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Books > Science & Mathematics > Mathematics > Geometry

Oliver Byrne. The First Six Books of the Elements of Euclid (English, French, German, Hardcover, Multilingual edition): Taschen Oliver Byrne. The First Six Books of the Elements of Euclid (English, French, German, Hardcover, Multilingual edition)
Taschen
R1,279 R1,023 Discovery Miles 10 230 Save R256 (20%) Ships in 9 - 15 working days

Nearly a century before Mondrian made geometrical red, yellow, and blue lines famous, 19th-century mathematician Oliver Byrne employed the color scheme for his 1847 edition of Euclid's mathematical and geometric treatise Elements. Byrne's idea was to use color to make learning easier and "diffuse permanent knowledge." The result has been described as one of the oddest and most beautiful books of the 19th century. The facsimile of Byrne's vivid publication is now available in a beautiful new edition. A masterwork of art and science, it is as beautiful in the boldness of its red, yellow, and blue figures and diagrams as it is in the mathematical precision of its theories. In the simplicity of forms and colors, the pages anticipate the vigor of De Stijl and Bauhaus design. In making complex information at once accessible and aesthetically engaging, this work is a forerunner to the information graphics that today define much of our data consumption.

Morse Theory for Hamiltonian Systems (Paperback): Alberto Abbondandolo Morse Theory for Hamiltonian Systems (Paperback)
Alberto Abbondandolo
R4,488 Discovery Miles 44 880 Ships in 12 - 17 working days

This Research Note explores existence and multiplicity questions for periodic solutions of first order, non-convex Hamiltonian systems. It introduces a new Morse (index) theory that is easier to use, less technical, and more flexible than existing theories and features techniques and results that, until now, have appeared only in scattered journals.

Morse Theory for Hamiltonian Systems provides a detailed description of the Maslov index, introduces the notion of relative Morse index, and describes the functional setup for the variational theory of Hamiltonian systems, including a new proof of the equivalence between the Hamiltonian and the Lagrangian index. It also examines the superquadratic Hamiltonian, proving the existence of periodic orbits that do not necessarily satisfy the Rabinowitz condition, studies asymptotically linear systems in detail, and discusses the Arnold conjectures about the number of fixed points of Hamiltonian diffeomorphisms of compact symplectic manifolds.

In six succinct chapters, the author provides a self-contained treatment with full proofs. The purely abstract functional aspects have been clearly separated from the applications to Hamiltonian systems, so many of the results can be applied in and other areas of current research, such as wave equations, Chern-Simon functionals, and Lorentzian geometry. Morse Theory for Hamiltonian Systems not only offers clear, well-written prose and a unified account of results and techniques, but it also stimulates curiosity by leading readers into the fascinating world of symplectic topology.

The Curve Shortening Problem (Hardcover): Kai-Seng Chou, Xi-Ping Zhu The Curve Shortening Problem (Hardcover)
Kai-Seng Chou, Xi-Ping Zhu
R4,501 Discovery Miles 45 010 Ships in 12 - 17 working days

Although research in curve shortening flow has been very active for nearly 20 years, the results of those efforts have remained scattered throughout the literature. For the first time, The Curve Shortening Problem collects and illuminates those results in a comprehensive, rigorous, and self-contained account of the fundamental results.

The authors present a complete treatment of the Gage-Hamilton theorem, a clear, detailed exposition of Grayson's convexity theorem, a systematic discussion of invariant solutions, applications to the existence of simple closed geodesics on a surface, and a new, almost convexity theorem for the generalized curve shortening problem.

Many questions regarding curve shortening remain outstanding. With its careful exposition and complete guide to the literature, The Curve Shortening Problem provides not only an outstanding starting point for graduate students and new investigations, but a superb reference that presents intriguing new results for those already active in the field.

Geometric Modeling with Splines - An Introduction (Hardcover): Elaine Cohen, Richard F. Riesenfeld, Gershon Elber Geometric Modeling with Splines - An Introduction (Hardcover)
Elaine Cohen, Richard F. Riesenfeld, Gershon Elber
R5,149 Discovery Miles 51 490 Ships in 12 - 17 working days

Written by researchers who have helped to found and shape the field, this book provides an introduction to geometric modelling. The authors present a broad base of fundamentally important techniques for curve and surface representations in computer-aided modelling with a focus on how the techniques can be used in design. In achieving a balance between mathematical rigour and broad applicability, they show how theoretical properties can be harnessed to practical algorithms, how a somewhat more abstract treatment can occasionally provide unifying elegance and implement a rational advantage.

