Geometry Books
Birkhauser Verlag AG Geometry, Structure and Randomness in
Book SynopsisThis book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.Table of ContentsImre Bárány: Tensors, colours, octahedral.- Maria Chudnovsky: Cliques and stable sets in undirected graphs.- Mauro Di Nasso: A taste of nonstandard methods in combinatorics of numbers.- Béla Bollobás, Zoltán Füredi, Ida Kantor, G. O. H. Katona and Imre Leader: A coding problem for pairs of subsets.- Jirí Matousek: String graphs and separators.- Jaroslav Nesetril and Patrice Ossona de Mendez: On first-order definable colorings.- Ryan Schwartz and József Solymosi: Combinatorial applications of the subspace theorem.- Peter Hegarty and Dmitry Zhelezov: Can connected commuting graphs of finite groups have arbitrarily large diameter?
£24.69
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
Springer Verlag, Singapore Dilations, Completely Positive Maps and Geometry
Book SynopsisThis book introduces the dilation theory of operators on Hilbert spaces and its relationship to complex geometry. Classical as well as very modern topics are covered in the book. On the one hand, it introduces the reader to the characteristic function, a classical object used by Sz.-Nagy and Foias and still a topic of current research. On the other hand, it describes the dilation theory of the symmetrized bidisc which has been developed mostly in the present century and is a very active topic of research. It also describes an abstract theory of dilation in the setting of set theory. This was developed very recently.A good portion of the book discusses various geometrical objects like the bidisc, the Euclidean unit ball, and the symmetrized bidisc. It shows the similarities and differences between the dilation theory in these domains. While completely positive maps play a big role in the dilation theory of the Euclidean unit ball, this is not so in the symmetrized bidisc for example. There, the central role is played by an operator equation. Targeted to graduate students and researchers, the book introduces the reader to different techniques applicable in different domains.Table of ContentsDilation for One Operator.- C*-Algebras and Completely Positive Maps.- Dilation Theory in Two Variables - The Bidisc.- Dilation Theory in Several Variables - the Euclidean Ball.- The Euclidean Ball - The Drury Arveson Space.- Dilation Theory in Several Variables - The Symmetrized Bidisc.- An Abstract Dilation Theory.
£82.49
£26.24
Forgotten Books Les Mathématiques Appliquées aux BeauxArts Classic Reprint
£23.99
Hardpress Publishing An Elementary Treatise on Plane and Solid Geometry 1
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£13.25
Hardpress Publishing lments De Gomtrie Descriptive 1
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£16.10
HardPress Publishing Der Goldene Schnitt und Die Anwendung Desselben in Der Kunst
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£10.90
Hardpress Publishing Thorie Gomtrique Des Engrenages Destins Transmettre Le Mouvement De Rotation Entre Deux Axes Situs Ou Non Situs Dans Un Mme Plan 1
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£12.95
Hardpress Publishing De Contorni Delle Ombre Ordinarie Trattato 1
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£14.82
£35.99
Obelisco HIJOS DE LA GEOMETRIA
Book Synopsis
£24.67
Elsevier Science Geometric Measure Theory
Trade Review"Morgan’s book offers the best access I know into this difficult subject. It won’t make the reader an expert, but it does open the door to more detailed treatments. An excellent bibliography is provided." --MAA ReviewsTable of Contents1. Geometric Measure Theory2. Measures3. Lipschitz Functions and Rectifiable Sets4. Normal and Rectifiable Currents5. The Compactness Theorem and the Existence of Area-Minimizing Surfaces6. Examples of Area-Minimizing Surfaces7. The Approximation Theorem8. Survey of Regularity Results9. Monotonicity and Oriented Tangent Cones10. The Regularity of Area-Minimizing Hypersurfaces11. Flat Chains Modulo v, Varifolds, and (M,E,)-Minimal Sets12. Miscellaneous Useful Results13. Soap Bubble Clusters14. Proof of Double Bubble Conjecture15. The Hexagonal Honeycomb and Kelvin Conjectures16. Immiscible Fluids and Crystals17. Isoperimetric Theorems in General Codimension18. Manifolds with Density and Perelman's Proof of the Poincaré Conjecture19. Double Bubbles in Spheres, Gauss Space, and Tori20. The Log-Convex Density Conjecture21. Solutions to Exercises
