Euclidean geometry Books
Taschen GmbH Oliver Byrne. The First Six Books of the Elements
Book SynopsisNearly 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 seminal publication is now available in a beautiful new edition. A masterwork of art and science, it is as remarkable 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.Trade Review“Every graphic designer, book lover and math nerd will be awestruck.” * The New York Times *
£62.78
HarperCollins Publishers The Road to Geometry
Book Synopsis Euclid's Elements of Geometry was a book that changed the world. Trade Review Praise for The Book of Wonders ‘An astonishingly readable and informative history of the greatest mathematical bestseller of all time, from ancient Greece to dark energy. The writing is vivid and the stories are gripping. Highly recommended!’Ian Stewart, author of Significant Figures ‘Benjamin Wardhaugh is an excellent storyteller and his collected short story approach to the history of The Elements works splendidly… simultaneously educational, entertaining and illuminating … A highly desirable read for all those, both professional and amateur, who interest themselves in the histories of mathematics, science and knowledge … over almost two and a half millennia’Thony Christie, The Renaissance Mathematicus ‘A fascinating tour through 2300 years of reading, re-imagining, & responding to perhaps most important textbook ever written’ Seb Falk, author of The Light Ages Praise for Benjamin Wardhaugh’s Gunpowder and Geometry ‘Meticulous yet lively biography, even those who have never heard of its subject could hardly disagree’ Sunday Times ‘Wardhaugh graphically describes the conditions Hutton escaped from and the importance of Newcastle and its coal to the changes taking place in Britain in the second half of the eighteenth century . . . like something from the pages of a Jane Austen novel . . . Wardhaugh has done a good job of rescuing Hutton from obscurity and setting the man and his achievements in the context of their times . . . This account of how “the pit boy turned professor” became “one of the most revered British scientists of his day” is well worth reading’ Literary Review
£21.25
Wooden Books Compound Polytopes polygons tilings polyhedra
Book Synopsis
£8.50
HarperCollins Publishers Encounters with Euclid How an Ancient Greek
Book SynopsisAn astonishingly readable and informative history of the greatest mathematical bestseller of all time The writing is vivid and the stories are gripping. Highly recommended ' IAN STEWART, AUTHOR OF SIGNIFICANT FIGURESEuclid's Elements of Geometry was a book that changed the world. In this sweeping history, Benjamin Wardhaugh traces how the ancient Greek text on mathematics often hailed as the world's first textbook shaped two thousand years of art, philosophy and literature, as well as science and maths.With stories of influence on every continent, and encounters with the likes of Ptolemy and Isaac Newton, Hobbes and Lewis Carroll, Wardhaugh gives dramatic life to the evolution of mathematics.Previously published as The Book of WondersTrade Review‘An astonishingly readable and informative history of the greatest mathematical bestseller of all time, from ancient Greece to dark energy. The writing is vivid and the stories are gripping. Highly recommended!’Ian Stewart, author of Significant Figures ‘Benjamin Wardhaugh is an excellent storyteller and his collected short story approach to the history of The Elements works splendidly… simultaneously educational, entertaining and illuminating … A highly desirable read for all those, both professional and amateur, who interest themselves in the histories of mathematics, science and knowledge … over almost two and a half millennia’Thony Christie, The Renaissance Mathematicus Praise for Benjamin Wardhaugh’s Gunpowder and Geometry ‘Meticulous yet lively biography, even those who have never heard of its subject could hardly disagree’ Sunday Times ‘Wardhaugh graphically describes the conditions Hutton escaped from and the importance of Newcastle and its coal to the changes taking place in Britain in the second half of the eighteenth century . . . like something from the pages of a Jane Austen novel . . . Wardhaugh has done a good job of rescuing Hutton from obscurity and setting the man and his achievements in the context of their times . . . This account of how “the pit boy turned professor” became “one of the most revered British scientists of his day” is well worth reading’ Literary Review ‘As this book argues persuasively, he changed a whole culture: by simple dint of his genial celebrity as well as a europhile passion for developments in France and elsewhere, he helped to elevate mathematics to a rank equal with the other sciences. It is impossible not to warm to such a man in Wardhaugh’s wryly sympathetic telling . . . Spirited and elegantly erudite’ Daily Telegraph
£16.57
Clarendon Press Elementary Geometry
