Geometry Books
Cambridge University Press Flavors of Geometry
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£37.99
Cambridge University Press Convex Geometric Analysis 34 Mathematical Sciences Research Institute Publications Series Number 34
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£105.45
Cambridge University Press Computational Geometry in C Second Edition
Book SynopsisThis is the revised and expanded 1998 edition of a popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The basic techniques used in computational geometry are all covered: polygon triangulations, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. The code in this edition is significantly improved from the first edition (more efficient and more robust), and four new routines are included. Java versions foTrade Review'… the author does an excellent job of explaining difficult concepts in an accessible, even entertaining, manner … If this is your field, this is your book!' Developers Review'The balanced combination of careful descriptions, examples, algorithms and exercises makes it a pleasure to read …'. Zentralblatt'Anyone who wants to know what this field is all about should read this book! The book is a pleasure to read, as questions that arise naturally in the reader's mind are answered, in almost all cases, in the following paragraph. The style strikes an ideal balance between rigor and informality. Mr O'Rourke must be a wonderful teacher and I envy his students.' Miriam L. Lucian, Society for Industrial and Applied MathematicsTable of Contents1. Polygon triangulation; 2. Polygon partitioning; 3. Convex hulls in two dimensions; 4. Convex hulls in three dimensions; 5. Voronoi diagrams; 6. Arrangements; 7. Search and intersection; 8. Motion planning; 9. Sources.
£45.59
Cambridge University Press Elliptic Curves in Cryptography 265 London Mathematical Society Lecture Note Series Series Number 265
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£62.69
Cambridge University Press Elliptic Curves Function Theory Geometry Arithmetic
Book SynopsisThe subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre. This 1997 book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and modern developments. It combines three of the fundamental themes of mathematics: complex function theory, geometry, and arithmetic. After an informal preparatory chapter, the book follows an historical path, beginning with the work of Abel and Gauss on elliptic integrals and elliptic functions. This is followed by chapters on theta functions, modular groups and modular functions, the quintic, the imaginary quadratic field, and on elliptic curves. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the subject for graduate students and researchers in mathematics and physics, with many exercises with hints scattered throughout the text.Trade Review'The book is a welcome extension of the existing literature about this important topic … It is recommended to students of mathematics and physics interested in the applications of the theory and the theory itself.' European Mathematical Society'With an easy mind the reviewer can recommend this book to those who want to become acquainted with the subject and to those who look for a book which can serve as guide for a course on the subject … the exemplary way in which Elliptic Curves is written, made reviewing a pleasure.' Niew Archief voor WiskundeTable of Contents1. First ideas: complex manifolds, Riemann surfaces, and projective curves; 2. Elliptic functions and elliptic integrals; 3. Theta functions; 4. Modular groups and molecular functions; 5. Ikosaeder and the quintic; 6. Imaginary quadratic fields; 7. The arithmetic of elliptic fields.
