Geometry Books
World Scientific Publishing Co Pte Ltd Backgrounds Of Arithmetic And Geometry: An
Book SynopsisThe book is an introduction to the foundations of Mathematics. The use of the constructive method in Arithmetic and the axiomatic method in Geometry gives a unitary understanding of the backgrounds of geometry, of its development and of its organic link with the study of real numbers and algebraic structures.Table of ContentsElements of set theory; arithmetics; axiomatic theories; algebraic background of geometry; bases of Euclidean geometry; Birkhoff's axiomatics; geometrical transformations; Erlangen programme; Bachmann's axiomatics.
£79.80
World Scientific Publishing Co Pte Ltd Solving Problems In Our Spatial World
Book Synopsis'The reference list is excellent. This is a worthwhile (though 'niche') book that will be attractive to a particular sector of the general reading public interested in mathematical riddles and puzzles. Professional educators might well employ it in integrated learning settings. Summing Up: Recommended. All readers.'CHOICEImmerse yourself in the fascinating world of geometry and spatial ability — either individually or in small groups, either as challenges or play problems! Here are four reasons why you should work with this book:This book offers a very unique opportunity to enhance your spatial ability, your mathematical competence, and your logical thinking. The authors arranged 45 problems — including more than 120 tasks — in a well-balanced order, which have been tested with a variety of populations.
£52.25
World Scientific Publishing Co Pte Ltd Geometric And Topological Methods For Quantum
Book SynopsisThis volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school.Table of ContentsNoncommutative Geometry: Hopf Algebras in Noncommutative Geometry (J C Varilly); The Noncommutative Geometry of Aperiodic Solids (J Bellissard); Noncommutative Geometry and Abstract Integration Theory (M-T Benameur); Topological Field Theory: Introduction to Quantum Invariants of 3-Manifolds, Topological Quantum Field Theories and Modular Categories (C Blanchet); An Introduction to Donaldson-Witten Theory (M Marino); Supergravity and String Theory: (Super)-Gravities Beyond 4 Dimensions (J Zanelli); Introductory Lectures on String Theory and the AdS/CFT Correspondence (A Pankiewicz & S Theisen); Short Communications: Group Contractions and Its Consequences Upon Representations of Different Spatial Symmetry Groups (M Ayala-Sanchez & R W Haase); Phase Anomalies as Trace Anomalies in Chern-Simons Theory (A Cardona); Deligne Cohomology for Orbifolds, Discrete Torsion and B-Fields (E Lupercio & B Uribe).
£197.60
World Scientific Publishing Co Pte Ltd Weighted Inequalities Of Hardy Type
Book SynopsisInequalities play an important role in almost all branches of mathematics as well as in other areas of science and engineering. This book surveys the present state of the theory of weighted integral inequalities of Hardy type, including modifications concerning Hardy-Steklov operators, and some basic results about Hardy type inequalities and their limit (Carleman-Knopp type) inequalities. It also describes some rather new fields such as higher order and fractional order Hardy type inequalities and integral inequalities on the cone of monotone functions together with some applications and open problems. The book can serve as a reference and a source of inspiration for researchers working in these and related areas, but could also be used for advanced graduate courses.Table of ContentsHardy's Inequality and Related Topics; Some Weighted Norm Inequalities; The Hardy-Steklov Operator; Higher Order Hardy Inequalities; Fractional Order Hardy Inequalities; Integral Operators on the Cone of Monotone Functions.
£90.25
World Scientific Publishing Co Pte Ltd Groups, Combinatorics And Geometry
Book SynopsisOver the past 20 years, the theory of groups — in particular simple groups, finite and algebraic — has influenced a number of diverse areas of mathematics. Such areas include topics where groups have been traditionally applied, such as algebraic combinatorics, finite geometries, Galois theory and permutation groups, as well as several more recent developments. Among the latter are probabilistic and computational group theory, the theory of algebraic groups over number fields, and model theory, in each of which there has been a major recent impetus provided by simple group theory. In addition, there is still great interest in local analysis in finite groups, with substantial new input from methods of geometry and amalgams, and particular emphasis on the revision project for the classification of finite simple groups.This important book contains 20 survey articles covering many of the above developments. It should prove invaluable for those working in the theory of groups and its applications.Table of ContentsCurtis-Phan-Tits Theory, C.D. Bennett et al; Derangements in Simple and Primitive Groups, J. Fulman & R. Guralnick; Computing with Matrix Groups, W.M. Kantor & A. Seress; Bases of Primitive Permutation Groups, M.W. Liebeck & A. Shalev; Modular Subgroup Arithmetic, T.W. Muller; Counting Nets in the Monster, S.P. Norton; Overgroups of Finite Quasiprimitive Permutation Groups, C.E. Praeger; Old Groups Can Learn New Tricks, L. Pyber; Structure and Presentations of Lie-Type Groups, F.G. Timmesfeld; Computing in the Monster, R.A. Wilson; and other papers.
