Geometry Books
Barrons Educational Services Regents Exams and Answers Geometry Sixth Edition
Book Synopsis
£17.09
Barrons Educational Services Lets Review Regents Geometry Sixth Edition
Book Synopsis
£17.09
Shelter Harbor Press Geometry (Inside Mathematics): Understanding
Book SynopsisAge range 14+One of the hardest questions that mathematics teachers have to answer is 'Why?' Schoolroom sums are crucial in learning the awesome power of mathematics, but they are often a world away from how the knowledge is applied and where it came from. Inside Mathematics: Geometry is there to fill that gap. The word 'geometry' means to 'measure the Earth.' Ancient mathematicians wanting to do more than count money and merchandise used geometry to model the natural world and then the world of numbers that lies behind it. What began by scratching circles and squares in the dirt has led to to infinitely large shapes you could hold in your hand, a Universe in which straight lines can be curved, and Internet search engines that handle information as structures with hundreds of dimensions. Inside Mathematics: Geometry introduces the amazing people who figured out how shapes work and how they can be used to unlock secrets of nature. Written to engage, and enthuse young people, it show readers how ideas of long-dead geniuses ended up in their homework assignment: Trigonometry is not just about triangles — it can tell you how big the Universe is. Not every polyhedron has three dimensions: The tesseract of sci-fi movies really exists as a four-dimensional cube that can turn itself inside out.
£17.53
Wooden Books Sacred Geometry
Book Synopsis
£7.95
Arcler Education Inc Introduction to Computational Geometry
Book SynopsisComputational Geometry is a branch of mathematics that deals with the solution of geometric problems that emerge in a variety of applications such as geographic information systems, robotics, and computer graphics, among others. Computational Geometry is covered in depth in this Handbook, which provides an overview of key concepts and results in the field. It can be used as a reference and study aid for those interested in the topic. Not only are the most cutting-edge methods and answers given, but also several alternative approaches to issue solving and problem solving strategies.
£143.20
Springer Nature Switzerland AG Geometry, Lie Theory and Applications: The Abel
Book SynopsisThis book consists of contributions from the participants of the Abel Symposium 2019 held in Ålesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity.The chapters are written by leading international researchers, and consist of both survey and research articles. The book gives the reader an insight into the current research in differential geometry and Lie theory, as well as applications of these topics, in particular to general relativity and string theory.Table of ContentsFour-dimensional homogeneous generalizations of Einstein Metrics.- Conformal and isometric embeddings of gravitational instantons.- Recent results on closed G2-structures, by Anna Fino and Alberto Raffero.- Almost Zoll affine surfaces.- Distinguished curves and fist integrals on Poincare-Einstein and other conformally singular geometries.- A car as parabolic geometry.- Legendrian cone structures and contact prolongations.- The search for solitons on homogeneous spaces.- On Ricci negative Lie groups.- Semi-Riemannian cones.- Building new Einstein spaces by deforming symmetric Einstein spaces.- Remarks on highly supersymmetric backgrounds of 11-dimensional supergravity.- Krichever-Novikov type algebras.