£50.34
Cambridge University Press Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces 269 London Mathematical Society Lecture Note Series Series Number 269
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£65.99
Cambridge University Press Polyhedra
Book SynopsisPolyhedra have cropped up in many different guises throughout recorded history. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics and group theory. This book comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics. The author strikes a balance between covering the historical development of the theory surrounding polyhedra, and presenting a rigorous treatment of the mathematics involved. It is attractively illustrated with dozens of diagrams to illustrate ideas that might otherwise prove difficult to grasp. Historians of mathematics as well as those more interested in the mathematics itself, will find this unique book fascinating.Trade Review'The topic itself … is easily visualised and it has a long history as part of our culture, interacting with philosophy, art and chemistry. Cromwell's treatment admirably exploits all these opportunities, with many interesting digressions and a lively historical commentary … popular exposition at a high level.' Sir Michael Atiyah, The Times Higher Education Supplement'… plenty to fascinate.' New Scientist'… Peter Cromwell has done us a great service by writing this handsome, scholarly and beautifully illustrated book.' Peter Giblin, The London Mathematical Society Newsletter'This remarkable book goes far beyond the superficial, providing a solid and fascinating account of the history and mathematics of polyhedra, especially regular polyhedra. It is likely to become the classic book on the topic.' MAA Online' … a fascinating book … the book holds many surprises and will find rich use among students of both mathematics and computer science.' Choice' … a well got-up book with an abundant and beautiful material of illustration. The study of polyhedra, as the author explicitly states, 'is currently enjoying something of a renaissance'. This work itself will surely help this renaissance, and may be an enjoyable reading for a very wide audience.' Acta. Sci. Math.' … the book should have a wide and appreciative audience of all ages.' The Times Higher Education Supplement' … this book contains a thorough treatment of all that is known about polyhedra … A very interesting and detailed account.' European Mathematical Society' … well-illustrated throughout with line diagrams, as well as several colour plates of the author's own superb models. The writing is clear and entertaining, and reassuringly anticipates many of the reader's questions.' Thomas Bending, The Mathematical GazetteTable of ContentsIntroduction; 1. Indivisible, inexpressible and unavoidable; 2. Rules and regularity; 3. Decline and rebirth of polyhedral geometry; 4. Fantasy, harmony and uniformity; 5. Surfaces, solids and spheres; 6. Equality, rigidity and flexibility; 7. Stars, stellations, and skeletons; 8. Symmetry, shape and structure; 9. Counting, colouring and computing; 10. Combination, transformation and decoration; Appendices.
£53.19
Cambridge University Press Methods in Banach Space Theory Proceedings of the V Conference on Banach Spaces Caceres Spain 1318 September 2004 337 London Mathematical Society Lecture Note Series Series Number 337
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£61.71
Cambridge University Press Elliptic Cohomology Geometry Applications and Higher Chromatic Analogues 342 London Mathematical Society Lecture Note Series Series Number 342
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£61.71
Cambridge University Press Algebraic Cycles and Motives 344 London
Book SynopsisThese two volumes provide a self-contained account of research on algebraic cycles and motives. Twenty-two contributions from leading figures survey the key research strands, including: Abel-Jacobi/regulator maps and normal functions; Voevodsky's triangulated category of mixed motives; conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups.Table of ContentsPart II. Research Articles: 8. Beilinson's Hodge conjecture with coefficients M. Asakura and S. Saito; 9. On the splitting of the Bloch-Beilinson filtration A. Beauville; 10. Künneth projectors S. Bloch and H. Esnault; 11. The Brill-Noether curve of a stable bundle on a genus two curve S. Brivio and A. Verra; 12. On Tannaka duality for vector bundles on p-adic curves C. Deninger and A. Werner; 13. On finite-dimensional motives and Murre's conjecture U. Jannsen; 14. On the transcendental part of the motive of a surface B. Kahn, J. P. Murre and C. Pedrini; 15. A note on finite dimensional motives S. I. Kimura; 16. Real regulators on Milnor complexes, II J. D. Lewis; 17. Motives for Picard modular surfaces A. Miller, S. Müller-Stach, S. Wortmann, Y.-H.Yang, K. Zuo; 18. The regulator map for complete intersections J. Nagel; 19. Hodge number polynomials for nearby and vanishing cohomology C. Peters and J. Steenbrink; 20. Direct image of logarithmic complexes M. Saito; 21. Mordell-Weil lattices of certain elliptic K3's T. Shioda; 22. Motives from diffraction J. Stienstra.