£151.05
World Scientific Publishing Co Pte Ltd Inspired By S S Chern: A Memorial Volume In Honor
Book SynopsisShiing-Shen Chern (1911-2004) was one of the leading differential geometers of the twentieth century. In 1946, he founded the Mathematical Institute of Academia Sinica in Shanghai, which was later moved to Nanking. In 1981, he founded the Mathematical Sciences Research Institute (MSRI) at Berkeley and acted as the director until 1984. In 1985, he founded the Nankai Institute of Mathematics in Tianjin. He was awarded the National Medal of Science in 1975; the Wolf Prize in mathematics in 1984; and the Shaw Prize in mathematical sciences in 2004.Chern's works span all the classic fields of differential geometry: the Chern-Simons theory; the Chern-Weil theory, linking curvature invariants to characteristic classes; Chern classes; and other areas such as projective differential geometry and webs that are mathematically rich but currently have a lower profile. He also published work in integral geometry, value distribution theory of holomorphic functions, and minimal submanifolds.Inspired by Chern and his work, former colleagues, students and friends — themselves highly regarded mathematicians in their own right — come together to honor and celebrate Chern's huge contributions. The volume, organized by Phillip Griffiths of the Institute for Advanced Study (Princeton), contains contributions by Michael Atiyah (University of Edinburgh), C-M Bai (Nankai), Robert Bryant (Duke University), Kung-Ching Chang (Peking University), Jeff Cheeger (New York University), Simon K Donaldson (Imperial College), Hélène Esnault (Universität Duisburg-Essen), Mo-Lin Ge (Nankai), Mark Green (University of California at Los Angeles), Phillip Griffiths (Institute for Advanced Study), F Reese Harvey (Rice University), Alain Hénaut (Université Bordeaux 1), Niky Kamran (McGill University), Bruce Kleiner (Yale), H Blaine Lawson, Jr (Suny at Stony Brook), Yiming Long (Nankai), Xiaonan Ma (UMR 7640 du CNRS), Luc Pirio (IRMAR, France), Graeme Segal (Oxford), Gang Tian (MIT), Jean-Marie Trepreau (Institut de Mathématiques de Jussieu), Jeff Viaclovsky (MIT), Wei Wang (Nankai), Wentsun Wu (Chinese Academy of Sciences), C N Yang (Tsinghua), Tan Zhang (Murray State University), Weiping Zhang (Nankai) and others.Table of ContentsIn Memory of Professor S S Chern (C N Yang); Twisted K-Theory and Cohomology (M Atiyah); Yangian and Its Applications (C-M Bai et al.); Geodesically Reversible Finsler 2-Spheres of Constant Curvature (R L Bryant); Multiple Solutions of the Prescribed Mean Curvature Equation (K C Chang & T Zhang); On the Differentiability of Lipschitz Maps from Metric Measure Spaces to Banach Spaces (J Cheeger & B Kleiner); Two-Forms on Four-Manifolds and Elliptic Equations (S K Donaldson); Partial Connection for p-Torsion Line Bundles in Characteristic p > 0 (H Esnault); Algebraic Cycles and Singularities of Normal Functions, II (M Green & P Griffiths); Planar Web Geometry Through Abelian Relations and Singularities (A Henaut); Transitive Analytic Lie Pseudo-Groups (N Kamran); Stability of Closed Characteristics on Compact Convex Hypersurfaces (Y Long & W Wang); -Invariant and Flat Vector Bundles II (X Ma & W Zhang); On Planar Webs with Infinitesimal Automorphisms (D Marin et al.); Projective Linking and Boundaries of Positive Holomorphic Chains in Projective Manifolds, Part II (F R Harvey & H B Lawson, Jr); Aspects of Metric Geometry of Four Manifolds (G Tian); Algebrisation Des Tissus De Codimension 1: La Generalisation D'un Theoreme De Bol (J-M Trepreau); Conformal Geometry and Fully Nonlinear Equations (J Viaclovsky); Memory of My First Research Teacher: The Great Geometer Chern Shiing-Shen (W Wu); Some Open Gromov-Witten Invariants of the Resolved Conifold (J Zhou).