Book SynopsisThis text is a careful introduction to geometry. While developing geometry for its own sake, the book also emphasizes the links between geometry and other branches of pure and applied mathematics.Trade Review'This text is a careful introduction to Euclidean geometry that emphasizes its connections with other subjects. Glimpses of more advanced topics in pure mathematics are balanced by a straightforward treatment of the geometry needed for mechanics and classical applied mathematics.' L'Enseignement Mathématique, 3-4 1993'a simple, clean introduction to Euclidean and differential geometry ... It could be read by an enthusiastic sixth-former but is entirely suitable for use in a first-year undergraduate course.' Ian Stewart, New Scientist'In less than 300 pages of text, the author clearly and precisely explains all (or most) of the geometry classically expected to be learned by beginning mathematics and physics students, and he does it in a thoroughly modern manner, with brief historical anecdotes and indications of practical utility, bringing in new tools as they become useful. This is an excellent new text, much to be recommended.' John H. Halton, University of North Carolina at Chapel Hill, American Scientist, Volume 83, 1995 January-FebruaryTable of ContentsAxioms for geometry; Vector geometry; Congruence axioms; Euclidean geometry; Coordinates and equations; Plane geometry; Conics and other curves; Solid geometry; Area and volume; Quadric surfaces; Differential geometry of curves; Differential geometry of surfaces.
£60.30
Oxford University Press Geometry A Very Short Introduction Very Short
Book SynopsisThe study of geometry is at least 2500 years old, and it is within this field that the concept of mathematical proof - deductive reasoning from a set of axioms - first arose. To this day geometry remains a very active area of research in mathematics. This Very Short Introduction covers the areas of mathematics falling under geometry, starting with topics such as Euclidean and non-Euclidean geometries, and ranging to curved spaces, projective geometry in Renaissance art, and geometry of space-time inside a black hole. Starting from the basics, Maciej Dunajski proceeds from concrete examples (of mathematical objects like Platonic solids, or theorems like the Pythagorean theorem) to general principles. Throughout, he outlines the role geometry plays in the broader context of science and art. Very Short Introductions: Brilliant, Sharp, Inspiring ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.Trade ReviewIt is a lovely little book, to be recommended for sixth-formers or first year undergraduates: it will open their eyes to the amazing beauty and power of this ancient and modern subject. * Stephen Huggett, London Mathematical Society Newsletter, March 2023 *Various geometries are presented, each with particularly engaging examples of problems that are formulated in that particular geometry. * Victor V. Pambuccian, zb Math Open *Table of Contents1: What is geometry? 2: Euclidean geometry 3: Non-Euclidean geometry 4: Geometry of curved spaces 5: Projective geometry 6: Other geometries 7: Geometry of the physical world Further Reading Index
£9.49
Dover Publications Inc. Advanced Euclidean Geometry
Book SynopsisThis classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.
£15.19
Cambridge University Press Quasicrystals and Geometry
Book SynopsisQuasicrystals and Geometry brings together for the first time the many strands of contemporary research in quasicrystal geometry and weaves them into a coherent whole. The author describes the historical and scientific context of this work, and carefully explains what has been proved and what is conjectured. This, together with a bibliography of over 250 references, provides a solid background for further study. The discovery in 1984 of crystals with 'forbidden' symmetry posed fascinating and challenging problems in many fields of mathematics, as well as in the solid state sciences. Increasingly, mathematicians and physicists are becoming intrigued by the quasicrystal phenomenon, and the result has been an exponential growth in the literature on the geometry of diffraction patterns, the behaviour of the Fibonacci and other nonperiodic sequences, and the fascinating properties of the Penrose tilings and their many relatives.Trade Review'In this excellent monograph, Marjorie Senechal … gives us insight into what happened when established ideas had to be reexamined, modified or overturned … Her several published reports and this book convey both the searches for new directions and the excitement of new results and are worthwhile narratives of ten exciting years.' Science'This is a little gem of a book, with a quasicrystalline elegance to it.' American Scientist'… this is a nice, timely and valuable book and is recommended to anyone interested in learning about this subject.' European Mathematical Society NewsletterTable of ContentsPreface; 1. Past as prologue; 2. Lattices, Voronoi cells, and quasicrystals; 3. Introduction to diffraction geometry; 4. Order on the line; 5. Tiles and tilings; 6. Penrose tilings of the plane; 7. The aperiodic zoo; 8. An atlas of tiling transforms; Appendix I. A mathematician's toolbag; Appendix II. De Bruijn's generalized functions; References.