£62.09
Taylor & Francis Ltd CurvedFolding Origami Design
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£156.75
Taylor & Francis Ltd Volumetric Discrete Geometry Discrete Mathematics and Its Applications
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£104.50
Taylor & Francis Ltd A First Course In Chaotic Dynamical Systems
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£80.74
Taylor & Francis Ltd Digital Geometry in Image Processing
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£56.99
Taylor & Francis Ltd An Invariant Approach to Statistical Analysis of Shapes
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£58.89
Taylor & Francis Ltd Introductory Theory of Topological Vector SPates 167 Books in Soils Plants and the Environment
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£58.89
Taylor & Francis Ltd Advanced Game Development with Programmable Graphics Hardware
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£54.14
Taylor & Francis Ltd Fundamental Groups and Covering Spaces
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£56.04
Taylor & Francis Ltd Variational Methods in Lorentzian Geometry
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£56.04
Taylor & Francis Ltd Geometric Concepts for Geometric Design
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£56.04
Taylor & Francis Ltd Differential Algebras in Topology
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£56.04
Taylor & Francis Ltd Point Set Theory
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£56.04
Taylor & Francis Ltd Wavelet Subdivision Methods
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£58.89
Taylor & Francis Ltd Topics on Continua Chapman HallCRC Pure and Applied Mathematics
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£56.04
Taylor & Francis Ltd Real And Complex Singularities
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£56.04
Taylor & Francis Ltd Variational Problems in Topology The Geometry of Length Area and Volume
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£56.04
Taylor & Francis Ltd Practical Linear Algebra
Book SynopsisLinear algebra is growing in importance. 3D entertainment, animations in movies and video games are developed using linear algebra. Animated characters are generated using equations straight out of this book. Linear algebra is used to extract knowledge from the massive amounts of data generated from modern technology.The Fourth Edition of this popular text introduces linear algebra in a comprehensive, geometric, and algorithmic way. The authors start with the fundamentals in 2D and 3D, then move on to higher dimensions, expanding on the fundamentals and introducing new topics, which are necessary for many real-life applications and the development of abstract thought. Applications are introduced to motivate topics.The subtitle, A Geometry Toolbox, hints at the book's geometric approach, which is supported by many sketches and figures. Furthermore, the book covers applications of triangles, polygons, conics, and curves. Examples demonstrate each topTable of Contents1. Descartes' Discovery. 1.1. Local and Global Coordinates: 2D. 1.2. Going from Global to Local. 1.3. Local and Global Coordinates: 3D. 1.4. Stepping Outside the Box. 1.5. Application: Creating Coordinates. 1.6. Exercises. 2. Here and There: Points and Vectors in 2D. 2.1. Points and Vectors. 2.2. What's the Difference? 2.3. Vector Fields. 2.4. Length of a Vector. 2.5. Combining Points. 2.6. Independence. 2.7. Dot Product. 2.8. Application: Lighting Model. 2.9. Orthogonal Projections. 2.10. Inequalities. 2.11. Exercises. 3. Lining Up: 2D Lines. 3.1. Defining a Line. 3.2. Parametric Equation of a Line. 3.3. Implicit Equation of a Line. 3.4. Explicit Equation of a Line. 3.5. Converting Between Line Forms. 3.6. Distance of a Point to a Line. 3.7. The Foot of a Point. 3.8. A Meeting Place: Computing Intersections. 3.9. Application: Closest Point of Approach. 3.10. Exercises. 4. Changing Shapes: Linear Maps in 2D. 4.1. Skew Target Boxes. 4.2. The Matrix Form. 4.3. Linear Spaces. 4.4. Scalings. 4.5 Reflections. 4.6. Rotations. 4.7. Shears. 4.8. Projections. 4.9. Application: Free-form Deformations. 4.10. Areas and Linear Maps: Determinants. 4.11. Composing Linear Maps. 4.12. More on Matrix Multiplication. 