£156.75
Nova Science Publishers Inc Four-Dimensional Atomic Structure and Law
Book Synopsis
£999.99
American Mathematical Society Gauge Theory and the Topology of Fourmanifolds
Book SynopsisOffers a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. This book predates Donaldson's applications of the subject to 4-manifold topology, where the central concern was the geometry of the moduli space.Table of ContentsGeometric invariant theory and the moduli of bundles: Geometric invariant theory by D. Gieseker The numerical criterion by D. Gieseker The moduli of stable bundles by D. Gieseker References by D. Gieseker Anti-self-dual connections and stable vector bundles: Hermitian bundles, Hermitian connections and their curvatures by J. Li Hermitian-Einstein connections and stable vector bundles by J. Li The existence of Hermitian-Einstein metrics by J. Li References by J. Li An introduction to gauge theory: The context of Gauge theory by J. W. Morgan Principal bundles and connections by J. W. Morgan Curvature and characteristic classes by J. W. Morgan The space of connections by J. W. Morgan The ASD equations and the moduli space by J. W. Morgan Compactness and gluing theorems by J. W. Morgan The Donaldson polynomial invariants by J. W. Morgan The connected sum theorem by J. W. Morgan References by J. W. Morgan Computing Donaldson invariants: Overview by R. J. Stern -2 spheres and the blowup formula by R. J. Stern Simple-type criteria and elliptic surfaces by R. J. Stern Elementary rational blowdowns by R. J. Stern Taut configurations and Horikowa surfaces by R. J. Stern References by R. J. Stern Donaldson-Floer theory: Introduction by C. Taubes and J. A. Bryan Quantization by C. Taubes and J. A. Bryan Simplicial decomposition of $\Cal{M}^0_X$ by C. Taubes and J. A. Bryan Half-infinite dimensional spaces by C. Taubes and J. A. Bryan References by C. Taubes and J. A. Bryan.
£99.90
Chicago Review Press Junk Drawer Geometry
Book SynopsisTrade Review"This book is full of experiments and gee-whiz coolness." - Times Record"Definitely worth adding to your study of Geometry" - A Net In Time" Junk Drawer Geometry is a great way to make learning math fun!" -- Midwest Book Review"The titular phrase 'Junk drawer geometry' is right on---all materials are inexpensive and easy to gather. A great addition to STEM collections and makerspaces." -- School Library Journal"This entertaining and instructional book is ideal for students studying geometry, exploring STEM concepts, or those who just love solving math puzzles." -- Booklist
£13.25
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Proofs from THE BOOK
Book SynopsisThis revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters.From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition" “… It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. […] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.”From the Reviews"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... "Notices of the AMS, August 1999"... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..."LMS Newsletter, January 1999"Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011 Table of ContentsNumber Theory: 1. Six proofs of the infinity of primes.- 2. Bertrand’s postulate.- 3. Binomial coefficients are (almost) never powers.- 4. Representing numbers as sums of two squares.- 5. The law of quadratic reciprocity.- 6. Every finite division ring is a field.- 7. The spectral theorem and Hadamard’s determinant problem.- 8. Some irrational numbers.- 9. Three times π2/6.- Geometry: 10. Hilbert’s third problem: decomposing polyhedral.- 11. Lines in the plane and decompositions of graphs.- 12. The slope problem.- 13. Three applications of Euler’s formula.- 14. Cauchy’s rigidity theorem.- 15. The Borromean rings don’t exist.- 16. Touching simplices.- 17. Every large point set has an obtuse angle.- 18. Borsuk’s conjecture.- Analysis: 19. Sets, functions, and the continuum hypothesis.- 20. In praise of inequalities.- 21. The fundamental theorem of algebra.- 22. One square and an odd number of triangles.- 23. A theorem of Pólya on polynomials.- 24. Van der Waerden's permanent conjecture.- 25. On a lemma of Littlewood and Offord.- 26. Cotangent and the Herglotz trick.- 27. Buffon’s needle problem.- Combinatorics: 28. Pigeon-hole and double counting.- 29. Tiling rectangles.- 30. Three famous theorems on finite sets.- 31. Shuffling cards.- 32. Lattice paths and determinants.- 33. Cayley’s formula for the number of trees.- 34. Identities versus bijections.- 35. The finite Kakeya problem.- 36. Completing Latin squares.- Graph Theory: 37. Permanents and the power of entropy.- 38. The Dinitz problem.- 39. Five-coloring plane graphs.- 40. How to guard a museum.- 41. Turán’s graph theorem.- 42. Communicating without errors.- 43. The chromatic number of Kneser graphs.- 44. Of friends and politicians.- 45. Probability makes counting (sometimes) easy.- About the Illustrations.- Index.
£47.49
Princeton University Press The Structure of Groups with a Quasiconvex
Book Synopsis
£63.00
The University of Chicago Press Group Actions in Ergodic Theory Geometry and
Book SynopsisTrade Review"Zimmer is one of the most influential contemporary American mathematicians. The corpus of Zimmer's contributions stands out by its coherence and its grand vision. Much more than being a strong problem-solver, more even than being a theory-builder, Zimmer is a mathematician with an overarching sense of the destination, with a domineering command of all relevant available techniques, with the inspiration to bring to life those techniques that were not available yet, with, in conclusion and to use a trivial formulation, a program."--Nicolas Monod, cole polytechnique f d rale de Lausanne --Nicolas Monod, cole polytechnique f d rale de Lausanne
£53.20
The University of Chicago Press Groups of Circle Diffeomorphisms
Book SynopsisGroup actions are an efficient way of describing symmetries in objects by defining the essential elements of a given object as a set. The symmetries of the object are then defined as the symmetry group of this set. This title explores group actions on the simplest closed manifold, the circle.
£42.75
MIT Press Functional Differential Geometry
Book SynopsisAn explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory.Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level.The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors'' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding.