£61.71
Cambridge University Press Geometric Folding Algorithms Linkages Origami Polyhedra
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£53.43
Cambridge University Press Groups Graphs and Trees An Introduction to the Geometry of Infinite Groups London Mathematical Society Student Texts Series Number 73
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£37.99
Cambridge University Press Zariski Geometries Geometry from the Logicians Point of View 360 London Mathematical Society Lecture Note Series Series Number 360
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£59.22
Cambridge University Press Smooth Compactifications of Locally Symmetric Varieties
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£53.19
Cambridge University Press Soliton Equations and their AlgebroGeometric Solutions Volume 1 11Dimensional Continuous Models Cambridge Studies in Advanced Mathematics Series Number 79
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£133.95
Cambridge University Press Geometric and Cohomological Methods in Group Theory
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£53.99
Cambridge University Press How to Fold It The Mathematics of Linkages Origami and Polyhedra
Book SynopsisDiscover and understand mathematical theorems through paper folding, starting with high school algebra and geometry through to more advanced concepts.Trade Review'The major theorems presented are remarkable - results that may surprise the reader include the fact that, with the right folds, any shape or collection of shapes (even ones with holes in) … composed of straight lines may be cut out from a sheet of paper with just a single cut.' London Mathematical Society Newsletter'In this beautiful and inspiring book with many colour figures the reader can find a fascinating mathematical approach to linkages, foldings and unfoldings. Many exercises with detailed solutions give the reader the chance to control the acquired skills.' Hansueli Hosli, Zentralblatt MATH'… a great book for someone who wants to learn about the mathematics behind origami without being overwhelmed by the mathematics itself. This is a great book for a high school or undergraduate student to get introduced to the open problems in computational origami.' Brittany Terese Fasy and David L. Millman, SIGACT NewsTable of ContentsPart I. Linkages: 1. Robot arms; 2. Straight-line linkages and the pantograph; 3. Protein folding and pop-up cards; Part II. Origami: 4. Flat vertex folds; 5. Fold and one-cut; 6. The shopping bag theorem; Part III. Polyhedra: 7. Durer's problem: edge unfolding; 8. Unfolding orthogonal polyhedra; 9. Folding polygons to convex polyhedra; 10. Further reading; 11. Glossary; 12. Answers to exercises; 13. Permissions and acknowledgments.
£100.70
Cambridge University Press LMS 276 Singularities Plane Curves London Mathematical Society Lecture Note Series Series Number 276
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£69.99
Cambridge University Press Derivation and Integration 140 Cambridge Tracts in Mathematics Series Number 140
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£105.45
Cambridge University Press Characters and Automorphism Groups of Compact Riemann Surfaces 280 London Mathematical Society Lecture Note Series Series Number 280
Book SynopsisUsing modern methods from computational group theory and representation theory, this book addresses a classical topic in the theory of complex functions. It is suitable for graduate students and researchers.Trade Review'… by bringing together a number of very effective techniques, and by presenting a mass of specific evidence, Breuer has done the mathematical community a considerable service … the presentation of the material is excellent, with attractive layout … a valuable addition to the literature, which should be essential reading for anyone interested in the connections between Riemann surfaces and finite groups.' G. Jones, Proceedings of the Edinburgh Mathematical SocietyTable of ContentsPreface; Notation; 1. Compact Riemann surfaces; 2. Group characters; 3. Automorphisms of compact Riemann surfaces; 4. Generation of groups; 5. Classification for small genus; 6. Classification for fixed group: real characters; 7. Classification for fixed group: nonreal irrationalities; Appendix A. Abelian inariants; Appendix B. Irreducible characters; Appendix C. Maillet's determinant; Bibliography; Index.
£57.57
Cambridge University Press An Algebraic Introduction to KTheory 87 Encyclopedia of Mathematics and its Applications Series Number 87
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£152.95
Cambridge University Press Isoperimetric Inequalities Differential Geometric and Analytic Perspectives 145 Cambridge Tracts in Mathematics Series Number 145
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£105.45
Cambridge University Press Galois Groups and Fundamental Groups
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£133.95
Cambridge University Press Harmonic Maps Conservation Laws and Moving Frames 150 Cambridge Tracts in Mathematics Series Number 150
Book SynopsisThe author presents an accessible and self-contained introduction to harmonic map theory and its analytical aspects, covering recent developments in the regularity theory of weakly harmonic maps. The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions. The reader is then presented with a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions. A self-contained presentation of 'exotic' functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results. The importance of conservation laws is stressed and the concept of a 'Coulomb moving frame' is explained in detail. The book ends with further applications and illustrations of Coulomb moving frames to the theory of surfaces.Trade Review'The book is very well written and it contains truly beautiful geometrical analysis. It also contains a quick, direct introduction to the current research.' EMS NewsletterTable of ContentsPreface; Introduction; Acknowledgements; Notations; 1. Geometric and analytic setting; 2. Harmonic maps with symmetries; 3. Compensations and exotic function spaces; 4. Harmonic maps without symmetries; 5. Surfaces with mean curvature in L2; References.
