives Gesetz der Addition. Unabhängigkeit.- 6. Quaternionen.- 7. Funktionenkörper.- 8. Geordnete Schiefkörper.- 9. Einseitig distributives Zahlensystem.- 10. Die Gleichung xa + xb = c.- 11. Über Axiome.- 3. Affine Geometrie.- 1. Homogene affine Transformationen.- 2. Bezugsmengen.- 3. Lineare Abhängigkeit von Vektoren.- 4. Vektorbasis und lineare Abhängigkeit.- 5. Lineare Mannigfaltigkeiten.- 6. Allgemeine homogene lineare Transformationen.- 7. Geometrische Formulierung der Kongruenzbedingung.- 8. Affine Geometrie.- 9. Affine Abbildungen und Projektionen.- 10. Projektive Transformationen.- 11. Kennzeichnung der Transformationen.- II. Axiomatischer Aufbau der Geometrie.- 1. Grundsätze.- 2. Vollständigkeit.- 3. Auswahl der Axiome.- 4. Gewebe und Gruppen.- 1. Die Inzidenzaxiome des 3-Gewebes.- 2. Definition der Vektorgleichheit.- 3. Das erste Schließungsaxiom, ?.1.- 4. Transitivität der Vektorgleichheit. Eindeutigkeit.- 5. Die drei Vektorgruppen.- 6. Isomorphic der Vektorgruppen.- 7. Analytische Darstellung eines 3-Gewebes.- 8. Konstruktion eines Gewebes aus einer Gruppe.- 9. Abbildungen eines Gewebes in sich.- 10. Translationen.- 11. Uneigentliche Punkte.- 12. Kommutative Vektorgruppe und Figur ?.2.- 13. Figur ?.1 folgt aus ?. 2.- 14. Die Axiome der Anordnung.- 15. Richtungsgleichheit als Vektoreigenschaft.- 16. Vektoren als geordnete Gruppe.- 17. Gewebe und reelle Zahlen.- 18. Stetigkeit und Sechseckgewebe.- 19. Mittelpunkt einer Strecke.- 20. Netz der Punkte Ar,8.- 21. Archimedisches Axiom im Sechseckgewebe.- 22. Gewebe und affine Ebene.- 23. Kollineationen.- 5. Die Vektoren der affinen Ebene.- 1. Inzidenzaxiome eines 4-Gewebes.- 2. Geradenisomorphismen und Figur ?. 3.- 3. Die Parallelen der D-Geraden.- 4. Der kleine Desarguessche Satz ?.?.- 5. Dreieckssätze.- 6. Proportionen.- 7. Vektoren der affinen Ebene.- 8. Zerlegung eines Vektors in n gleiche Teile.- 9. Rationales Netz. Anordnungsaxiome.- 10. Kommutative Vektorgruppe.- 11. Figur ?.2 und Figur ?.?.- 12. Parallelismus in der affinen Geometrie.- 13. Vektorgleichheit von Dreiecken.- 14. Proportionen. Vektoren.- 6. Gewebe und Zahlensysteme.- 1. Die Geradenautomorphismen als Gruppe.- 2. Die Multiplikation der A-Vektoren.- 3. Das Zahlensystem der Vektorpaare.- 4. D-Maßzahlen.- 5. Streckenverhältnisse als Zahlensystem.- 6. Analytische Darstellung.- 7. Kollineationen.- 8. Zweites distributives Gesetz und Figur ?.4.- 9. Das 4-Gewebe mit der Figur ?.4.- 10. Analytische Darstellung eines 4-Gewebes mit Figur ?.4.- 11. Streckenverhältnisse als Schiefkörper.- 12. Literatur über Gewebe.- 7. Affine und projektive Geometrie.- 1. Die Axiome der ebenen affinen Geometrie.- 2. Begründung der Streckenrechnung aus den affinen Axiomen.- 3. Fundamentalsatz der affinen Geometrie.- 4. Die räumlichen Inzidenzaxiome und der Satz von Desargues…..- 5. Die projektiven Inzidenzaxiome.- 6. Der Satz von Desargues in der projektiven Ebene.- 7. Die Streckenverhältnisse in der projektiven Ebene.- 8. Der Fundamentalsatz der projektiven Geometrie.- 9. Der Satz von Pascal.- 10. Der Satz von Desargues folgt aus dem Satz von Pascal.- 11. Strecken Verhältnisse auf Grund des Pascalschen und kleinen Desargues- schen Satzes.- 12. Widerspruchsfreiheit der Axiome.- 13. Unabhängigkeit der Axiome.- 14. Algebraischer und geometrischer Aufbau.- 15. Der empirische Raum.