£142.49
Springer Nature Switzerland AG Complex Symmetries
Book SynopsisThis volume is a collection of essays on complex symmetries. It is curated, emphasizing the analysis of the symmetries, not the various phenomena that display those symmetries themselves. With this, the volume provides insight to nonspecialist readers into how individual simple symmetries constitute complex symmetry. The authors and the topics cover many different disciplines in various sciences and arts. Simple symmetries, such as reflection, rotation, translation, similitude, and a few other simple manifestations of the phenomenon, are all around, and we are aware of them in our everyday lives. However, there are myriads of complex symmetries (composed of a bulk of simple symmetries) as well. For example, the well-known helix represents the combination of translational and rotational symmetry. Nature produces a great variety of such complex symmetries. So do the arts. The contributions in this volume analyse selected examples (not limited to geometric symmetries). These include physical symmetries, functional (meaning not morphological) symmetries, such as symmetries in the construction of the genetic code, symmetries in human perception (e.g., in geometry education as well as in constructing physical theories), symmetries in fractal structures and structural morphology, including quasicrystal and fullerene structures in stable bindings and their applications in crystallography and architectural design, as well as color symmetries in the arts. The volume is rounded of with beautiful illustrations and presents a fascinating panorama of this interdisciplinary topic.Table of ContentsGyörgy Darvas: Complex Symmetries, Introduction.- Douglas Dunham: Complex Symmetries in Repeating Hyperbolic Patterns.- Paul Hertz: Ignotheory: A Compositional System for Intermedia Art Based on Tiling Patterns and Labelled Graphs.- Ashish Kumar Upadhyay: Symmetries of Maps on Surfaces.- Koji Miyazaki and Motonaga Ishii: Symmetry in Projection of 4-dimensional Regular Polychora.- Guy Inchbald: Morphic Polytopes and Symmetries.- Takeshi Sugimoto: Inducing the Symmetries out of the Complexity: The Kepler Triangle and its Kin as a Model Problem.- Jim Lehman: Synchronizing the Isotropic Vctor Matrix with the Stellated Vector Matrix.- András Recski: An Analogy and Several Symmetries.- Dmitriy Gurevich: Discrete Lattices on the Single Bearing Spiral: From Geometry to Botany.- Simone Brasili and Riccardo Piergallini: Symmetry and Invariance: Interdisciplinary teaching.- Eleonóra Stettner and György Emese: Dilative Rotation, Dilative Reflection in Mathematics, Nature, Art, and Education.- János Szász Saxon and Gábor Kis: Relationship of Symmetry and Combinatorics in the Poly-universe Game.- Marina Voinova: Symmetry in Arrow-like Salt Crystals.- László Szabados: Symmetries in Stellar, Galactic, and Extragalactic Astronomy.- Sergey V. Petoukhov, Elena S. Petukhova and Vladimir V. Verevkin: Symmetries and the Genetic, Code.- Kas Oosterhuis: Global Symmetry Local Asymmetry: In the Realized Buildings by the Innovation Studio ONL BV.- Katarzyna Szymańska-Stułka: Theme, Motive, Structure and Symmetry – Pentasonata by Andrzej Panufnik.- FréIlgen: Fluid Symmetry: Logical to Artists, Mesmerizing to Viewers.- Paul B. Ré: Complex Symmetries in Réograms.- Patrice Jeener: Graphic Illustrations of Complex Symmetries.
£999.99
de Gruyter Geometrodynamics of Gauge Fields
Book Synopsis
£111.62
de Gruyter Geometrische Modelle Zur Analyse Empirischer
Book Synopsis
£134.09
de Gruyter Die Fraktale Geometrie Der Natur
Book Synopsis
£141.54
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Positivity in Algebraic Geometry II: Positivity