£49.40
Springer-Verlag New York Inc. Geometry
Book SynopsisAt last: geometry in an exemplary, accessible and attractive form! The authors emphasise both the intellectually stimulating parts of geometry and routine arguments or computations in concrete or classical cases, as well as practical and physical applications.Table of ContentsIntroduction. 1: Distance and Algebra. 2: Coordinates. 3: Area and the Pythagoras Theorem. 4: The Distance Formula. 5: Some Applications of Right Triangles. 6: Polygons. 7: Congruent Triangles. 8: Dilations and Similarities. 9: Volumes. 10: Vectors and Dot Product. 11: Transformations. 12: Isometries. Index.
£49.49
John Wiley & Sons Inc College Geometry
Book SynopsisFrom two authors who embrace technology in the classroom and value the role of collaborative learning comes College Geometry Using The Geometer''s Sketchpad, a book that is ideal for geometry courses for both mathematics and math education majors. The book''s truly discovery-based approach guides students to learn geometry through explorations of topics ranging from triangles and circles to transformational, taxicab, and hyperbolic geometries. In the process, students hone their understanding of geometry and their ability to write rigorous mathematical proofs.Table of ContentsPREFACE xv ONE Using The Geometer’s Sketchpad 1 TWO Constructing → Proving 21 THREE Mathematical Arguments and Triangle Geometry 53 FOUR Circle Geometry and Proofs 85 FIVE Analytic Geometry 111 SIX Taxicab Geometry 143 SEVEN Finite Geometries 161 EIGHT Transformational Geometry 185 NINE Isometries and Matrices 209 TEN Symmetry in the Plane 229 ELEVEN Hyperbolic Geometry 253 TWELVE Projective Geometry 287 APPENDIX A Trigonometry 317 APPENDIX B Calculating with Matrices 329 BIBLIOGRAPHY 337 INDEX 341
£120.56
Dover Publications Inc. Introduction to the Geometry of N Dimensions
Book Synopsis
£13.04
Princeton University Press The Topology of Fibre Bundles
Book SynopsisFibre bundles are an integral part of differential geometry. This book begins with an introduction to bundles, including such topics as differentiable manifolds and covering spaces. It then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles.Table of ContentsPart I. THE GENERAL THEORY OF BUNDLES 1. Introduction 3 2. Coordinate bundles and fibre bundles 6 3. Construction of a bundle from coordinate transformations 14 4. The product bundle 16 5. The Ehresmann-Feldbau definition of bundle 18 6. Differentiable manifolds and tensor bundles 20 7. Factor spaces of groups 28 8. The principal bundle and the principal map 35 9. Associated bundles and relative bundles 43 10. The induced bundle 47 11. Homotopies of maps of bundles 49 12. Construction of cross-sections 54 13. Bundles having a totally disconnected group 59 14. Covering spaces 67 Part II. THE HOMOTOPY THEORY OF BUNDLES 15. Homotopy groups 72 16. The operations of Pi1 on Pi n 83 17. The homotopy sequence of a bundle 90 18. The classification of bundles over the n-sphere 96 19. Universal bundles and the classification theorem 100 20. The fibering of spheres by spheres 105 21. The homotopy groups of spheres 110 22. Homotopy groups of the orthogonal groups 114 23. A characteristic map for the bundle Rn+1 over S n 118 24. A characteristic map for the bundle Un over S 2n - 1 124 25. The homotopy groups of miscellaneous manifolds 131 26. Sphere bundles over spheres 134 27. The tangent bundle of S n 140 28. On the non-existence of fiberings of spheres by spheres 144 Part III. THE COHOMOLOGY THEORY OF BUNDLES 29. The stepwise extension of a cross-section 148 30. Bundles of coefficients 151 31. Cohomology groups based on a bundle of coefficients 155 32. The obstruction cocycle 166 33. The difference cochain 169 34. Extension and deformation theorems 174 35. The primary obstruction and the characteristic cohomology class 177 36. The primary difference of two cross-sections 181 37. Extensions of functions, and the homotopy classification of maps 184 38. The Whitney characteristic classes of a sphere bundle 190 39. The Stiefel characteristic classes of differentiable manifolds 199 40. Quadratic forms on manifolds 204 41. Complex analytic manifolds and exterior forms of degree 2 209 Appendix 218 Bibliography 223 Index 228
£73.80
Princeton University Press Discrete and Computational Geometry
Book SynopsisAn essential introduction to discrete and computational geometryDiscrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only) Trade Review"Discrete and Computational Geometry meets an urgent need for an undergraduate text bridging the theoretical sides and the applied sides of the field. It is an excellent choice as a textbook for an undergraduate course in discrete and computational geometry! The presented material should be accessible for most mathematics or computer science majors in their second or third year in college. The book also is a valuable resource for graduate students and researchers."--Egon Schulte, Zentralblatt MATH "[W]e recommend this book for an undergraduate course on computational geometry. In fact, we hope to use this book ourselves when we teach such a class."--Brittany Terese Fasy and David L. Millman, SigAct News