4.13. Matrix Arithmetic Rules. 4.14. Exercises. 5. 2 x 2 Linear Systems. 5.1. Skew Target Boxes Revisited. 5.2. The Matrix Form. 5.3. A Direct Approach: Cramer's Rule. 5.4. Gauss Elimination. 5.5. Pivoting. 5.6. Unsolvable Systems. 5.7. Underdetermined Systems. 5.8. Homogeneous Systems. 5.9. Kernel. 5.10. Undoing Maps: Inverse Matrices. 5.11. Defining a Map. 5.12. Change of Basis. 5.13. Application: Intersecting Lines. 5.14. Exercises. 6. Moving Things Around: Affine Maps in 2D. 6.1. Coordinate Transformations. 6.2. Affine and Linear Maps. 6.3. Translations. 6.4. Application: Animation. 6.5. Mapping Triangles to Triangles. 6.6. Composing Affine Maps. 6.7. Exercises. 7. Eigen Things. 7.1. Fixed Directions. 7.2. Eigenvalues. 7.3. Eigenvectors. 7.4. Striving for More Generality. 7.5. The Geometry of Symmetric Matrices and the Eigendecomposition. 7.6. Quadratic Forms. 7.7. Repeating Maps. 7.8. Exercises. 8. 3D Geometry. 8.1. From 2D to 3D. 8.2. Cross Product. 8.3. Lines. 8.4. Planes. 8.5. Scalar Triple Product. 8.6. Application: Lighting and Shading. 8.7. Exercises. 9. Linear Maps in 3D. 9.1. Matrices and Linear Maps. 9.2. Linear Spaces. 9.3. Scalings. 9.4. Reflections. 9.5 Shears. 9.6. Rotations. 9.7. Projections. 9.8. Volumes and Linear Maps: Determinants. 9.9. Combining Linear Maps. 9.10. Inverse Matrices. 9.11. Application: Mapping Normals. 9.12. More on Matrices. 9.13. Exercises. 10. Affine Maps in 3D. 10.1. Affine Maps. 10.2. Translations. 10.3. Mapping Tetrahedra. 10.4. Parallel Projections. 10.5. Homogeneous Coordinates and Perspective Maps. 10.6. Application: Building Instance Models. 10.7. Exercises. 11. Interactions in 3D. 11.1. Distance Between a Point and a Plane. 11.2. Distance Between Two Lines. 11.3. Lines and Planes: Intersections. 11.4. Intersecting a Triangle and a Line. 11.5. Reflections. 11.6. Intersecting Three Planes. 11.7. Intersecting Two Planes. 11.8. Creating Orthonormal Coordinate Systems. 11.9. Application: Camera Model. 11.10. Exercises. 12. Gauss for Linear Systems. 12.1. The Problem. 12.2. The Solution via Gauss Elimination. 12.3. Homogeneous Linear Systems. 12.4. Inverse Matrices. 12.5. LU Decomposition. 12.6. Determinants. 12.7. Least Squares. 12.8. Application: Fitting Data from a Femoral Head. 12.9. Exercises. 13. Alternative System Solvers. 13.1. The Householder Method. 13.2. Vector Norms. 13.3. Matrix Norms. 13.4. The Condition Number. 13.5. Vector Sequences. 13.6. Iterative Methods: Gauss-Jacobi and Gauss-Seidel. 13.7. Application: Mesh Smoothing. 13.8. Exercises. 14. General Linear Spaces. 14.1. Basic Properties of Linear Spaces. 14.2. Linear Maps. 14.3. Inner Products. 14.4. Gram-Schmidt Orthonormalization. 14.5. QR Decompositon. 14.6. A Gallery of Spaces. 14.7. Least Squares. 14.8. Application: Music Analysis. 14.9. Exercises. 15. Eigen Things Revisited. 15.1. The Basics Revisited. 15.2. Similarity and Diagonalization. 15.3. Quadratic Forms. 15.4. The Power Method. 15.5. Application: Google Eigenvector. 15.6. QR Algorithm. 15.7. Eigenfunctions. 15.8. Application: Inuenza Modelling. 15.9. Exercises. 16. The Singular Value Decomposition. 16.1. The Geometry of the 2 x 2 Case. 16.2. The General Case. 16.3. SVD Steps. 16.4. Singular Values and Volumes. 16.5. The Pseudoinverse. 16.6. Least Squares. 16.7. Application: Image Compression. 16.8. Principal Components Analysis. 16.9. Application: Face Authentication. 16.10. Exercises. 17. Breaking It Up: Triangles. 17.1. Barycentric Coordinates. 17.2. Affine Invariance. 17.3. Some Special Points. 17.4. 2D Triangulations. 17.5. A Data Structure. 17.6. Application: Point Location. 17.7. 3D Triangulations. 17.8. Exercises. 18. Putting Lines Together: Polylines and Polygons. 18.1 Polylines. 18.2. Polygons. 18.3. Convexity. 18.4. Types of Polygons. 18.5. Unusual Polygons. 18.6. Turning Angles and Winding Numbers. 18.7. Area. 18.8. Application: Planarity Test. 18.9. Application: Inside or Outside? 18.10. Exercises. 19. Conics. 19.1. The General Conic. 19.2. Analyzing Conics. 19.3. General Conic to Standard Position. 19.4. The Action Ellipse. 19.5. Exercises. 20. Curves. 20.1. Parametric Curves. 20.2. Properties of Bézier Curves. 20.3. The Matrix Form. 20.4. Derivatives. 20.5. Composite Curves. 20.6. The Geometry of Planar Curves. 20.7. Application: Moving along a Curve. 20.8. Exercises. A. Applications. B. Glossary. C. Selected Exercises Solutions. Bibliography.