Book SynopsisTwo volume work containing a contemporary account on "Positivity in Algebraic Geometry". Both volumes also available as hardcover editions as Vols. 48 and 49 in the series "Ergebnisse der Mathematik und ihrer Grenzgebiete". A good deal of the material has not previously appeared in book form. Volume II is more at the research level and somewhat more specialized than Volume I. Volume II contains a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. Contains many concrete examples, applications, and pointers to further developmentsTrade ReviewFrom the reviews: "The main theme of this ... monograph is a comprehensive description of the fields of complex algebraic geometry connected with the notion of positivity. ... The book is written for mathematicians interested in the modern development of algebraic geometry." (EMS Newsletter, September, 2006)Table of ContentsNotation and Conventions.- Two: Positivity for Vector Bundles.- 6 Ample and Nef Vector Bundles.- 6.1 Classical Theory.- 6.1.A Definition and First Properties.- 6.1.B Cohomological Properties.- 6.1.C Criteria for Amplitude.- 6.1.D Metric Approaches to Positivity of Vector Bundles.- 6.2 Q-Twisted and Nef Bundles.- 6.2.A Twists by Q-Divisors.- 6.2.B Nef Bundles.- 6.3 Examples and Constructions.- 6.3.A Normal and Tangent Bundles.- 6.3.B Ample Cotangent Bundles and Hyperbolicity.- 6.3.C Picard Bundles.- 6.3.D The Bundle Associated to a Branched Covering.- 6.3.E Direct Images of Canonical Bundles.- 6.3.F Some Constructions of Positive Vector Bundles.- 6.4 Ample Vector Bundles on Curves.- 6.4.A Review of Semistability.- 6.4.B Semistability and Amplitude.- Notes.- 7 Geometric Properties of Ample Bundles.- 7.1 Topology.- 7.1.A Sommese’s Theorem.- 7.1.B Theorem of Bloch and Gieseker.- 7.1.C A Barth-Type Theorem for Branched Coverings.- 7.2 Degeneracy Loci.- 7.2.A Statements and First Examples.- 7.2.B Proof of Connectedness of Degeneracy Loci.- 7.2.C Some Applications.- 7.2.D Variants and Extensions.- 7.3 Vanishing Theorems.- 7.3.A Vanishing Theorems of Griffiths and Le Potier.- 7.3.B Generalizations.- Notes.- 8 Numerical Properties of Ample Bundles.- 8.1 Preliminaries from Intersection Theory.- 8.1.A Chern Classes for Q-Twisted Bundles.- 8.1.B Cone Classes.- 8.1.C Cone Classes for Q-Twists.- 8.2 Positivity Theorems.- 8.2.A Positivity of Chern Classes.- 8.2.B Positivity of Cone Classes.- 8.3 Positive Polynomials for Ample Bundles.- 8.4 Some Applications.- 8.4.A Positivity of Intersection Products.- 8.4.B Non-Emptiness of Degeneracy Loci.- 8.4.C Singularities of Hypersurfaces Along a Curve.- Notes.- Three: Multiplier Ideals and Their Applications.- 9 Multiplier Ideal Sheaves.- 9.1 Preliminaries.- 9.1.A Q-Divisors.- 9.1.B Normal Crossing Divisors and Log Resolutions.- 9.1.C The Kawamata—Viehweg Vanishing Theorem.- 9.2 Definition and First Properties.- 9.2.A Definition of Multiplier Ideals.- 9.2.B First Properties.- 9.3 Examples and Complements.- 9.3.A Multiplier Ideals and Multiplicity.- 9.3.B Invariants Arising from Multiplier Ideals.- 9.3.C Monomial Ideals.- 9.3.D Analytic Construction of Multiplier Ideals.- 9.3.E Adjoint Ideals.- 9.3.F Multiplier and Jacobian Ideals.- 9.3.G Multiplier Ideals on Singular Varieties.- 9.4 Vanishing Theorems for Multiplier Ideals.- 9.4.A Local Vanishing for Multiplier Ideals.- 9.4.B The Nadel Vanishing Theorem.- 9.4.C Vanishing on Singular Varieties.- 9.4.D Nadel’s Theorem in the Analytic Setting.- 9.4.E Non-Vanishing and Global Generation.- 9.5 Geometric Properties of Multiplier Ideals.- 9.5.A Restrictions of Multiplier Ideals.- 9.5.B Subadditivity.- 9.5.C The Summation Theorem.- 9.5.D Multiplier Ideals in Families.- 9.5.E Coverings.- 9.6 Skoda’s Theorem.- 9.6.A Integral Closure of Ideals.- 9.6.B Skoda’s Theorem: Statements.- 9.6.C Skoda’s Theorem: Proofs.- 9.6.D Variants.- Notes.- 10 Some Applications of Multiplier Ideals.- 10.1 Singularities.- 10.1.A Singularities of Projective Hypersurfaces.- 10.1.B Singularities of Theta Divisors.- 10.1.C A Criterion for Separation of Jets of Adjoint Series.- 10.2 Matsusaka’s Theorem.- 10.3 Nakamaye’s Theorem on Base Loci.- 10.4 Global Generation of Adjoint Linear Series.- 10.4.A Fujita Conjecture and Angehrn—Siu Theorem.- 10.4.B Loci of Log-Canonical Singularities.- 10.4.C Proof of the Theorem of Angehrn and Siu.- 10.5 The Effective Nullstellensatz.- Notes.- 11 Asymptotic Constructions.- 11.1 Construction of Asymptotic Multiplier Ideals.- 11.1.A Complete Linear Series.- 11.1.B Graded Systems of Ideals and Linear Series.- 11.2 Properties of Asymptotic Multiplier Ideals.- 11.2.A Local Statements.- 11.2.B Global Results.- 11.2.C Multiplicativity of Plurigenera.- 11.3 Growth of Graded Families and Symbolic Powers.- 11.4 Fujita’s Approximation Theorem.- 11.4.A Statement and First Consequences.- 11.4.B Proof of Fujita’s Theorem.- 11.4.C The Dual of the Pseudoeffective Cone.- 11.5.- Notes.- References.- Glossary of Notation.