£59.50
Princeton University Press The Pythagorean Theorem
Book SynopsisBy any measure, the Pythagorean theorem is the most famous statement in all of mathematics. In this book, the author reveals the full story of this ubiquitous geometric theorem. It shows that the theorem, although attributed to Pythagoras, was known to the Babylonians more than a thousand years earlier.Trade ReviewHonorable Mention for the 2007 Best Professional/Scholarly Book in Mathematics, Association of American Publishers "This excellent biography of the theorem is like a history of thought written in lines and circles, moving from ancient clay tablets to Einstein's blackboards... There is something intoxicating about seeing one truth revealed in so many ways. It all makes for hours of glorious mathematical distraction."--Ben Longstaff, New Scientist "[The Pythagorean Theorem] is aimed at the reader with an interest in the history of mathematics. It should also appeal to most well-educated people...It is a story based on a theme and guided by a timeline...As a popular account of important ideas and their development, the book should be read by anyone with a good education. It deserves to succeed."--Peter M. Neumann, Times Higher Education Supplement "Based on this recent book, Maor just keeps getting better. Already recognized for his excellent books on infinity, the number e, and trigonometry, Maor offers this new work as a comprehensive overview of the Pythagorean Theorem...If one has never read a book by Eli Maor, this book is a great place to start."--J. Johnson, Choice "Maor expertly tells the story of how this simple theorem known to schoolchildren is part and parcel of much of mathematics itself... Even mathematically savvy readers will gain insights into the inner workings and beauty of mathematics."--Amy Shell-Gellasch, MAA Reviews "Maor's book is a concise history of the Pythagorean theorem, including the mathematicians, cultures, and people influenced by it. The work is well written and supported by several proofs and exampled from Chinese, Arabic, and European sources the document how these unique cultures came to understand and apply the Pythagorean theorem. [The book] provides thoughtful commentary on the historical connections this fascinating theorem has to many cultures and people."--Michael C. Fish, Mathematics Teacher "This book will make for good supplementary reading for high school students, high school teachers, and those with a general interest in mathematics... The author's enthusiasm for his subject is evident throughout the book."--James J. Tattersull, Mathematical Reviews "This book goes beyond the theorem and its proofs to set it beautifully in the context of its time and subsequent history."--Eric S. Rosenthal, Mathematics Magazine "This is an excellent book on the history of the Pythagorean Theorem... This book is suitable to any student who has basic knowledge of calculus but the layperson will also find it interesting... Maor has an exceptional method of writing very technical mathematics in a seamlessly way."--Kuldeep, Mathematics and My Diary "All in all, this affordable book, as with Maor's previous titles, is rollicking good fun and highly recommended to anyone with even the slightest interest in the history of mathematics."--Francis A, Grabowski, European Legacy "The Pythagorean Theorem is rich in information, careful in its presentation, and at times personal in its approach... The variety of its topics and the engaging way they are presented make The Pythagorean Theorem a pleasure to read."--Cecil Rousseau, College Math JournalTable of ContentsList of Color Plates ix Preface xi Prologue: Cambridge, England, 1993 1 Chapter 1: Mesopotamia, 1800 bce 4 Sidebar 1: Did the Egyptians Know It? 13 Chapter 2: Pythagoras 17 Chapter 3: Euclid's Elements 32 Sidebar 2: The Pythagorean Theorem in Art, Poetry, and Prose 45 Chapter 4: Archimedes 50 Chapter 5: Translators and Commentators, 500-1500 ce 57 Chapter 6: Francois Viete Makes History 76 Chapter 7: From the Infinite to the Infinitesimal 82 Sidebar 3: A Remarkable Formula by Euler 94 Chapter 8: 371 Proofs, and Then Some 98 Sidebar 4: The Folding Bag 115 Sidebar 5: Einstein Meets Pythagoras 117 Sidebar 6: A Most Unusual Proof 119 Chapter 9: A Theme and Variations 123 Sidebar 7: A Pythagorean Curiosity 140 Sidebar 8: A Case of Overuse 142 Chapter 10: Strange Coordinates 145 Chapter 11: Notation, Notation, Notation 158 Chapter 12: From Flat Space to Curved Spacetime 168 Sidebar 9: A Case of Misuse 177 Chapter 13: Prelude to Relativity 181 Chapter 14: From Bern to Berlin, 1905-1915 188 Sidebar 10: Four Pythagorean Brainteasers 197 Chapter 15: But Is It Universal? 201 Chapter 16: Afterthoughts 208 Epilogue: Samos, 2005 213 Appendixes A. How did the Babylonians Approximate? 219 B. Pythagorean Triples 221 C. Sums of Two Squares 223 D. A Proof that is Irrational 227 E. Archimedes' Formula for Circumscribing Polygons 229 F. Proof of some Formulas from Chapter 7 231 G. Deriving the Equation x2/3 ??y2/3 ??1 235 H. Solutions to Brainteasers 237 Chronology 241 Bibliography 247 Illustrations Credits 251 Index 253