£78.84
Taylor & Francis Ltd Geometry Symmetries and Classical Physics
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£128.25
Taylor & Francis Ltd Polynomials Dynamics and Choice
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£45.99
Taylor & Francis Ltd Polynomials Dynamics and Choice
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£114.00
Taylor & Francis Ltd Introduction to Lorentz Geometry
Book SynopsisLorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity. Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe, such as: What is the shape of the universe? What is a spacetime? What is the relation between gravity and curvature? Why exactly is time treated in a different manner than other spatial dimensions? Introduction to Lorentz Geometry: Curves and Surfaces intends to provide the reader with the minimum mathematical background needed to pursue these very interesting questions, by presenting the classical theory of curves and surfaces in both Euclidean and Lorentzian ambient spaces simultaneously. Features: Over 300 exercises Suitable for senior undergraduates and graduates studying Mathematics and Physics Written in an accessible style wTable of Contents1. Welcome to Lorentz-Minkowski Space. 1.1. Pseudo–Euclidean Spaces. 1.2. Subspaces of Rᵑᵥ. 1.3. Contextualization in Special Relativity. 1.4. Isometries in Rᵑᵥ. 1.5. Investigating O1(2, R) And O1(3, R). 1.6 Cross Product in Rᵑᵥ. 2. Local Theory of Curves. 2.1. Parametrized Curves in Rᵑᵥ. 2.2. Curves in the Plane. 2.3. Curves in Space. 3. Surfaces in Space. 3.1. Basic Topology of Surfaces. 3.2. Casual type of Surfaces, First Fundamental Form. 3.3. Second Fundamental Form and Curvatures. 3.4. The Diagonalization Problem. 3.5. Curves in Surface. 3.6. Geodesics, Variational Methods and Energy. 3.7. The Fundamental Theorem of Surfaces. 4. Abstract Surfaces and Further Topics. 4.1. Pseudo-Riemannian Metrics. 4.2. Riemann’s Classification Theorem. 4.3. Split-Complex Numbers and Critical Surfaces. 4.4 Digression: Completeness and Causality
£36.99
Taylor & Francis Ltd Geometry for the Artist
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£118.75
Taylor & Francis Ltd A Sampler of Useful Computational Tools for Applied Geometry Computer Graphics and Image Processing
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£44.99
Taylor & Francis Ltd FourDimensional Manifolds and Projective Structure
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£99.75
Elsevier Science Analysis on Real and Complex Manifolds
Table of Contents1. Differentiable Functions in Rn. Taylor's Formula. Partitions of Unity. Inverse Functions, Implicit Functions and the Rank Theorem. Sard's Theorem and Functional Dependence. Borel's Theorem on Taylor Series. Whitney's Approximation Theorem. An Approximation Theorem for Holomorphic Functions. Ordinary Differential Equations. 2. Manifolds. Basic Definitions. The Tangent and Cotangent Bundles. Grassmann Manifolds. Vector Fields and Differential Forms. Submanifolds. Exterior Differentiation. Orientation. Manifolds with Boundary. Integration. One Parameter Groups. The Frobenius Theorem. Almost Complex Manifolds. The Lemmata of Poincaré and Grothendieck. Applications: Hartog's Continuation Theorem and the Oka-Weil Theorem. Immersions and Imbeddings: Whitney's Theorems. Thom's Transversality Theorem. 3. Linear Elliptic Differential Operators. Vector Bundles. Fourier Transforms. Linear Differential Operators. The Sobolev Spaces. The Lemmata of Rellich and Sobolev. The Inequalities of Garding and Friedrichs. Elliptic Operators with C8 Coefficients: The Regularity Theorem. Elliptic Operators with Analytic Coefficients. The Finiteness Theorem. The Approximation Theorem and Its Application to Open Riemann Surfaces