Differential Geometry with Applications to Mechanics and Physics (Hardcover): Yves Talpaert Differential Geometry with Applications to Mechanics and Physics (Hardcover)
Yves Talpaert
R8,645 Discovery Miles 86 450 Ships in 12 - 17 working days

An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.

Algebraic Geometry for Associative Algebras (Hardcover): Freddy Van Oystaeyen Algebraic Geometry for Associative Algebras (Hardcover)
Freddy Van Oystaeyen
R6,843 Discovery Miles 68 430 Ships in 12 - 17 working days

This work focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry. It offers a scheme theory that sustains the duality between algebraic geometry and commutative algebra to the noncommutative level.

Curves for the Mathematically Curious - An Anthology of the Unpredictable, Historical, Beautiful, and Romantic (Paperback):... Curves for the Mathematically Curious - An Anthology of the Unpredictable, Historical, Beautiful, and Romantic (Paperback)
Julian Havil
R583 R478 Discovery Miles 4 780 Save R105 (18%) Ships in 10 - 15 working days

Ten amazing curves personally selected by one of today's most important math writers Curves for the Mathematically Curious is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter gives an account of the history and definition of one curve, providing a glimpse into the elegant and often surprising mathematics involved in its creation and evolution. In telling the ten stories, Havil introduces many mathematicians and other innovators, some whose fame has withstood the passing of years and others who have slipped into comparative obscurity. You will meet Pierre Bezier, who is known for his ubiquitous and eponymous curves, and Adolphe Quetelet, who trumpeted the ubiquity of the normal curve but whose name now hides behind the modern body mass index. These and other ingenious thinkers engaged with the challenges, incongruities, and insights to be found in these remarkable curves-and now you can share in this adventure. Curves for the Mathematically Curious is a rigorous and enriching mathematical experience for anyone interested in curves, and the book is designed so that readers who choose can follow the details with pencil and paper. Every curve has a story worth telling.

Dynamics of Transcendental Functions (Hardcover): Xin-Hou Hua Dynamics of Transcendental Functions (Hardcover)
Xin-Hou Hua
R3,482 Discovery Miles 34 820 Ships in 12 - 17 working days

In this extensive work, the authors give a complete self-contained exposition on the subject of classic function theory and the most recent developments in transcendental iteration. They clearly present the theory of iteration of transcendental functions and their analytic and geometric aspects. Attention is concentrated for the first time on the dynamics of transcendental functions to compliment the growing body of work on rational functions. The subjects covered in detail include the fixed point theory, basic properties of Fatou and Julia sets, components of Fatou sets, the geometry of Julia sets, and the Hausdorff dimension of the Julia set.

NURBS for Curve & Surface Design - From Projective Geometry to Practical Use (Hardcover, 2nd edition): Gerald Farin NURBS for Curve & Surface Design - From Projective Geometry to Practical Use (Hardcover, 2nd edition)
Gerald Farin
R2,301 Discovery Miles 23 010 Ships in 12 - 17 working days

Non-Uniform Rational B-Splines have become the de facto standard in CAD/CAM and computer graphics. This well-known book covers NURBS from their geometric beginnings to their industrial applications. The second edition incorporates new results and a chapter on Pythagorean curves, a development that shows promise in applications such as NC machining or robot motion control. Includes more than fifty new figures.

The two-dimensional Riemann problem in gas dynamics (Hardcover): Jiequan Li, Tong Zhang, Shuli Yang The two-dimensional Riemann problem in gas dynamics (Hardcover)
Jiequan Li, Tong Zhang, Shuli Yang
R5,101 Discovery Miles 51 010 Ships in 12 - 17 working days