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Book SynopsisDie „Geometrie und ihre Anwendungen“ ist für Personen geschrieben, die von relativ einfachen Problemen der ebenen Geometrie bis hin zu schwierigeren Aufgaben der Raumgeometrie Interesse an geometrischen Zusammenhängen haben. Ähnlich wie beim „mathematischen Werkzeugkasten“ stehen Anwendungen aus verschiedenen Disziplinen wie dem Ingenieurwesen, der Biologie, Physik, Astronomie, Geografie, Fotografie, Kunstgeschichte, ja sogar der Musik im Vordergrund. Die Anwendungsbeispiele veranschaulichen wichtige Begriffe der Geometrie wie Normalprojektion und Zentralprojektion, Krümmung von Kurven und Flächen, der Geometrie der Bewegung und sogar der Geometrie nichteuklidischer Räume. Stets hat die Raumvorstellung Vorrang. Das Buch kann daher auch von Personen ohne spezielle mathematische Vorbildung gelesen werden. Damit aber auch mathematisch Versierte nicht zu kurz kommen, wird ein analytisches Konzept mitgeliefert. Zwei praktische Kurse runden das Werk ab: zum geometrischen Freihandzeichnen und zur Geometrie des Fotografierens. Leicht verständliche Tipps sollen den Leser zur Fähigkeit hinführen, selbstständig prägnante und korrekte Raumskizzen zu machen, die der Schlüssel für alles tiefere Verständnis in der Geometrie sind. Dass geometrische Einsichten wiederum auch förderlich für Ästhetik und Aussagekraft von Fotos sind, beweisen nicht zuletzt Hunderte von Fotos in allen Kapiteln. Der Leser kann, je nach Vorbildung, an den verschiedensten Stellen beginnen. Durch Querverweise ist der Zusammenhang mit anderen Abschnitten rasch hergestellt. Die vierte Auflage ist gegenüber der dritten Auflage noch einmal um nahezu 200 Seiten ergänzt worden und enthält neben vielen neuen Anwendungsbeispielen zusätzliche neue Kapitel, etwa über optische Täuschungen und Fraktale.Table of ContentsEinleitung.- 1 Eine idealisierte Welt aus einfachen Bausteinen.- 2 Projektionen und Schatten: Die Reduktion der Dimension.- 3 Polyeder: Vielflächig und vielseitig.- 4 Gekrümmt und doch einfach.- 5 Mehr über Kegelschnitte und abwickelbare Flächen.- 6 Prototypen.- 7 Weitere bemerkenswerte Flächenklassen.- 8 Die unendliche Vielfalt der gekrümmten Flächen.- 9 Fotografische Abbildung und individuelle Wahrnehmung.- 10 Alles bewegt sich: Kinematik.- 11 Bewegung im Raum.- 12 Die Vielfalt der Füllmuster.- 13 Die Natur der Geometrie und die Geometrie der Natur.- Anhang A: Ein Kurs im Freihandzeichnen.- Anhang B: Ein geometrischer Fotografiekurs.- Literaturverzeichnis.- Index.