£999.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Proofs from THE BOOK
Book SynopsisThis revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises.From the Reviews"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... "Notices of the AMS, August 1999"... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999"Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... "SIGACT News, December 2011.Trade Review“This book by Aigner and Ziegler, now in its fifth edition, seeks to pay homage to the late Paul Erdõs by attempting to provide an approximation of ‘The Book.’ … Throughout, illustrations and figures are used to support the arguments in the main text; these can greatly help the readability of the proofs, especially for novices like me. … the book is a marvelous project and this new edition provides a good amount of fresh material.” (Harry Strange, Computing Reviews, March, 2015)Table of ContentsNumber Theory: 1. Six proofs of the infinity of primes.- 2. Bertrand’s postulate.- 3. Binomial coefficients are (almost) never powers.- 4. Representing numbers as sums of two squares.- 5. The law of quadratic reciprocity.- 6. Every finite division ring is a field.- 7. The spectral theorem and Hadamard’s determinant problem.- 8. Some irrational numbers.- 9. Three times π2/6.- Geometry: 10. Hilbert’s third problem: decomposing polyhedral.- 11. Lines in the plane and decompositions of graphs.- 12. The slope problem.- 13. Three applications of Euler’s formula.- 14. Cauchy’s rigidity theorem.- 15. The Borromean rings don’t exist.- 16. Touching simplices.- 17. Every large point set has an obtuse angle.- 18. Borsuk’s conjecture.- Analysis: 19. Sets, functions, and the continuum hypothesis.- 20. In praise of inequalities.- 21. The fundamental theorem of algebra.- 22. One square and an odd number of triangles.- 23. A theorem of Pólya on polynomials.- 24. On a lemma of Littlewood and Offord.- 25. Cotangent and the Herglotz trick.- 26. Buffon’s needle problem.- Combinatorics: 27. Pigeon-hole and double counting.- 28. Tiling rectangles.- 29. Three famous theorems on finite sets.- 30. Shuffling cards.- 31. Lattice paths and determinants.- 32. Cayley’s formula for the number of trees.- 33. Identities versus bijections.- 34. The finite Kakeya problem.- 35. Completing Latin squares.- Graph Theory: 36. The Dinitz problem.- 37. Permanents and the power of entropy.- 38. Five-coloring plane graphs.- 39. How to guard a museum.- 40. Turán’s graph theorem.- 41. Communicating without errors.- 42. The chromatic number of Kneser graphs.- 43. Of friends and politicians.- 44. Probability makes counting (sometimes) easy.- About the Illustrations.- Index.