£44.99
Taylor & Francis Ltd Harmonic Maps Into Homogeneous Spaces
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£166.25
Taylor & Francis Ltd Differential Forms on Singular Varieties
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£147.25
Taylor & Francis Ltd A Geometrical Approach to Physics
Book SynopsisThis book provides an accessible introduction to using the tools of differential geometry to tackle a wide range of topics in physics, with the concepts developed through numerous examples to help the reader become familiar with the techniques.Physical applications are used to develop the techniques and demonstrate their wide-ranging applicability. Formalism is introduced sparingly and step-by-step, where it is needed, and chapters contain exercises for readers to test their understanding. Worked solutions to the exercises are included.It is an ideal textbook for advanced undergraduate or postgraduate courses on mathematical methods for physicists, for students whose background is in physics rather than mathematics. It is assumed that the reader has no prior knowledge of mathematical methods beyond the content of a standard undergraduate physics degree.The purpose of the book is to act as a gateway' to more advanced books on the applications of differential geom
£45.99
Taylor & Francis Ltd Elementary Introduction to Quantum Geometry
Book SynopsisThis graduate textbook provides an introduction to quantum gravity, when spacetime is two-dimensional. The quantization of gravity is the main missing piece of theoretical physics, but in two dimensions it can be done explicitly with elementary mathematical tools, but it still has most of the conceptional riddles present in higher dimensional (not yet known) quantum gravity. It provides an introduction to a very interdisciplinary field, uniting physics (quantum geometry) and mathematics (combinatorics) in a non-technical way, requiring no prior knowledge of quantum field theory or general relativity. Using the path integral, the chapters provide self-contained descriptions of random walks, random trees and random surfaces as statistical systems where the free relativistic particle, the relativistic bosonic string and two-dimensional quantum gravity are obtained as scaling limits at phase transition points of these statistical systems. The geometric nature of the theoriTable of Contents1. Preliminary Material Part 1: the Path Integral. 2. The Free Relativistic particle. 3. One-Dimensional Quantum Gravity. 4. Branched Polymers. 5. Random Surfaces and Bosonic Strings. 6. Two-Dimensional Quantum Gravity. 7. The Fractal Structure of 2D Gravity. 8. The Causal Dynamical Triangulation model. Appendix A: Preliminary Material Part 2: Green Functions. Appendix B: Problem Sets 1-12. Appendix C: Solutions to Problem Sets 1-13.