£105.45
Cambridge University Press Hinged Dissections
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£108.30
Cambridge University Press Algebra and Geometry
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£90.24
Cambridge University Press 3D Computer Graphics
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£75.99
Cambridge University Press Computational Algebraic Geometry 58 London Mathematical Society Student Texts Series Number 58
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£94.99
Cambridge University Press Projective Differential Geometry Old and New
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£105.45
Cambridge University Press The Geometry of Efficient Fair Division
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£128.25
Cambridge University Press Combinatorial and Computational Geometry 52 Mathematical Sciences Research Institute Publications Series Number 52
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£87.40
Cambridge University Press Theory and Modeling of Rotating Fluids
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£139.65
Cambridge University Press The CubeA Window to Convex and Discrete Geometry
Book SynopsisThis tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them.Trade Review"Because this book is a love letter to the unity of mathematics, readers can hardly but come to share Zong's undisguised enthusiasm...Highly recommended." -- ChoiceTable of ContentsPreface; Basic notation; 0. Introduction; 1. Cross sections; 2. Projections; 3. Inscribed simplices; 4. Triangulations; 5. 0/1 polytopes; 6. Minkowski's conjecture; 7. Furtwangler's conjecture; 8. Keller's conjecture; Bibliography; Index.
£105.45
Cambridge University Press Geometric Folding Algorithms
Book SynopsisEmphasizing algorithmic and computational aspects, this fascinating treatment of the geometry of folding and unfolding presents hundreds of results and over 60 open problems. Aimed at advanced undergraduates and graduates in mathematics or computer science, this lavishly illustrated book will entertain a broad audience, from school students to researchers.Trade Review'Demaine and O'Rourke are among the best-qualified authors for a book on this subject; and the book that they have written is a delight … it is exceptionally clear and readable. It could be read for pleasure by any mathematics undergraduate, and much of it (though not all) by amateurs with a high school mathematics background … although there are sections that some amateurs will skip, the level is always kept as elementary as locally possible. This book should be in all university libraries, and many professional and amateur mathematicians will want to add it to their personal collections.' Robert Dawson (Halifax), Zentralblatt Math'This book is one of those rare mathematics books that I had a hard time putting down. I wanted to keep reading to find the next insight. … This is a serious mathematics book whose explorations have significant applications and real mathematical profundity, wonderfully mixed with some fun recreational mathematics. … The book has a useful index and an extensive bibliography, so when you finish reading, it will remain a valuable resource far into the future. There is a lot of material in this book and it is really a lot of fun. I highly, highly recommend this book to anyone with even a passing interest in folding mathematics.' MAA Reviews'The authors explain step-by-step interesting solutions of some folding problems. This splendidly illustrated book can be interesting for advanced undergraduate students in mathematics and computer science as well as for geometers and computer specialists who can find many new ideas and impulses …' EMS NewsletterTable of ContentsIntroduction; Part I. Linkages: 1. Problem classification and examples; 2. Upper and lower bounds; 3. Planar linkage mechanisms; 4. Rigid frameworks; 5. Reconfiguration of chains; 6. Locked chains; 7. Interlocked chains; 8. Joint-constrained motion; 9. Protein folding; Part II. Paper: 10. Introduction; 11. Foundations; 12. Simple crease patterns; 13. General crease patterns; 14. Map folding; 15. Silhouettes and gift wrapping; 16. The tree method; 17. One complete straight cut; 18. Flattening polyhedra; 19. Geometric constructibility; 20. Rigid origami and curved creases; Part III. Polyhedra: 21. Introduction and overview; 22. Edge unfolding of polyhedra; 23. Reconstruction of polyhedra; 24. Shortest paths and geodesics; 25. Folding polygons to polyhedra; 26. Higher dimensions.