£999.99
Princeton University Press Some Problems of Unlikely Intersections in
Book SynopsisConsiders the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. This book considers algebraic subgroups that meet a given subvariety in a set of unlikely dimension.Trade Review"Zannier's book is well written and a pleasure to read... [T]he author always makes an effort to point out key ideas and key steps, so a reader who wants to read and understand the complete proofs in this technically demanding field will find this monograph to be an extremely helpful entree into the subject... [T]he reviewer highly recommends Zannier's book as an excellent survey of and introduction to the important and hot topic of unlikely intersections in arithmetic geometry."--Joseph H. Silverman, Bulletin of the AMS "This book is indeed a great source of knowledge and inspiration for everybody interested in the unlikely intersection problems. The author must be commended for doing this job, and doing it so well."--Yuri Bilu, Mathematical Reviews ClippingsTable of Contents*FrontMatter, pg. i*Contents, pg. v*Preface, pg. ix*Notation and Conventions, pg. xi*Introduction: An Overview of Some Problems of Unlikely Intersections, pg. 1*Chapter 1: Unlikely Intersections in Multiplicative Groups and the Zilber Conjecture, pg. 15*Chapter 2: An Arithmetical Analogue, pg. 43*Chapter 3 Unlikely Intersections in Elliptic Surfaces and Problems of Masser, pg. 62*Chapter 4: About the Andre-Oort Conjecture, pg. 96*Appendix A: Distribution of Rational Points on Subanalytic Surfaces, pg. 128*Appendix B: Uniformity in Unlikely Intersections: An Example for Lines in Three Dimensions, pg. 136*Appendix C: Silverman's Bounded Height Theorem for Elliptic Curves: A Direct Proof, pg. 138*Appendix D: Lower Bounds for Degrees of Torsion Points: The Transcendence Approach, pg. 140*Appendix E: A Transcendence Measure for a Quotient of Periods, pg. 143*Appendix F: Counting Rational Points on Analytic Curves: A Transcendence Approach, pg. 145*Appendix G: Mixed Problems: Another Approach, pg. 147*Bibliography, pg. 149*Index, pg. 159
£999.99
Princeton University Press Office Hours with a Geometric Group Theorist
Book SynopsisTrade Review"One of Choice Reviews' Outstanding Academic Titles of 2018""In a book with this many authors, it might be expected that their individual contributions would vary significantly in terms of accessibility and readability, but in fact this turned out (presumably as a result of careful editing) not to be the case: the office hours are of uniformly high quality in both of these regards. Their informal, conversational tone should appeal to students (and also to non-specialist faculty who want to learn something about these topics)."---Mark Hunacek, Mathematical Gazette
£45.00
Princeton University Press A Course on Surgery Theory
Book SynopsisTrade Review"A valuable source of knowledge (for graduate students and researchers) on surgery theory and its applications."---Krzysztof M. Pawałowski, ZbMATH Open
£131.75
Princeton University Press A Course on Surgery Theory
Book Synopsis
£63.00
Princeton University Press How to Solve It
Book SynopsisA perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning aTrade Review"Every prospective teacher should read it. In particular, graduate students will find it invaluable. The traditional mathematics professor who reads a paper before one of the Mathematical Societies might also learn something from the book: 'He writes a, he says b, he means c; but it should be d.' "--E. T. Bell, Mathematical Monthly "[This] elementary textbook on heuristic reasoning, shows anew how keen its author is on questions of method and the formulation of methodological principles. Exposition and illustrative material are of a disarmingly elementary character, but very carefully thought out and selected."--Herman Weyl, Mathematical Review "I recommend it highly to any person who is seriously interested in finding out methods of solving problems, and who does not object to being entertained while he does it."--Scientific Monthly "Any young person seeking a career in the sciences would do well to ponder this important contribution to the teacher's art."--A. C. Schaeffer, American Journal of Psychology "Every mathematics student should experience and live this book"--Mathematics Magazine "In an age that all solutions should be provided with the least possible effort, this book brings a very important message: mathematics and problem solving in general needs a lot of practice and experience obtained by challenging creative thinking, and certainly not by copying predefined recipes provided by others. Let's hope this classic will remain a source of inspiration for several generations to come."--A. Bultheel, European Mathematical Society
£16.14
Princeton University Press Whats Next The Mathematical Legacy of William P.
Book Synopsis
£999.99
Princeton University Press Whats Next The Mathematical Legacy of William P.