£73.14
Taylor & Francis Ltd Mathematical Conundrums
Book SynopsisWant to sharpen your mathematical wits? If so, then Mathematical Conundrums is for you. Daily Telegraph enigmatologist, Barry R. Clarke, presents over 120 fiendish problems that will test both your ingenuity and persistence. Between these covers are puzzles in geometry, arithmetic, and algebra (there is even a section for computer programmers). And, for the smartest readers who wish to stretch their mind to its limits, a selection of engaging logic and visual lateral puzzles is included. Although no puzzle requires a greater knowledge of mathematics than the high school curriculum, this collection will take you to the edge. But are you equal to the challenge? Features High-school level of mathematics is the only pre-requisite Variety of algebraic, route-drawing, and geometrical conundrums Hints section for the lateral puzzles Warm-up excercises to sharpen the wits Full solutions to every problem Barry R. Clarke has published over 1,500 puzzles in The Daily Telegraph and has contributed enigmas to New Scientist, The Sunday Times, Readerâs Digest, The Sunday Telegraph, and Prospect magazine. His book Challenging Logic Puzzles Mensa has sold over 100,000 copies. As well as a PhD in Shakespeare Studies, Barry has a masterâs degree and academic publications in quantum physics. He is now working on a revised theory of the hydrogen atom. Other skills include mathematics tutor, filmmaker, comedy-sketch writer, cartoonist, computer programmer, and blues guitarist! For more information please visit http://barryispuzzled.com.Table of Contents1. Introduction. 2. Mind sharpeners. 3. Geometry. 4. Arithmetic. 5. Algebra. 6. Programmable Puzzles. 7. Logic. 8. Visual-lateral
£23.99
Taylor & Francis Ltd A First Course In Chaotic Dynamical Systems
Book SynopsisA First Course in Chaotic Dynamical Systems: Theory and Experiment, Second EditionThe long-anticipated revision of this well-liked textbook offers many new additions. In the twenty-five years since the original version of this book was published, much has happened in dynamical systems. Mandelbrot and Julia sets were barely ten years old when the first edition appeared, and most of the research involving these objects then centered around iterations of quadratic functions. This research has expanded to include all sorts of different types of functions, including higher-degree polynomials, rational maps, exponential and trigonometric functions, and many others. Several new sections in this edition are devoted to these topics. The area of dynamical systems covered in A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition is quite accessible to sTable of ContentsPreface to the Second Edition, 1. A Visual and Historical Tour, 2. Examples of Dynamical Systems, 3. Orbits, 4. Graphical Analysis, 5. Fixed and Periodic Points, 6. Bifurcations, 7. The Quadratic Family, 8. Transition to Chaos, 9. Symbolic Dynamics, 10. Chaos, 11. Sharkovsky’s Theorem, 12. Role of the Critical Point, 13. Newton’s Method, 14. Fractals, 15. Complex Functions, 16. The Julia Set, 17. The Mandelbrot Set, 18. Other Complex Dynamical Systems, Appendices, Bibliography, Index
£43.99
Taylor & Francis Ltd Encounters with Chaos and Fractals
Book SynopsisEncounters with Chaos and Fractals, Third Edition provides an accessible introduction to chaotic dynamics and fractal geometry. It incorporates important mathematical concepts and backs up the definitions and results with motivation, examples, and applications.
£73.14
Taylor & Francis Ltd Six Simple Twists
Book SynopsisThis new edition of Six Simple Twists: The Pleat Pattern Approach to Origami Tessellation Design introduces an innovative pleat pattern technique for origami designs that is easily accessible to anyone who enjoys the geometry of paper. The book begins with six basic forms meant to ease the reader into the style, and then systematically scaffolds the instructions to build a strong understanding of the techniques, leading to instructions on a limitless number of patterns. It then describes a process of designing additional building blocks. At the end, what emerges is a fascinating artform that will enrich folders for many years. Unlike standard, project-based origami books, Six Simple Twists focuses on how to design, rather than construct. In this thoroughly updated second edition, the book explores new techniques and example tessellations, with full-page images, and mathematical analysis of the patterns. A reader will, through practice, gain the abiTrade Review"The second edition of Six Simple Twists is a marvelous expansion of the original; like the first edition it provides an introduction to the vast, wide world of origami twist tessellations, with a focus on those based on a hexagonal grid. Through copious and detailed photographs, he shows not just the structure, but how individual folds are actuated, and then how they may be combined in beautiful ways. An expanded selection of photographs of works by worldwide artists provides both inspiration and challenge for the budding tessellator and experienced artist alike."