£145.35
Cambridge University Press Hyperbolic Geometry from a Local Viewpoint 68 London Mathematical Society Student Texts Series Number 68
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£100.70
Cambridge University Press Rigidity in Higher Rank Abelian Group Actions Volume 1 Introduction and Cocycle Problem Cambridge Tracts in Mathematics Series Number 185
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£105.45
Cambridge University Press Monopoles and ThreeManifolds 10 New Mathematical Monographs Series Number 10
Book SynopsisThis 2007 book provides a comprehensive treatment of Floer homology, based on the Seiberg–Witten equations. Suitable for beginning graduate students and researchers in the field, this book provides a full discussion of a central part of the study of the topology of manifolds.Trade Review'… there are mathematics books that are classics; these are books that tell a particular story in the right way. As such, they will never go out of date and never be bettered. Kronheimer and Mrowka's book is almost surely such a book. If you want to learn about Floer homology in the Seiberg–Witten context, you will do no better than to read Kronheimer and Mrowka's masterpiece Monopoles and Three-Manifolds.' Clifford Henry Taubes, Bulletin of the American Mathematical Society'This long-awaited book is a complete and detailed exposition of the Floer theory for Seiberg-Witten invariants. It is very nicely written and contains all proofs of results. This makes the book an essential tool for both researchers and students working in this area of mathematics.' Mathematical Reviews'This book is the definitive bible for anyone wanting to learn the full story of the various Seiberg-Witten Floer homology theories … There are mathematics books that are classics. As such, they will never go out of date and never be improved. The present masterpiece is almost surely such a book.' Alexander Felshtyn, Zentralblatt MATHTable of ContentsPreface; 1. Outlines; 2. The Seiberg–Witten equations and compactness; 3. Hilbert manifolds and perturbations; 4. Moduli spaces and transversality; 5. Compactness and gluing; 6. Floer homology; 7. Cobordisms and invariance; 8. Non-exact perturbations; 9. Calculations; 10. Further developments; References; Glossary of notation; Index.
£175.75
Cambridge University Press Algebra and Geometry
Book SynopsisDescribing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry. It covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups and aspects of geometry including groups of isometries, rotations, and spherical geometry. The book emphasises the interactions between topics, and each topic is constantly illustrated by using it to describe and discuss the others. Many ideas are developed gradually, with each aspect presented at a time when its importance becomes clearer. To aid in this, the text is divided into short chapters, each with exercises at the end. The related website features an HTML version of the book, extra text at higher and lower levels, and more exercises and examples. It also links to an electronic maths thesaurus, giving definitions, examples and links both to the book and to external sources.Trade Review'The presentation is traditional, informal, and relaxed.' Zentralblatt MATHTable of ContentsPreface; 1. Groups and permutations; 2. The real numbers; 3. The complex plane; 4. Vectors in three-dimensional space; 5. Spherical geometry; 6. Quaternions and isometries; 7. Vector spaces; 8. Linear equations; 9. Matrices; 10. Eigenvectors; 11. Linear maps of Euclidean space; 12. Groups; 13. Möbius transformations; 14. Group actions; 15. Hyperbolic geometry; Index.
£43.69
Cambridge University Press Corporate Lawyers and Corporate Governance International Corporate Law and Financial Market Regulation
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£118.75
Cambridge University Press Groups Graphs and Trees An Introduction to the Geometry of Infinite Groups London Mathematical Society Student Texts Series Number 73
Book SynopsisThis book presents a modern, geometric approach to group theory. An accessible and engaging approach to the subject, with many exercises and figures to develop geometric intuition. Ideal for advanced undergraduates, it will also interest graduate students and researchers as a gentle introduction to geometric group theory.Trade Review'Meier has the rare ability to make complex concepts accessible to novices while simultaneously challenging the experienced. … With well-chosen illustrations and examples, Meier succeeds brilliantly in this unique approach.' SciTech Book News'… totally accessible to undergraduate students and would be a good textbook for an advanced undergraduate course in group theory, or a graduate course in geometric group theory.' Mathematical Review'… an excellent introduction to geometric group theory. … Carefully chosen examples are an essential part of the exposition and they really help to understand general constructions.' EMS NewsletterTable of ContentsPreface; 1. Cayley's theorems; 2. Groups generated by reflections; 3. Groups acting on trees; 4. Baumslag-Solitar groups; 5. Words and Dehn's word problem; 6. A finitely-generated, infinite, Torsion group; 7. Regular languages and normal forms; 8. The Lamplighter group; 9. The geometry of infinite groups; 10. Thompson's group; 11. The large-scale geometry of groups; Bibliography; Index.