The Riemann problem is the most fundamental problem in the entire field of non-linear hyperbolic conservation laws. Since first posed and solved in 1860, great progress has been achieved in the one-dimensional case. However, the two-dimensional case is substantially different. Although research interest in it has lasted more than a century, it has yielded almost no analytical demonstration. It remains a great challenge for mathematicians. This volume presents work on the two-dimensional Riemann problem carried out over the last 20 years by a Chinese group. The authors explore four models: scalar conservation laws, compressible Euler equations, zero-pressure gas dynamics, and pressure-gradient equations. They use the method of generalized characteristic analysis plus numerical experiments to demonstrate the elementary field interaction patterns of shocks, rarefaction waves, and slip lines. They also discover a most interesting feature for zero-pressure gas dynamics: a new kind of elementary wave appearing in the interaction of slip lines-a weighted Dirac delta shock of the density function. The Two-Dimensional Riemann Problem in Gas Dynamics establishes the rigorous mathematical theory of delta-shocks and Mach reflection-like patterns for zero-pressure gas dynamics, clarifies the boundaries of interaction of elementary waves, demonstrates the interesting spatial interaction of slip lines, and proposes a series of open problems. With applications ranging from engineering to astrophysics, and as the first book to examine the two-dimensional Riemann problem, this volume will prove fascinating to mathematicians and hold great interest for physicists and engineers.

Vertex Operator Algebras, Number Theory and Related Topics (Paperback): Matthew Krauel, Michael Tuite, Gaywalee Yamskulna Vertex Operator Algebras, Number Theory and Related Topics (Paperback)
Matthew Krauel, Michael Tuite, Gaywalee Yamskulna
R2,957 Discovery Miles 29 570 Ships in 12 - 17 working days

This volume contains the proceedings of the International Conference on Vertex Operator Algebras, Number Theory, and Related Topics, held from June 11-15, 2018, at California State University, Sacramento, California. The mathematics of vertex operator algebras, vector-valued modular forms and finite group theory continues to provide a rich and vibrant landscape in mathematics and physics. The resurgence of moonshine related to the Mathieu group and other groups, the increasing role of algebraic geometry and the development of irrational vertex operator algebras are just a few of the exciting and active areas at present. The proceedings centre around active research on vertex operator algebras and vector-valued modular forms and offer original contributions to the areas of vertex algebras and number theory, surveys on some of the most important topics relevant to these fields, introductions to new fields related to these and open problems from some of the leaders in these areas.

Generalized Cauchy-Riemann Systems with a Singular Point (Hardcover): Zafar D. Usmanov Generalized Cauchy-Riemann Systems with a Singular Point (Hardcover)
Zafar D. Usmanov
R4,783 Discovery Miles 47 830 Ships in 12 - 17 working days

A theory of generalized Cauchy-Riemann systems with polar singularities of order not less than one is presented and its application to study of infinitesimal bending of surfaces having positive curvature and an isolated flat point is given. The book contains results of investigations obtained by the author and his collaborators.

Moduli of Vector Bundles (Paperback): Masaki Maruyama Moduli of Vector Bundles (Paperback)
Masaki Maruyama
R7,140 Discovery Miles 71 400 Ships in 12 - 17 working days

"Contains papers presented at the 35th Taniguchi International Symposium held recently in Sanda and Kyoto, Japan. Details the latest developments concerning moduli spaces of vector bundles or instantons and their application. Covers a broad array of topics in both differential and algebraic geometry."

Elliptic and Parabolic Methods in Geometry (Hardcover, New): Ben Chow, Robert Gulliver, Silvio Levy, John Sullivan Elliptic and Parabolic Methods in Geometry (Hardcover, New)
Ben Chow, Robert Gulliver, Silvio Levy, John Sullivan
R3,040 Discovery Miles 30 400 Ships in 12 - 17 working days

A dozen papers selected from a May 1994 workshop in Minneapolis document the potential of using computers and computer graphics to study a wide range of open questions in geometry. Among the topics are numerical examples of compact surfaces of constant mean curvature, the geometric behavior of harmo

Further Advances in Twistor Theory - Volume II: Integrable Systems, Conformal Geometry and Gravitation (Paperback): L. J.... Further Advances in Twistor Theory - Volume II: Integrable Systems, Conformal Geometry and Gravitation (Paperback)
L. J. Mason, L. Hughston
R4,061 R3,321 Discovery Miles 33 210 Save R740 (18%) Ships in 12 - 17 working days