– Robert Lang, author of Origami Design Secrets: Mathematical Methods for an Ancient Art"In this wonderfully expanded new edition, Ben Parker not only describes the basic elements composing his intricate pleated paper artworks, he also unlocks their secrets and logic and teaches their molecules and several examples in a clear format, allowing the reader to create new folded patterns, through both practical and technical approaches!"– Alessandro Beber, author of Origami New Worlds"This new edition of Six Simple Twists is a tremendous expansion of the first edition. Through the thorough investigation of the foundational elements of origami tessellation, Ben has laid the groundwork for understanding design and application of geometry in paper. The second edition expands and refines the insights of the first with copious illustrations and examples, clear definitions and thought provoking exercises. For anyone fascinated by the geometry of origami, or even curious about place of origami in the field of geometry, this edition is absolutely necessary."– Joel Cooper, Origami artist"Ben's second edition is full to the brim with new and exciting insights into the craft and mechanisms of origami tessellations, extending the first edition by a couple hundred pages. He provides extensive explanations and deep insights into the maths behind the scenes and accompanies it with a plethora of projects for you to fold at home."– Peter Keller, Origami artist"As soon as we open the pages of this book, Benjamin DiLeonardo-Parker’s enthusiasm for the design and creation of origami tessellations is clear. The author reveals the patterns that can be formed by paper pleats and their combinations and demonstrates how by folding paper in different configurations the beautiful structures known as origami tessellations can be constructed. The author explains to his readers how to fold tessellations and encourages them to apply their learning to explore the subject to generate their own folding techniques and create their own designs, offering case studies to experiment with. The book is generously supplied with photographs and diagrams illustrating each step of the techniques, and a comprehensive glossary is provided. The author’s creativity and attention to detail are a delight. This second edition is a greatly expanded version of its predecessor [1], benefiting from more instruction in basic skills and pleat manipulation methods, enhanced illustration of the processes, a greater range of demonstrated patterns, an improved notation system, and further mathematical analysis of the behaviour of twists.[. . .] The thorough, detailed, methodical treatment of this subject will surely inspire readers of this book to try out the techniques for themselves, and to embark upon creating many of the tessellations described here, and, with experience gained, even attempting their own tessellation designs. I certainly feel encouraged to reach for some paper and get folding."– Dorothy Leddy, London Mathematical SocietyTable of ContentsPart I1.00 - Why Study Pleat Patterns?1.01 - Basics and Preparation1.02 - How Pleat Patterns Differ from Traditional Origami1.03 - How to Read the Diagrams and Fold Parity1.04 - Folding Uniform Parallel Creases1.05 - Grid Axes and How to Fold a Hexagon1.06 - How to Fold a Triangle Grid1.07 - Simple Pleat1.08 - The Six Simple Twists1.09 - Triangle Twist1.10 - Triangle Spread1.11 - Hex Twist1.12 - Hex Spread1.13 - Rhombic Twist1.14 - Arrow Twist1.15 - Anatomy of a Molecule1.16 - Pleat Intersection NotationPart II2.00 - How to Use the Six Simple Twists2.01 - 32nd’s Grid2.02 - Locking and Unlocking Pleats2.03 - Triangle Twist Tessellation2.04 - 3.6.3.6 Tessellation2.05 - Tessellation Basics2.06 - Applying Tessellation Knowledge Folding2.07 - Triangle Weave Tessellation2.08 - 3.6.3.6 Weave Tessellation2.09 - 6.6.6 Hexagonal Failing Cluster2.10 - Modifications2.11 - Backtwisting2.12 - Twist Handedness and Pleat Symmetry2.13 - Pleat Flattening2.14 - Triangle Twist Tessellation with Flattened Pleats2.15 - Hidden Circles Pattern2.16 - Rhombic Twist Tessellation2.17 - Rhombic Twist Variants2.18 - Twist Sinking2.19 - Twist Expansion2.20 - Nub Offset Tessellation2.21 - Shift Rosette Tessellation2.22 - Ridge Creation2.23 - Button Molecule 2.24 - Button Molecule Tessellation2.25 - Triangle Flagstone Tessellation and Offsetting Pleats2.26 - 3.6.3.6 Flagstone Tessellation2.27 - Crooked Split2.28 - Snowflake Tessellation2.29 - Tulip Split2.30 - Tulip Split Tessellation2.31 - Molecule Size and Different Grid Densities2.32 - “Front” and “Back” Sides2.33 - Tendril Tessellation2.34 - Inverting a Pleat2.35 - Iso-Area Triangle Twist Tessellation2.36. - Pleat Pushing2.37 - Platform Tess2.38 - Triple Twist TessPart III3.00 - Pleat Patterns as Artwork3.01 - Gallery3.02 - Pleat-to-Molecule Analysis3.03 - Twist Archetype Sets3.04 - Molecule Database3.05 - Archetype Composition3.06 - Actions and Notation3.07 - Splitting Equation3.08 - Normal Polygon Models3.09 - Circle Cutout Model3.10 - Molecule-to-Pleat Analysis3.11 - Sectioning Model of Perfect Twist Design3.12 - Brocard PointsFinal thoughtsPleat Notation Thoughts By Matthew BenetGlossary
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Cambridge University Press Hinged Dissections
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