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Book SynopsisThe conical approach provides a geometrical understanding of optimization and is a powerful research tool and useful problem-solving technique (for example, in decision support and real time control applications). Conical optimality conditions are first stated in a very general optimization framework, and then applied to linear programming. A complete theory along with primal and dual algorithms is given, and solutions and algorithms are also provided for vector and robust linear optimization. The advantages of parameter dependence of conical methods are fully discussed. In addition to numerical results, the book provides source codes and detailed documentation of a Modula-2 implementation for the main algorithms.Table of ContentsPart I: General Theory Part II: Further Advanced Results Part III: Implementations and Numerical Results

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Book SynopsisStarting from the foundations, this text presents an almost entirely self-contained treatment of differentiable spaces of nonpositive curvature, focusing on the symmetric spaces in which every geodesic lies in a flat Euclidean space of dimension at least two.

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Book SynopsisTrade Review"Zimmer is one of the most influential contemporary American mathematicians. The corpus of Zimmer's contributions stands out by its coherence and its grand vision. Much more than being a strong problem-solver, more even than being a theory-builder, Zimmer is a mathematician with an overarching sense of the destination, with a domineering command of all relevant available techniques, with the inspiration to bring to life those techniques that were not available yet, with, in conclusion and to use a trivial formulation, a program."--Nicolas Monod, cole polytechnique f d rale de Lausanne --Nicolas Monod, cole polytechnique f d rale de Lausanne

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Book SynopsisGroup actions are an efficient way of describing symmetries in objects by defining the essential elements of a given object as a set. The symmetries of the object are then defined as the symmetry group of this set. This title explores group actions on the simplest closed manifold, the circle.

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Book SynopsisThis text provides topologists with a new way of looking at the classification theory of singular spaces. Divided into three parts, the book begins with an overview of high-dimensional manifold theory. It then offers the parallel theory for stratified spaces. Applications are also included.Table of ContentsPart 1 Manifold theory: algebraic K-theory and topology; surgery theory; spacification and functoriality; applications. Part 2 General theory: definitions and examples; classification of stratified spaces; transverse stratified classification; PT category; controlled topology; proof of main theorems in topology. Part 3 Applications and illustrations: manifolds and embedding theory revisited; supernormal spaces and varieties; group actions; rigidity conjectures.

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Book SynopsisFrom two authors who embrace technology in the classroom and value the role of collaborative learning comes College Geometry Using The Geometer''s Sketchpad, a book that is ideal for geometry courses for both mathematics and math education majors. The book''s truly discovery-based approach guides students to learn geometry through explorations of topics ranging from triangles and circles to transformational, taxicab, and hyperbolic geometries. In the process, students hone their understanding of geometry and their ability to write rigorous mathematical proofs.Table of ContentsPREFACE xv ONE Using The Geometer’s Sketchpad 1 TWO Constructing → Proving 21 THREE Mathematical Arguments and Triangle Geometry 53 FOUR Circle Geometry and Proofs 85 FIVE Analytic Geometry 111 SIX Taxicab Geometry 143 SEVEN Finite Geometries 161 EIGHT Transformational Geometry 185 NINE Isometries and Matrices 209 TEN Symmetry in the Plane 229 ELEVEN Hyperbolic Geometry 253 TWELVE Projective Geometry 287 APPENDIX A Trigonometry 317 APPENDIX B Calculating with Matrices 329 BIBLIOGRAPHY 337 INDEX 341