Twistor theory is the remarkable mathematical framework that was discovered by Roger Penrose in the course of research into gravitation and quantum theory. It have since developed into a broad, many-faceted programme that attempts to resolve basic problems in physics by encoding the structure of physical fields and indeed space-time itself into the complex analytic geometry of twistor space. Twistor theory has important applications in diverse areas of mathematics and mathematical physics. These include powerful techniques for the solution of nonlinear equations, in particular the self-duality equations both for the Yang-Mills and the Einstein equations, new approaches to the representation theory of Lie groups, and the quasi-local definition of mass in general relativity, to name but a few. This volume and its companions comprise an abundance of new material, including an extensive collection of Twistor Newsletter articles written over a period of 15 years. These trace the development of the twistor programme and its applications over that period and offer an overview on the current status of various aspects of that programme. The articles have been written in an informal and easy-to-read style and have been arranged by the editors into chapter supplemented by detailed introductions, making each volume self-contained and accessible to graduate students and nonspecialists from other fields. Volume II explores applications of flat twistor space to nonlinear problems. It contains articles on integrable or soluble nonlinear equations, conformal differential geometry, various aspects of general relativity, and the development of Penrose's quasi-local mass construction.

Continuum Theory & Dynamical Systems (Paperback, illustrated edition): Thelma West Continuum Theory & Dynamical Systems (Paperback, illustrated edition)
Thelma West
R7,141 Discovery Miles 71 410 Ships in 12 - 17 working days

Based on the conference/workshop on Continuum Theory and Dynamical Systems held in Lafayette, Louisiana, this reference illustrates the current expansion of knowledge on the relationship between these subjects. It presents new problems in hyperspaces, induced maps, universal maps, fixed-point sets, disconnected numbers and quotient maps.;Explaining the definitions and techniques used in the two fields and providing results from both areas, this volume: examines prime end (accessible) rotation numbers for chaotic sets and Henon maps; discussed the connection between the rotation shadowing property and the structure of the rotation set for annulus homeomorphisms; offers a Nielson-type theorum concerning the minimum number of fixed points for an area preserving homeomorphism of the two disc; constructs a closed unit disc that admits many inequivalent homeomorphisms that are Denjoy on the boundary and distinct irrational rotations on the interior; gives a geometric description of a horseshoe-type mapping of a plane disc into itself whose attracting set is not chainable; and considers semigroups generated by maps topologically conjugate to contractions.;Written by experts who provide a cross-disciplinary perspective, this volume is intended for applied mathematicians, topologists, geomesters, physicists and graduate-level students in these disciplines.

Several Complex Variables and the Geometry of Real Hypersurfaces (Hardcover, New): John P. D'Angelo Several Complex Variables and the Geometry of Real Hypersurfaces (Hardcover, New)
John P. D'Angelo; Series edited by Steven G. Krantz
R7,137 Discovery Miles 71 370 Ships in 12 - 17 working days

Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with a real analytic boundary. The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. You will learn how to decide whether a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface, and why it's important. The book concludes with two sets of problems: routine problems and difficult problems (many of which are unsolved).
Principal prerequisites for using this book include a thorough understanding of advanced calculus and standard knowledge of complex analysis in one variable. Several Complex Variables and the Geometry of Real Hypersurfaces will be a useful text for advanced graduate students and professionals working in complex analysis.

Discrete Iterated Function Systems (Hardcover): Mario Peruggia Discrete Iterated Function Systems (Hardcover)
Mario Peruggia
R4,497 Discovery Miles 44 970 Ships in 12 - 17 working days

Written for researchers and developers applying Integrated Function Systems in the creation of fractal images, this book presents a modification of a widely used probabilistic algorithm for generating IFS-encoded images. The book also includes a discussion of how IFS techniques can be applied to produce animated motion pictures.

Geometric Concepts for Geometric Design (Hardcover): Hartmut Prautzsch, Wolfgang Boehm Geometric Concepts for Geometric Design (Hardcover)
Hartmut Prautzsch, Wolfgang Boehm
R5,103 Discovery Miles 51 030 Ships in 12 - 17 working days

This book is a comprehensive tool both for self-study and for use as a text in classical geometry. It explains the concepts that form the basis for computer-aided geometric design.

The Atiyah-Patodi-Singer Index Theorem (Hardcover): Richard Melrose The Atiyah-Patodi-Singer Index Theorem (Hardcover)
Richard Melrose
R3,485 Discovery Miles 34 850 Ships in 12 - 17 working days

Based on the lecture notes of a graduate course given at MIT, this sophisticated treatment leads to a variety of current research topics and will undoubtedly serve as a guide to further studies.