£43.99
PRINCETON UNIV PR Encounters with Euclid
Book Synopsis
£23.70
MP-AMM American Mathematical Nonlinear Analysis on Manifolds Sobolev Spaces
Book SynopsisOffers lectures given at the Courant Institute on the theory of Sobolev spaces on Riemannian manifolds. This volume includes a brief introduction to differential and Riemannian geometry. It deals with the general theory of Sobolev spaces for compact manifolds, and also presents special types of Sobolev inequalities under constraints.Table of ContentsElements of Riemannian geometry Sobolev spaces: The compact setting Sobolev spaces: The noncompact setting Best constants in the compact setting I Best constants in the compact setting II Optimal inequalities with constraints Best constants in the noncompact setting Euclidean-type Sobolev inequalities The influence of symmetries Manifolds with boundary Bibliography.
£36.05
Cambridge University Press Sets of Finite Perimeter and Geometric
Book SynopsisThis engaging graduate-level introduction to geometric measure theory bridges analysis and geometry, taking readers from basic theory to some of the most celebrated results in modern analysis. Explanatory pictures, detailed proofs, exercises and helpful remarks make it suitable for self-study and also a useful reference for researchers.Trade Review'The book is a clear exposition of the theory of sets of finite perimeter, that introduces this topic in a very elegant and original way, and shows some deep and important results and applications … Although most of the results contained in this book are classical, some of them appear in this volume for the first time in book form, and even the more classical topics which one may find in several other books are presented here with a strong touch of originality which makes this book pretty unique … I strongly recommend this excellent book to every researcher or graduate student in the field of calculus of variations and geometric measure theory.' Alessio Figalli, Canadian Mathematical Society Notes'The first aim of the book is to provide an introduction for beginners to the theory of sets of finite perimeter, presenting results concerning the existence, symmetry, regularity and structure of singularities in some variational problems involving length and area … The secondary aim … is to provide a multi-leveled introduction to the study of other variational problems … an interested reader is able to enter with relative ease several parts of geometric measure theory and to apply some tools from this theory in the study of other problems from mathematics … This is a well-written book by a specialist in the field … It provides generous guidance to the reader [and] is recommended … not only to beginners who can find an up-to-date source in the field but also to specialists … It is an invitation to understand and to approach some deep and difficult problems from mathematics and physics.' Vasile Oproiu, Zentralblatt MATHTable of ContentsPart I. Radon Measures on Rn: 1. Outer measures; 2. Borel and Radon measures; 3. Hausdorff measures; 4. Radon measures and continuous functions; 5. Differentiation of Radon measures; 6. Two further applications of differentiation theory; 7. Lipschitz functions; 8. Area formula; 9. Gauss–Green theorem; 10. Rectifiable sets and blow-ups of Radon measures; 11. Tangential differentiability and the area formula; Part II. Sets of Finite Perimeter: 12. Sets of finite perimeter and the Direct Method; 13. The coarea formula and the approximation theorem; 14. The Euclidean isoperimetric problem; 15. Reduced boundary and De Giorgi's structure theorem; 16. Federer's theorem and comparison sets; 17. First and second variation of perimeter; 18. Slicing boundaries of sets of finite perimeter; 19. Equilibrium shapes of liquids and sessile drops; 20. Anisotropic surface energies; Part III. Regularity Theory and Analysis of Singularities: 21. (Λ, r0)-perimeter minimizers; 22. Excess and the height bound; 23. The Lipschitz approximation theorem; 24. The reverse Poincaré inequality; 25. Harmonic approximation and excess improvement; 26. Iteration, partial regularity, and singular sets; 27. Higher regularity theorems; 28. Analysis of singularities; Part IV. Minimizing Clusters: 29. Existence of minimizing clusters; 30. Regularity of minimizing clusters; References; Index.