Book Synopsis
£70.20
Princeton University Press The Structure of Groups with a Quasiconvex
Book Synopsis
£131.75
Princeton University Press Introductory Lectures on Equivariant Cohomology
Book SynopsisTrade Review"Very well-written, self contained and gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology."---Marek Golasiński, Zentralblatt MATH
£999.99
Princeton University Press Arithmetic and Geometry
Book Synopsis
£59.50
Princeton University Press Arithmetic and Geometry
Book Synopsis
£131.75
Princeton University Press Perspective and Projective Geometry
Book SynopsisTrade Review"Offering a plethora of discussion starters, conjecture catalysts, and exercises, Perspective and Projective Geometry invites students to connect math with art and aesthetics. It pulls no punches with respect to the rigor of the mathematics. But it also gives newer math students the necessary tools to engage with the material and discover knowledge for themselves."—Evelyn Lamb, blogger for Scientific American"For years, Annalisa Crannell has brought her insights and excitement for perspective, both in geometry and art, to her teaching, writing, and workshops. Now, with coauthors Mark Frantz and Fumiko Futamura, she has produced a superb textbook on this subject, ideal for classes or self-study."—Thomas Banchoff, former president of the Mathematical Association of America"Filled with ideas for rich and highly original classroom activities, Perspective and Projective Geometry guides students to make deep connections to the geometry in art. It is wholly different than any other textbook I’ve seen on projective geometry."—Jessica Sidman, Mount Holyoke College"From Menelaus and elations to window taping and writing mathematics, this book provides a delightful mesh of classical geometry, perspective in art, beautiful graphics, and an exploratorium of exercises. Perspective and Projective Geometry is enjoyable reading and a valuable textbook for a variety of courses."—Doug Norton, Villanova University
£49.50
Crown Publishing Group (NY) The Golden Ratio The Story of Phi the Worlds Most
Book SynopsisThroughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as The Golden Ratio, was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona
£12.41
Bloomsbury Publishing USA Islamic Design A Genius for Geometry Wooden Books
Book Synopsis
£13.50
Holiday House Perimeter Area and Volume
Book SynopsisGrab your jumbo popcorn—you''re invited to the premiere of a 3-D movie, all about those three dimensions!Trusted math picture book duo David A. Adler and Ed Miller tackle the differences between two- and three-dimensional objects in their signature bright and kid-friendly way. Explaining length, width, and height-- and all the different ways we represent those figures-- Adler shows how changing the dimensions of an object affects its size. . . . with some help from a cast of funny, friendly movie monsters. Explaining key vocabulary in simple text and offering numerous concrete examples and sample math problems with included solutions, Perimeter, Area, and Volume is a perfect introduction to two- and three-dimensional geometry. The star-studded cast of monsters will help you calculate the perimeter of the set, the area of the movie screen, and the volume of your box of popcorn.Learning about dimensions has never been so entertaining!
£8.54
Taylor & Francis Inc Discrete Geometry
Book SynopsisCelebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analyzes packings and coverings with congruent convex bodies , arrangements on the sphere, line transversals, Euclidean and spherical tilings, geometric graphs, polygons and polyhedra, and fixing systems for convex figures. This text also offers research and contributions from more than 50 esteemed international authorities, making it a valuable addition to any mathematical library.Trade Review"Offering research and contributions from more than 40 esteemed international authorities, Discrete Geometry is a fascinating collection for pure and applied mathematicians, geometers, topologists, combinatorialists, and upper-level undergraduate and graduate students in these disciplines." - L-Enseignement Mathematique, Vol. 50, 1-2, Jan-Jun 2004Table of ContentsTransversal lines to lines and intervals, Jorge L. Arocha, Javier Bracho, and Luis Montejano; on a shortest path problem of G. Fejes, Toth Donald R. Baggett and Andras Bezdek; a short survey of (r,q)-structures, Vojtech Balint; lattice points on the boundary of the integer hull, Imre Barany and Karoly Boroczky, Jr; the Erdos-Szekeres problem for planar points in arbitrary position, Tibor Bisztriczky and Gabor Fejes Toth, separation in totally-sewn 4-polytopes, Tibor Bisztriczky and Deborah Oliveros, on a class of equifacetted polytopes, Gerd Blind and Roswitha Blind; chessboard Ramsey numbers, Jens-P. Bode, Heiko Harborth, and Stefan Krause; maximal primitive fixing systems for convex figures, Vladimir Boltyanski and Hernan Gonzalez-Aguilar; the Newton-Gregory problem revisited, Karoly Boroczky, arrangements of 13 points on a sphere Karoly Boroczky and Laszlo Szabo; on point sets without k collinear points, Peter Brass; the Beckman-Quarles theorem for rational d-spaces, d even and d> 6, Robert Connelly and Joseph Zaks; edge-antipodal convex polytopes - a proof of Talata's conjecture, Balazs Csikos; single-split tilings of the sphere with right triangles, Robert J. MacG. Dawson; vertex-unfoldings of simplicial manifolds, Erik D. Demaine, David Eppstein, Jeff Erickson, George W. Hart, and Joseph O'Rourke; view-obstruction through trajectories of co-dimension three Vishwa C. Dumir and Rajinder J. Hans-Gill; fat 4-polytopes and fatter 3-spheres, David Eppstein, Greg Kuperberg, and Gunter M. Ziegler; arbitrarily large neighbourly families of congruent symmetric convex 3-polytopes, Jeff Erickson and Scott Kim; on the non-solidity of some packings and coverings with circles, August Florian and Aladar Heppes; on the mth Petty numbers of normed spaces Karoly Bezdek, Marton Naszodi and Balazs Visy; cubic polyhedra, Chaim Goodman-Strauss and John M. Sullivan; new uniform polyhedra, Branko Grunbaum; on the existence of a convex polygon with a specified number of interior points, Kiyoshi Hosono, Gyula Karolyi and Masatsugu Urabe; on-line 2-adic covering of the unit square by boxes, Janusz Januszewski and Marek Lassak; an example of a stable, even order quadrangle which is determined by its angle function, Janos Kincses; sets with a unique extension to a set of constant width, Marton Naszodi and Balazs Visy; the number of simplices embracing the origin, Janos Pach and Mario Szegedy; Helly-type theorems on definite supporting lines for k-disjoint families of convex bodies in the plane, Sorin Revenko and Valeriu Soltan; combinatorial aperiodicity of polyhedral prototiles, Egon Schulte; sequences of smoothed polygons, G.C. Shephard; on a packing inequality, Graham, Witsenhausen and Zassenhaus, Jorg M. Wills; covering a triangle with homothetic copies, Zoltan Furedi; open problems, Andras Bezdek.