Differential Geometry and Statistics (Hardcover, Softcover Repri): Valerie Isham Differential Geometry and Statistics (Hardcover, Softcover Repri)
Valerie Isham; M. K. Murray
R5,245 Discovery Miles 52 450 Ships in 12 - 17 working days

Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions there has been interest among statisticians in the application of differential geometry to statistics. This interest has increased rapidly in the last couple of decades with the work of a large number of researchers. Until now an impediment to the spread of these ideas into the wider community of statisticians is the lack of a suitable text introducing the modern co-ordinate free approach to differential geometry in a manner accessible to statisticians.

Free Resolutions in Commutative Algebra and Algebraic Geometry (Paperback, New): David Eisenbud Free Resolutions in Commutative Algebra and Algebraic Geometry (Paperback, New)
David Eisenbud
R1,841 Discovery Miles 18 410 Ships in 12 - 17 working days

The selected contributions in this volume originated at the Sundance conference, which was devoted to discussions of current work in the area of free resolutions. The papers include new research, not otherwise published, and expositions that develop current problems likely to influence future developments in the field.

On the Geometry of Some Special Projective Varieties (Paperback, 1st ed. 2016): Francesco Russo On the Geometry of Some Special Projective Varieties (Paperback, 1st ed. 2016)
Francesco Russo
R2,275 Discovery Miles 22 750 Ships in 12 - 17 working days

Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases. It also provides a solution of Hartshorne's Conjecture on Complete Intersections for the class of quadratic manifolds and new short proofs of previously known results, using the modern tools of Mori Theory and of rationally connected manifolds. The new approach to some of the problems considered can be resumed in the principle that, instead of studying a special embedded manifold uniruled by lines, one passes to analyze the original geometrical property on the manifold of lines passing through a general point and contained in the manifold. Once this embedded manifold, usually of lower codimension, is classified, one tries to reconstruct the original manifold, following a principle appearing also in other areas of geometry such as projective differential geometry or complex geometry.

Encounters with Euclid - How an Ancient Greek Geometry Text Shaped the World (Hardcover): Benjamin Wardhaugh Encounters with Euclid - How an Ancient Greek Geometry Text Shaped the World (Hardcover)
Benjamin Wardhaugh
R827 R694 Discovery Miles 6 940 Save R133 (16%) Ships in 10 - 15 working days

A sweeping cultural history of one of the most influential mathematical books ever written Euclid's Elements of Geometry is one of the fountainheads of mathematics—and of culture. Written around 300 BCE, it has traveled widely across the centuries, generating countless new ideas and inspiring such figures as Isaac Newton, Bertrand Russell, Abraham Lincoln, and Albert Einstein. Encounters with Euclid tells the story of this incomparable mathematical masterpiece, taking readers from its origins in the ancient world to its continuing influence today. In this lively and informative book, Benjamin Wardhaugh explains how Euclid’s text journeyed from antiquity to the Renaissance, introducing some of the many readers, copyists, and editors who left their mark on the Elements before handing it on. He shows how some read the book as a work of philosophy, while others viewed it as a practical guide to life. He examines the many different contexts in which Euclid's book and his geometry were put to use, from the Neoplatonic school at Athens and the artisans' studios of medieval Baghdad to the Jesuit mission in China and the workshops of Restoration London. Wardhaugh shows how the Elements inspired ideas in theology, art, and music, and how the book has acquired new relevance to the strange geometries of dark matter and curved space. Encounters with Euclid traces the life and afterlives of one of the most remarkable works of mathematics ever written, revealing its lasting role in the timeless search for order and reason in an unruly world.

Exploring Geometry (Paperback, 2nd edition): Michael Hvidsten Exploring Geometry (Paperback, 2nd edition)
Michael Hvidsten
R1,430 Discovery Miles 14 300 Ships in 12 - 17 working days

Exploring Geometry, Second Edition promotes student engagement with the beautiful ideas of geometry. Every major concept is introduced in its historical context and connects the idea with real-life. A system of experimentation followed by rigorous explanation and proof is central. Exploratory projects play an integral role in this text. Students develop a better sense of how to prove a result and visualize connections between statements, making these connections real. They develop the intuition needed to conjecture a theorem and devise a proof of what they have observed. Features: Second edition of a successful textbook for the first undergraduate course Every major concept is introduced in its historical context and connects the idea with real life Focuses on experimentation Projects help enhance student learning All major software programs can be used; free software from author

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