£52.24
Hindustan Book Agency An Expedition to Geometry
Book SynopsisThis book, taking a holistic view of geometry, introduces the reader to axiomatic, algebraic, analytic and differential geometry. Starting with an informal introduction to non-Euclidean plane geometries, the book develops the theory to put them on a rigorous footing. It may be considered as an explication of the Kleinian view of geometry a la Erlangen Programme. The treatment in the book, however, goes beyond the Kleinian view of geometry.Some noteworthy topics presented include: various results about triangles (including results on areas of geodesic triangles) in Euclidean, hyperbolic, and spherical planes affine and projective classification of conics twopoint homogeneity of the three planes and the fact that the set of distance preserving maps (isometries) are essentially the same as the set of lengths preserving maps of these planes. Geometric intuition is emphasized throughout the book. Figures are included wherever needed. The book has several exercises varying from computational problems to investigative or explorative open questions.Table of Contents 1. Introduction 2. Affine Geometry 3. Projective Geometry 4. Classification of Conics 5. Euclidean Geometry 6. Hyperbolic Plane Geometry 7. Spherical Plane Geometry 8. Theory of Surfaces 9. A Group Action
£34.16
Jainendra K Jain K-Theory
Book SynopsisThis volume contains the proceedings of the international colloquium organized by the Tata Institute of Fundamental Research in January 2016, one of a series of colloquia going back to 1956.The talks at the colloquium covered a wide spectrum of mathematics, ranging over algebraic geometry, topology, algebraic $K$-theory and number theory. Algebraic theory, $\mathbb{A}^1$-homotopy theory and topological $K$-theory formed important sub-streams in this colloquium. Several branches of $K$-theory, like algebraic cycles, triangulated categories of motives, motivic cohomology, motivic homotopy theory, Chow groups of varieties, Euler class theory, equivariant $K$-theory as well as classical $K$-theory have developed considerably in recent years, giving rise to newer directions to the subject as well as proving results of ``classical'' interest. The colloquium brought together experts in these various branches and their talks covered this wide spectrum, highlighting the interconnections and giving a better perspective of the whole subject area.This volume contains refereed articles by leading experts in these fields and includes original results as well as expository materials in these areas.
£158.40
Jainendra K Jain Flag Varieties: An Interplay of Geometry,
Book SynopsisFlag varieties are important geometric objects and their study involves an interplay of geometry, combinatorics, and representation theory. This book is a detailed account of this interplay.In the area of representation theory, the book presents a discussion of complex semisimple Lie algebras and of semisimple algebraic groups; in addition, the representation theory of symmetric groups is also discussed. In the area of algebraic geometry, the book gives a detailed account of Grassmann varieties, flag varieties, and their Schubert subvarieties. Because of their connections with root systems, many of the geometric results admit elegant combinatorial description, a typical example being the description of the singular locus of a Schubert variety. This is shown to be a consequence of standard monomial theory (abbreviated SMT). Thus the book includes SMT and some important applications - singular loci of Schubert varieties, toric degenerations of Schubert varieties, and the relationship between Schubert varieties and classical invariant theory.In this second edition, two recent results on Schubert varieties in the Grassmannian have been added, and some errors in the first edition corrected.Table of Contents Preface Introduction 1 Preliminaries 2 Structure Theory of Semisimple Rings 3 Representation Theory of Finite Groups 4 Representation Theory of the Symmetric Group 5 Symmetric Polynomials 6 Schur-Weyl Duality and the Relationship Between Representations of Sd and GLn (C) 7 Structure Theory of Complex Semisimple Lie Algebras 8 Representation Theory of Complex Semisimple Lie Algebras 9 Generalities on Algebraic Groups 10 Structure Theory of Reductive Groups 11 Representation Theory of Semisimple Algebraic Groups 12 Geometry of the Grassmannian, Flag and their Schubert Varieties via Standard Monomial Theory 13 Singular Locus of a Schubert Variety in the Flag Variety SLn / B 14 Applications 15 Free Resolutions of Some Schubert Singularities 16 Levi Subgroup Actions on Schubert Varieties, and Some Geometric Consequences Appendix A: Chevalley Groups References List of Symbols Index
£52.00