£89.30
Cambridge University Press Stacks Project Expository Collection
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£90.25
Cambridge University Press Computational Topology for Data Analysis
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£47.49
Cambridge University Press LargeScale Convex Optimization
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£56.99
Cambridge University Press The Calabi Problem for Fano Threefolds
Book SynopsisThis book determines whether the general member of each family of smooth Fano threefolds admits a KählerEinstein metric, using K-stability. Complemented by appendices outlining results needed to understand this active area, it will be essential reading for researchers and graduate students working on algebraic and complex geometry.Trade Review'The notion of K-stability for Fano manifold has origins in differential geometry and geometric analysis but is now also of fundamental importance in algebraic geometry, with recent developments in moduli theory. This monograph gives an account of a large body of research results from the last decade, studying in depth the case of Fano threefolds. The wealth of material combines in a most attractive way sophisticated modern theory and the detailed study of examples, with a classical flavour. The authors obtain complete results on the K-stability of generic elements of each of the 105 deformation classes. The concluding chapter contains some fascinating conjectures about the 34 families which may contain both stable and unstable manifolds, which will surely be the scene for much further work. The book will be an essential reference for many years to come.' Sir Simon Donaldson, F.R.S., Imperial College London'It is a difficult problem to check whether a given Fano variety is K-polystable. This book settles this problem for the general members of all the 105 deformation families of smooth Fano 3-folds. The book is recommended to anyone interested in K-stability and existence of Kähler-Einstein metrics on Fano varieties.' Caucher Birkar FRS, Tsinghua University and University of CambridgeTable of ContentsIntroduction; 1. K-stability; 2. Warm-up: smooth del Pezzo surfaces; 3. Proof of main theorem: known cases; 4. Proof of main theorem: special cases; 5. Proof of main theorem: remaining cases; 6. The big table; 7. Conclusion; Appendix. Technical results used in proof of main theorem; References; Index.
£71.25
Cambridge University Press The Geometry of Cubic Hypersurfaces
Book SynopsisThis detailed introduction to cubic hypersurfaces and all the techniques needed to study them leads the reader from classical topics to recent developments studying four-dimensional cubic hypersurfaces. With exercises and careful references to the wider literature, this is an ideal text for graduate students and researchers in algebraic geometry.Trade Review'What a beautiful book. Several turning points in algebraic geometry have in their background a cubic hypersurface. This superb exposition, by one of the masters in the field, takes the reader, in a friendly manner, through the fascinating, and occasionally mysterious, properties of these geometrical objects, and through them offers a glimpse of the underlying Hodge theory, of the theory of periods, the theory of motives, and the theory of derived categories. Graduate students, researchers, and colleagues will all find this unified treatment of cubic hypersurfaces profoundly inspiring.' Enrico Arbarello, Accademia Nazionale dei Lincei'This is just a fantastic book for students and experts alike. The geometry of cubics is a wonderful mix of the classical and the modern; Huybrechts consolidates the diverse results into a coherent account for the first time. His famously lucid writing clearly conveys the beauty of the geometry of these varieties. The book describes a plethora of techniques culminating in new (and really surprising) viewpoints on the subject.' Richard Thomas, Imperial College London'This exceedingly well written monograph covers material ranging from the very beginning of algebraic geometry, the 27 lines on a cubic surface, to highly relevant topical issues. The book will be a most valuable companion to algebraic geometers from graduate students to active researchers.' Klaus Hulek, Leibniz University HannoverTable of Contents1. Basic facts; 2. Fano varieties of lines; 3. Moduli spaces; 4. Cubic surfaces; 5. Cubic threefolds; 6. Cubic fourfolds; 7. Derived categories of cubic hypersurfaces; References; Subject index.