£74.09
Cambridge University Press The Thirteen Books of Euclids Elements Volume 1 Introduction and Books I II
Book SynopsisAfter studying both classics and mathematics at the University of Cambridge, Sir Thomas Little Heath (1861â1940) used his time away from his job as a civil servant to publish many works on the subject of ancient mathematics, both popular and academic. First published in 1926 as the second edition of a 1908 original, this book contains the first volume of his three-volume English translation of the thirteen books of Euclid's Elements, covering Books One and Two. This detailed text will be of value to anyone with an interest in Greek geometry and the history of mathematics.Table of ContentsIntroduction: 1. Euclid and the traditions about him; 2. Euclid's other works; 3. Greek commentators other than Proclus; 4. Proclus and his sources; 5. The text; 6. The scholia; 7. Euclid in Arabia; 8. Principal translations and editions; 9. On the nature of elements; The Elements: Book I: Definitions, postulates, common notions; Notes on definitions etc.; Propositions; Book II: Definitions; Note on geometrical algebra; Propositions; Excursus I. Pythagoras and the Pythagoreans; Excursus II. Popular names for Euclidean propositions; Greek index to vol. 1; English index to vol. 1.
£27.99
Lulu Press Euclids Elements in Greek Vol. I Books 14
£15.07
Nova Science Publishers Inc Hilbert Spaces and Its Applications
Book SynopsisThis book contains numerous selected contemporary topics, primarily in Hilbert space, although related extended material in Banach spaces and Riemannian manifolds is also included. A plethora of concrete problems from diverse disciplines are explored, such as: applied mathematics; mathematical biology; chemistry; economics; physics; scientific computing, and engineering. The solutions of such equations can only be found in closed form in special cases; this forces researchers and practitioners to focus on the development of iterative methods to generate a sequence converging to the solutions, provided that some convergence criteria depending on the initial data are satisfied. Due to the exponential development of technology, new iterative methods should be found to improve existing computers and create faster and more efficient ones. We have no doubt that this book will contribute significantly to the enrichment of knowledge and problem solving in the field of Hilbert spaces and related topics.Table of ContentsPreface; A Newton-Traub-Like Fifth Convergence Order Method in Hilbert Space; Correcting and extending the applicability of two fast algorithms for solving systems; Extended Directional Newton-Type Methods; Extended Kantorovich Theorem for Generalized Equations and Variational Inequalities; Extended the Applicability of Newtons Method for Equations with Monotone Operator; Improved Local Convergence for a Proximal Gauss-Newton Solver; Improved Error Estimates for Some Newton-type Methods; Two Non Classical Quantum Logic of Projections in Hilbert space; Extended Fourth Order Newton-Like Method under w-continuity for Solving Equations; On the semi-local convergence of Halleys method: An extension; Semi local convergence criterion of Newtons algorithm for singular systems under constant rank derivatives: An extension; Extending the Gauss-Newton-Algorithm under l-average continuity conditions; On the solution of generalized equations in Hilbert space; Newtons algorithm on Riemannian manifolds: Extended Kantorovichs theorem; Extended Gauss-Newton-Kurchatov Algorithm for least squares problems; Extended Gauss-Newton Algorithm for convex composite optimization; Extended local convergence of Newtons Algorithm on Riemannian manifolds; Uniqueness of the solution of equations in Hilbert space I; Uniqueness of the solution of equations in Hilbert space II; Extended Newtons Algorithm on Riemannian manifolds with values in a cone; Extended Gauss-Newton Algorithm on Riemannian manifolds under L- average Lipschitz conditions; New Results on Berezin Number Inequalities in Reproducing Kernel Hilbert Space; Glossary of Symbols; Index.