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Book SynopsisYou, too, can understand geometry just ask Dr. Math! Are things starting to get tougher in geometry class? Don''t panic. Dr. Maththe popular online math resourceis here to help you figure out even the trickiest of your geometry problems. Students just like you have been turning to Dr. Math for years asking questions about math problems, and the math doctors at The Math Forum have helped them find the answers with lots of clear explanations and helpful hints. Now, with Dr. Math Presents More Geometry, you''ll learn just what it takes to succeed in this subject. You''ll find the answers to dozens of real questions from students in a typical geometry class. You''ll also find plenty of hints and shortcuts for using coordinate geometry, finding angle relationships, and working with circles. Pretty soon, everything from the Pythagorean theorem to logic and proofs will make more sense. Plus, you''ll get plenty of tips for working with all kinds of real-life problems.<Table of ContentsIntroduction. PART 1. POINTS, LINES, PLANES, ANGLES, AND THEIR RELATIONSHIPS. 1. Angle relationships and perpendicular and parallel lines. 2. Proving lines parallel. 3. The parallel postulate. 4. Coordinates and distance. Resources on the Web. PART 2. LOGIC AND PROOF. 1. Introduction to logic. 2. Direct proof. 3. Indirect proof. Resources on the Web. PART 3. TRIANGLES: PROPERTIES, CONGRUENCE, AND SIMILARITY. 1. Triangle Inequality Property. 2. Centers of triangles. 3. Isosceles and equilateral triangles. 4. Congruence in triangles-SSS, SAS, ASA, and SSA. 5. Similarity in triangles. 6. Congruence proofs. Resources on the Web. PART 4. QUADRILATERALS AND OTHER POLYGONS. 1. Properties of Polygons. 2. Properties of Quadrilaterals. 3. Area and Perimeter of Quadrilaterals. Resources on the Web. PART 5. CIRCLES AND THEIR PARTS. 1. Tangents. 2. Arcs and Angles. 3. Chords. Resources on the Web.

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Book SynopsisThis book addresses the most efficient methods of pattern analysis using wavelet decomposition. Readers will learn to analyze data in order to emphasize the differences between closely related patterns and then categorize them in a way that is useful to system users.Trade Review"...provides a valuable summary of data reduction." (Technometrics, May 2002) "...effectively describes and summarizes an emerging new field, namely, scientific data modeling and analysis." (Mathematical Reviews, 2003h)Table of ContentsPreface. Acknowledgments. INTRODUCTION. Pattern Analysis as Data Reduction. Vector Spaces and Linear Transformations. OPTIMAL ORTHOGONAL PATTERN REPRESENTATIONS. The Karhunen-Loève Expansion. Additional Theory, Algorithms and Applications. TIME, FREQUENCY AND SCALE ANALYSIS. Fourier Analysis. Wavelet Expansions. ADAPTIVE NONLINEAR MAPPINGS. Radial Basis Functions. Neural Networks. Nonlinear Reduction Architectures. Appendix A Mathemetical Preliminaries. References. Index.

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Book SynopsisThis classic work is now available in an unabridged paperback edition. The Second Edition retains all the characterisitcs that made the first edition so popular: brilliant exposition, the flexibility permitted by relatively self-contained chapters, and broad coverage ranging from topics in the Euclidean plane, to affine geometry, projective geometry, differential geometry, and topology. The Second Edition incorporates improvements in the text and in some proofs, takes note of the solution of the 4-color map problem, and provides answers to most of the exercises.Table of ContentsPart I Triangles 3 Regular Polygons 26 Isometry in the Euclidean Plane 39 Two-Dimensional Crystallography 50 Similarity in the Euclidean Plane 67 Circles and Spheres 77 Isometry and Similarity in Euclidean Space 96 Part II Coordinates 107 Complex Numbers 135 The Five Platonic Solids 148 The Golden Section and Phyllotaxis 160 Part III Ordered Geometry 175 Affine Geometry 191 Projective Geometry 229 Absolute Geometry 263 Hyperbolic Geometry 287 Part IV Differential Geometry of Curves 307 The Tensor Notation 328 Differential Geometry of Surfaces 342 Geodesics 366 Topology of Surfaces 379 Four-Dimensional Geometry 396 Tables 413 References 415 Answers to Exercises 419 Index 459

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Book SynopsisThe Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media Second Edition Roland W. Lewis, University of Wales Swansea, UK Bernard A.Table of ContentsMechanics of Saturated and Partially Saturated Porous Media. Numerical Solution for Isothermal Consolidation. Solid-Phase Constitutive Relationships, Variable Permeabilities and Solution Procedures. Verification of Elastic and Elastoplastic Consolidation Programs. Modelling Subsidence: Numerical Aspects and Problems of Regional Scale. Modelling Subsidence: Case Studies. Modelling Three-Phase Flow in Deforming Saturated Oil Reservoirs. Fractured Reservoir Simulation. Heat and Fluid Flow in Deforming Porous Media. Secondary Consolidation Creep in Solids. Soil-Structure Interaction. Back Analysis in Consolidation. Large-Strain Quasi-Static and Dynamic Soil Behaviour. Subject Index.