£66.49
Cambridge University Press The Mathematics of Origami
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£94.50
Cambridge University Press Introduction to Vassiliev Knot Invariants
Book SynopsisWith hundreds of worked examples, exercises and illustrations, this detailed exposition of the theory of Vassiliev knot invariants opens the field to students with little or no knowledge in this area. It also serves as a guide to more advanced material. The book begins with a basic and informal introduction to knot theory, giving many examples of knot invariants before the class of Vassiliev invariants is introduced. This is followed by a detailed study of the algebras of Jacobi diagrams and 3-graphs, and the construction of functions on these algebras via Lie algebras. The authors then describe two constructions of a universal invariant with values in the algebra of Jacobi diagrams: via iterated integrals and via the Drinfeld associator, and extend the theory to framed knots. Various other topics are then discussed, such as Gauss diagram formulae, before the book ends with Vassiliev's original construction.Trade Review'It is clear that this book is a labour of love, and that no effort has been spared in making it a useful textbook and reference for those seeking to understand its subject. The target readership consists both of first-time learners, for whom pedagogically sound explanations and numerous well-chosen exercises are provided to enhance comprehension, and of experienced mathematicians, for whom many tables of data and readable concise guides to research literature are provided. Numerous figures are included to supplement written explanations. The content is well-modularized, in the sense that different sections of the book may be read independently of one another, and that when there is an essential dependence between sections then this fact is clearly pointed out and the relationship between the sections is explained. This, and a thorough index, combine to make this book not only a valuable textbook, but also a valuable reference.' Zentralblatt MATH'The book's excellent preface goes on to give an in embryo characterization of the objects in the title … As being a textbook - and an excellent one - the authors take us from a dense but accessible introduction to knots as such to quantum invariants, all in the first two chapters, and then go on to Vassiliev's finite type invariants. Then we get to chord diagrams, Lie algebra connections, Kontsevich's integral, work by Drinfeld, more stuff on the Kontsevich integral, material on braids, and more. The book closes with a chapter on '[t]he space of all knots'. It's very, very attractive material.' Michael Berg, MAA ReviewsTable of Contents1. Knots and their relatives; 2. Knot invariants; 3. Finite type invariants; 4. Chord diagrams; 5. Jacobi diagrams; 6. Lie algebra weight systems; 7. Algebra of 3-graphs; 8. The Kontsevich integral; 9. Framed knots and cabling operations; 10. The Drinfeld associator; 11. The Kontsevich integral: advanced features; 12. Braids and string links; 13. Gauss diagrams; 14. Miscellany; 15. The space of all knots; Appendix; References; Notations; Index.
£66.49
Cambridge University Press Categorical Homotopy Theory 24 New Mathematical Monographs Series Number 24
Book SynopsisThis categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.Table of ContentsPart I. Derived Functors and Homotopy (Co)limits: 1. All concepts are Kan extensions; 2. Derived functors via deformations; 3. Basic concepts of enriched category theory; 4. The unreasonably effective (co)bar construction; 5. Homotopy limits and colimits: the theory; 6. Homotopy limits and colimits: the practice; Part II. Enriched Homotopy Theory: 7. Weighted limits and colimits; 8. Categorical tools for homotopy (co)limit computations; 9. Weighted homotopy limits and colimits; 10. Derived enrichment; Part III. Model Categories and Weak Factorization Systems: 11. Weak factorization systems in model categories; 12. Algebraic perspectives on the small object argument; 13. Enriched factorizations and enriched lifting properties; 14. A brief tour of Reedy category theory; Part IV. Quasi-Categories: 15. Preliminaries on quasi-categories; 16. Simplicial categories and homotopy coherence; 17. Isomorphisms in quasi-categories; 18. A sampling of 2-categorical aspects of quasi-category theory.
£78.84