£138.39
Centre for the Study of Language & Information Euclid and His Twentieth Century Rivals: Diagrams in the Logic of Euclidean Geometry
Book SynopsisTwentieth-century developments in logic and mathematics have led many people to view Euclid's proofs as inherently informal, especially due to his use of diagrams. In "Euclid and His Twentieth-Century Rivals", Nathaniel Miller discusses the history of such diagrams in Euclidean geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of interest to mathematicians, computer scientists, and anyone interested in the use of diagrams in geometry.
£22.00
New Age International (UK) Ltd Plane Trigonometry: Part 1
Book Synopsis
£33.25
New Age International (UK) Ltd Plane Trigonometry: Part 2
Book Synopsis
£28.50
Springer International Publishing AG An Excursion through Elementary Mathematics,
Book SynopsisThis book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This second volume covers Plane Geometry, Trigonometry, Space Geometry, Vectors in the Plane, Solids and much more.As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level.The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.Trade Review“The authors provides an overview of elementary geometry in relationship with questions from mathematical Olympiads around the world. … The book also explores some problems proposed at various national and international mathematics Olympiads. This book is useful for high-school students interested in preparing for mathematical Olympiads.” (Teodora-Liliana Rǎdulescu, zbMATH 1395.51001, 2018)Table of Contents
£58.49
Museum Tusculanum Press Coloured Quadrangles: A Guide to the Tenth Book
Book SynopsisThis is meant as a guide to give access to the tenth book for those who may have lost faith in the commentaries by Thomas Heath, but who shrink from the long wanderings through the Greek text.
£7.99
World Scientific Publishing Co Pte Ltd Scissors Congruences, Group Homology And
Book SynopsisThese lecture notes are based on a series of lectures given at the Nankai Institute of Mathematics in the fall of 1998. They provide an overview of the work of the author and the late Chih-Han Sah on various aspects of Hilbert's Third Problem: Are two Euclidean polyhedra with the same volume “scissors-congruent”, i.e. can they be subdivided into finitely many pairwise congruent pieces? The book starts from the classical solution of this problem by M Dehn. But generalization to higher dimensions and other geometries quickly leads to a great variety of mathematical topics, such as homology of groups, algebraic K-theory, characteristic classes for flat bundles, and invariants for hyperbolic manifolds. Some of the material, particularly in the chapters on projective configurations, is published here for the first time.Table of ContentsIntroduction and history; scissors congruence group and homology; homology of flag complexes; translational scissors congruences; Euclidean scissors congruences; Sydler's theorem and non-commutative differential forms; spherical scissors congruences; hyperbolic scissors congruences; homology of Lie groups made discrete; invariants; simplices in spherical and hyperbolic 3-space; rigidity of Cheeger-Chern-Simons invariants; projective configurations and homology of the projective linear group; homology of indecomposable configurations; the case of PGI(3,F).
£67.45
World Scientific Publishing Co Pte Ltd Scissors Congruences, Group Homology And
Book SynopsisThese lecture notes are based on a series of lectures given at the Nankai Institute of Mathematics in the fall of 1998. They provide an overview of the work of the author and the late Chih-Han Sah on various aspects of Hilbert's Third Problem: Are two Euclidean polyhedra with the same volume “scissors-congruent”, i.e. can they be subdivided into finitely many pairwise congruent pieces? The book starts from the classical solution of this problem by M Dehn. But generalization to higher dimensions and other geometries quickly leads to a great variety of mathematical topics, such as homology of groups, algebraic K-theory, characteristic classes for flat bundles, and invariants for hyperbolic manifolds. Some of the material, particularly in the chapters on projective configurations, is published here for the first time.Table of ContentsIntroduction and history; scissors congruence group and homology; homology of flag complexes; translational scissors congruences; Euclidean scissors congruences; Sydler's theorem and non-commutative differential forms; spherical scissors congruences; hyperbolic scissors congruences; homology of Lie groups made discrete; invariants; simplices in spherical and hyperbolic 3-space; rigidity of Cheeger-Chern-Simons invariants; projective configurations and homology of the projective linear group; homology of indecomposable configurations; the case of PGI(3,F).