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Book SynopsisThis superb text describes a novel and powerful method for allowing design engineers to firstly model a linear problem in heat conduction, then build a solution in an explicit form and finally obtain a numerical solution. It constitutes a modelling and calculation tool based on a very efficient and systemic methodological approach. Solving the heat equations through integral transforms does not constitute a new subject. However, finding a solution generally constitutes only one part of the problem. In design problems, an initial thermal design has to be tested through the calculation of the temperature or flux field, followed by an analysis of this field in terms of constraints. A modified design is then proposed, followed by a new thermal field calculation, and so on until the right design is found. The thermal quadrupole method allows this often painful iterative procedure to be removed by allowing only one calculation. The chapters in this book increase in complexiTrade Review"The book can be highly recommended to anyone who works in the area of integral transforms and heat transfer". (Zentralblatt MATH, Vol.964, No.14, 2001)Table of ContentsInterest in the Quadrupole Approach. Linear Conduction and Simple Geometries. One-Dimensional Quadrupoles. Multidimensional Transfers. Time-Dependent Periodic Regimes. Advanced Quadrupoles. Mass Transfer in a Porous Medium. The Quadrupole Approach Applied to Heat Transfer in Semi-Transparent Materials. Inverse Laplace Transform. Appendices. Index.

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Book SynopsisFibre bundles are an integral part of differential geometry. This book begins with an introduction to bundles, including such topics as differentiable manifolds and covering spaces. It then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles.Table of ContentsPart I. THE GENERAL THEORY OF BUNDLES 1. Introduction 3 2. Coordinate bundles and fibre bundles 6 3. Construction of a bundle from coordinate transformations 14 4. The product bundle 16 5. The Ehresmann-Feldbau definition of bundle 18 6. Differentiable manifolds and tensor bundles 20 7. Factor spaces of groups 28 8. The principal bundle and the principal map 35 9. Associated bundles and relative bundles 43 10. The induced bundle 47 11. Homotopies of maps of bundles 49 12. Construction of cross-sections 54 13. Bundles having a totally disconnected group 59 14. Covering spaces 67 Part II. THE HOMOTOPY THEORY OF BUNDLES 15. Homotopy groups 72 16. The operations of Pi1 on Pi n 83 17. The homotopy sequence of a bundle 90 18. The classification of bundles over the n-sphere 96 19. Universal bundles and the classification theorem 100 20. The fibering of spheres by spheres 105 21. The homotopy groups of spheres 110 22. Homotopy groups of the orthogonal groups 114 23. A characteristic map for the bundle Rn+1 over S n 118 24. A characteristic map for the bundle Un over S 2n - 1 124 25. The homotopy groups of miscellaneous manifolds 131 26. Sphere bundles over spheres 134 27. The tangent bundle of S n 140 28. On the non-existence of fiberings of spheres by spheres 144 Part III. THE COHOMOLOGY THEORY OF BUNDLES 29. The stepwise extension of a cross-section 148 30. Bundles of coefficients 151 31. Cohomology groups based on a bundle of coefficients 155 32. The obstruction cocycle 166 33. The difference cochain 169 34. Extension and deformation theorems 174 35. The primary obstruction and the characteristic cohomology class 177 36. The primary difference of two cross-sections 181 37. Extensions of functions, and the homotopy classification of maps 184 38. The Whitney characteristic classes of a sphere bundle 190 39. The Stiefel characteristic classes of differentiable manifolds 199 40. Quadratic forms on manifolds 204 41. Complex analytic manifolds and exterior forms of degree 2 209 Appendix 218 Bibliography 223 Index 228

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