£40.85
World Scientific Publishing Co Pte Ltd Manifolds And Local Structures: A General Theory
Book SynopsisLocal structures, like differentiable manifolds, fibre bundles, vector bundles and foliations, can be obtained by gluing together a family of suitable 'elementary spaces', by means of partial homeomorphisms that fix the gluing conditions and form a sort of 'intrinsic atlas', instead of the more usual system of charts living in an external framework.An 'intrinsic manifold' is defined here as such an atlas, in a suitable category of elementary spaces: open euclidean spaces, or trivial bundles, or trivial vector bundles, and so on.This uniform approach allows us to move from one basis to another: for instance, the elementary tangent bundle of an open Euclidean space is automatically extended to the tangent bundle of any differentiable manifold. The same holds for tensor calculus.Technically, the goal of this book is to treat these structures as 'symmetric enriched categories' over a suitable basis, generally an ordered category of partial mappings.This approach to gluing structures is related to Ehresmann's one, based on inductive pseudogroups and inductive categories. A second source was the theory of enriched categories and Lawvere's unusual view of interesting mathematical structures as categories enriched over a suitable basis.
£108.00
World Scientific Publishing Co Pte Ltd Basic Lessons On Isometries, Similarities And
Book SynopsisThe aim of this book is to provide a complete synthetic exposition of plane isometries, similarities and inversions to readers who are interested in studying, teaching, and using this material.The topics developed in this book can provide new proofs and solutions to many results and problems of classical geometry, which are presented with different proofs in the literature. Their applications are numerous and some, such as the Steiner Chains and Point, are useful to engineers.The book contains many good examples, important applications and numerous exercises of various level and difficulty, which are classified in the three groups of: general exercises, geometrical constructions, and geometrical loci. Some lengthy exercises or groups of related exercises can be viewed as projects. On the basis of the above, this book, besides Classical Geometry, is an important addition to Mathematics Education.
£121.50
World Scientific Publishing Co Pte Ltd Basic Lessons On Isometries, Similarities And
Book SynopsisThe aim of this book is to provide a complete synthetic exposition of plane isometries, similarities and inversions to readers who are interested in studying, teaching, and using this material.The topics developed in this book can provide new proofs and solutions to many results and problems of classical geometry, which are presented with different proofs in the literature. Their applications are numerous and some, such as the Steiner Chains and Point, are useful to engineers.The book contains many good examples, important applications and numerous exercises of various level and difficulty, which are classified in the three groups of: general exercises, geometrical constructions, and geometrical loci. Some lengthy exercises or groups of related exercises can be viewed as projects. On the basis of the above, this book, besides Classical Geometry, is an important addition to Mathematics Education.
£63.00
World Scientific Publishing Co Pte Ltd Elements Of Digital Geometry, Mathematical
Book SynopsisThe author presents three distinct but related branches of science in this book: digital geometry, mathematical morphology, and discrete optimization. They are united by a common mindset as well as by the many applications where they are useful. In addition to being useful, each of these relatively new branches of science is also intellectually challenging.The book contains a systematic study of inverses of mappings between ordered sets, and so offers a uniquely helpful organization in the approach to several phenomena related to duality.To prepare the ground for discrete convexity, there are chapters on convexity in real vector spaces in anticipation of the many challenging problems coming up in digital geometry. To prepare for the study of new topologies introduced to serve in discrete spaces, there is also a chapter on classical topology.The book is intended for general readers with a modest background in mathematics and for advanced undergraduate students as well as beginning graduate students.
£130.50
World Scientific Publishing Co Pte Ltd Undergraduate Convexity: Problems And Solutions
Book SynopsisThis solutions manual thoroughly goes through the exercises found in Undergraduate Convexity: From Fourier and Motzkin to Kuhn and Tucker. Several solutions are accompanied by detailed illustrations and intuitive explanations. This book will pave the way for students to easily grasp the multitude of solution methods and aspects of convex sets and convex functions. Companion Textbook here
£30.40
World Scientific Publishing Co Pte Ltd Undergraduate Convexity: Problems And Solutions
Book SynopsisThis solutions manual thoroughly goes through the exercises found in Undergraduate Convexity: From Fourier and Motzkin to Kuhn and Tucker. Several solutions are accompanied by detailed illustrations and intuitive explanations. This book will pave the way for students to easily grasp the multitude of solution methods and aspects of convex sets and convex functions. Companion Textbook here
£53.20
World Scientific Publishing Co Pte Ltd Barycentric Calculus In Euclidean And Hyperbolic
Book SynopsisThe word barycentric is derived from the Greek word barys (heavy), and refers to center of gravity. Barycentric calculus is a method of treating geometry by considering a point as the center of gravity of certain other points to which weights are ascribed. Hence, in particular, barycentric calculus provides excellent insight into triangle centers. This unique book on barycentric calculus in Euclidean and hyperbolic geometry provides an introduction to the fascinating and beautiful subject of novel triangle centers in hyperbolic geometry along with analogies they share with familiar triangle centers in Euclidean geometry. As such, the book uncovers magnificent unifying notions that Euclidean and hyperbolic triangle centers share.In his earlier books the author adopted Cartesian coordinates, trigonometry and vector algebra for use in hyperbolic geometry that is fully analogous to the common use of Cartesian coordinates, trigonometry and vector algebra in Euclidean geometry. As a result, powerful tools that are commonly available in Euclidean geometry became available in hyperbolic geometry as well, enabling one to explore hyperbolic geometry in novel ways. In particular, this new book establishes hyperbolic barycentric coordinates that are used to determine various hyperbolic triangle centers just as Euclidean barycentric coordinates are commonly used to determine various Euclidean triangle centers.The hunt for Euclidean triangle centers is an old tradition in Euclidean geometry, resulting in a repertoire of more than three thousand triangle centers that are known by their barycentric coordinate representations. The aim of this book is to initiate a fully analogous hunt for hyperbolic triangle centers that will broaden the repertoire of hyperbolic triangle centers provided here.Table of ContentsEuclidean Barycentric Coordinates; The Classical Triangle Centers; Triangle Incircle and Excircles; Cartesian Models of Hyperbolic Geometry; The Interplay of Einstein and Vector Addition; Hyperbolic Barycentric Coordinates; Hyperbolic Triangle Centers; Hyperbolic Triangle Incircle and Excircles;
£97.20
World Scientific Publishing Co Pte Ltd Undergraduate Convexity: From Fourier And Motzkin
Book SynopsisBased on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples.Starting from linear inequalities and Fourier-Motzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the Karush-Kuhn-Tucker conditions, duality and an interior point algorithm. Study Guide hereTable of ContentsIntroduction; Basics; The Double Description Method; Closed Convex Sets; Convex Functions of One Variable; Differentiable Functions of Several Variables; Convex Functions of Several Variables; Convex Optimization.
£75.05
World Scientific Publishing Co Pte Ltd Voronoi Diagrams And Delaunay Triangulations
Book SynopsisVoronoi diagrams partition space according to the influence certain sites exert on their environment. Since the 17th century, such structures play an important role in many areas like Astronomy, Physics, Chemistry, Biology, Ecology, Economics, Mathematics and Computer Science. They help to describe zones of political influence, to determine the hospital nearest to an accident site, to compute collision-free paths for mobile robots, to reconstruct curves and surfaces from sample points, to refine triangular meshes, and to design location strategies for competing markets.This unique book offers a state-of-the-art view of Voronoi diagrams and their structure, and it provides efficient algorithms towards their computation.Readers with an entry-level background in algorithms can enjoy a guided tour of gently increasing difficulty through a fascinating area. Lecturers might find this volume a welcome source for their courses on computational geometry. Experts are offered a broader view, including many alternative solutions, and up-to-date references to the existing literature; they might benefit in their own research or application development.Table of ContentsElementary Properties; Basic Algorithms; Advanced Properties; Generalized Sites; Medical Axis; Higher Dimensions; Power Diagram; Higher Order Diagram; General Spaces and Distances; Abstract Diagrams; Distance Problems; Delaunay Related Graphs; Clustering; Motion Planning; Placement Problems; High Dimensional Solutions; Open Problems.
£75.05
World Scientific Publishing Co Pte Ltd Undergraduate Convexity: From Fourier And Motzkin
Book SynopsisBased on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples.Starting from linear inequalities and Fourier-Motzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the Karush-Kuhn-Tucker conditions, duality and an interior point algorithm. Study Guide hereTable of ContentsIntroduction; Basics; The Double Description Method; Closed Convex Sets; Convex Functions of One Variable; Differentiable Functions of Several Variables; Convex Functions of Several Variables; Convex Optimization.
£35.15
World Scientific Publishing Co Pte Ltd Half-discrete Hilbert-type Inequalities
Book SynopsisIn 1934, G. H. Hardy et al. published a book entitled “Inequalities”, in which a few theorems about Hilbert-type inequalities with homogeneous kernels of degree-one were considered. Since then, the theory of Hilbert-type discrete and integral inequalities is almost built by Prof. Bicheng Yang in their four published books.This monograph deals with half-discrete Hilbert-type inequalities. By means of building the theory of discrete and integral Hilbert-type inequalities, and applying the technique of Real Analysis and Summation Theory, some kinds of half-discrete Hilbert-type inequalities with the general homogeneous kernels and non-homogeneous kernels are built. The relating best possible constant factors are all obtained and proved. The equivalent forms, operator expressions and some kinds of reverses with the best constant factors are given. We also consider some multi-dimensional extensions and two kinds of multiple inequalities with parameters and variables, which are some extensions of the two-dimensional cases. As applications, a large number of examples with particular kernels are also discussed.The authors have been successful in applying Hilbert-type discrete and integral inequalities to the topic of half-discrete inequalities. The lemmas and theorems in this book provide an extensive account of these kinds of inequalities and operators. This book can help many readers make good progress in research on Hilbert-type inequalities and their applications.Table of ContentsIntroduction: Recent Developments of Hilbert-Type Inequalities with Applications; Preliminary Theorems: Improvements of Euler - Maclaurin's Summation Formula; A Half-Discrete Inequality with the General Homogeneous Kernel and Extensions; A Half-Discrete Inequality with a General Non-Homogeneous Kernel and Extensions; Two Kinds of Multi-dimensional Half-Discrete Inequalities; Two Kinds of Multiple Half-Discrete Hilbert-Type Inequalities.
£99.00
World Scientific Publishing Co Pte Ltd Plain Plane Geometry
Book SynopsisThe book constitutes an elementary course on Plane Euclidean Geometry, pitched at pre-university or at advanced high school level. It is a concise book treating the subject axiomatically, but since it is meant to be a first introduction to the subject, excessive rigour is avoided, making it appealing to a younger audience as well. The aim is to cover the basics of the subject, while keeping the subject lively by means of challenging and interesting exercises. This makes it relevant also for students participating in mathematics circles and in mathematics olympiads.Each section contains several problems, which are not purely drill exercises, but are intended to introduce a sense of 'play' in mathematics, and inculcate appreciation of the elegance and beauty of geometric results. There is an abundance of colour pictures illustrating results and their proofs. A section on hints and a further section on detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study.Table of ContentsGeometric Figures; Congruent Triangles; Quadrilaterals; Similar Triangles; Circles;
£75.05
World Scientific Publishing Co Pte Ltd Plain Plane Geometry
Book SynopsisThe book constitutes an elementary course on Plane Euclidean Geometry, pitched at pre-university or at advanced high school level. It is a concise book treating the subject axiomatically, but since it is meant to be a first introduction to the subject, excessive rigour is avoided, making it appealing to a younger audience as well. The aim is to cover the basics of the subject, while keeping the subject lively by means of challenging and interesting exercises. This makes it relevant also for students participating in mathematics circles and in mathematics olympiads.Each section contains several problems, which are not purely drill exercises, but are intended to introduce a sense of 'play' in mathematics, and inculcate appreciation of the elegance and beauty of geometric results. There is an abundance of colour pictures illustrating results and their proofs. A section on hints and a further section on detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study.Table of ContentsGeometric Figures; Congruent Triangles; Quadrilaterals; Similar Triangles; Circles;
£38.00
World Scientific Publishing Co Pte Ltd Barycentric Calculus In Euclidean And Hyperbolic Geometry A Comparative Introduction
£112.50