£247.00
Taylor & Francis Inc Subplane Covered Nets 222 Chapman HallCRC Pure
Book SynopsisThis work confronts the question of geometric processes of derivation, specifically the derivation of affine planes - keying in on construction techniques and types of transformations in which lines of a newly-created plane can be understood as subplanes of the original plane. The book provides a theory of subplane covered nets without restriction to the finite case or imposing commutativity conditions.Table of ContentsA brief overview; projective geometries; beginning derivation; spreads; derivable nets; the Hughes planes; Desarguesian planes; Pappian planes; characterizations of geometries; derivable nets and geometries; structure theory for derivable nets; dual spreads and Baer subplanes; derivation as a geometric process; embedding; classification of subplane covered nets; subplane covered affine planes; direct products; parallelisms; partial parallelisms with deficiency; Baer extensions; translation planes admitting Baer groups; spreads covered by pseudo-Reguli; conical and ruled planes over fields; spreads which are dual spreads; partial flocks of deficiency one; Skew-Hall planes.
£999.99
Taylor & Francis Ltd Topics on Continua Chapman HallCRC Pure and
Book SynopsisSpecialized as it might be, continuum theory is one of the most intriguing areas in mathematics. However, despite being popular journal fare, few books have thoroughly explored this interesting aspect of topology. In Topics on Continua, Sergio Macías, one of the field's leading scholars, presents four of his favorite continuum topics: inverse limits, Jones's set function T, homogenous continua, and n-fold hyperspaces, and in doing so, presents the most complete set of theorems and proofs ever contained in a single topology volume. Many of the results presented have previously appeared only in research papers, and some appear here for the first time. After building the requisite background and exploring the inverse limits of continua, the discussions focus on Professor Jones''s set function T and continua for which T is continuous. An introduction to topological groups and group actions lead to a proof of Effros''s Theorem, followed by a presentTable of ContentsPreliminaries, including an introduction to Product Topology. Inverse Limits and Related Topics. Jones Set Function T. A Theorem of E.G. Effros. Decomposition Theorems. n-Fold Hyperspaces. Questions.
£175.00
Cambridge University Press Oeuvres de Desargues
Book SynopsisThe French mathematician Gérard Desargues (15911661) was one of the founders of projective geometry. His writings, published in two volumes in 1864 by Noël-Germinal Poudra (17941894), reveal Desargues' important role in the scientific debates of the seventeenth century. Volume 2 contains reviews and criticism by Desargues' contemporaries.Table of ContentsPreliminaire; Analyse des ouvrages de Bosse; Notices sur Desargues; Diverses notices sur Desargues; Recueil et extraits de divers libelles contre Desargues; Advis charitable; Curabelle; Faiblesse pitoyable.
£45.28
John Wiley & Sons Inc Geometry of Surfaces
Book SynopsisPresents an in-depth analysis of geometry of part surfaces and provides the tools for solving complex engineering problems Geometry of Surfaces: A Practical Guide for Mechanical Engineers is a comprehensive guide to applied geometry of surfaces with focus on practical applications in various areas of mechanical engineering.Table of ContentsAbout the Author xiii Preface xv Acknowledgments xvii Glossary xix Notation xxi Introduction xxv Part I PART SURFACES 1 1 Geometry of a Part Surface 3 1.1 On the Analytical Description of Ideal Surfaces 3 1.2 On the Difference between Classical Differential Geometry and Engineering Geometry of Surfaces 6 1.3 On the Analytical Description of Part Surfaces 7 1.4 Boundary Surfaces for an Actual Part Surface 9 1.5 Natural Representation of a Desired Part Surface 11 1.6 Elements of Local Geometry of a Desired Part Surface 19 2 On the Possibility of Classification of Part Surfaces 27 2.1 Sculptured Part Surfaces 27 2.2 Planar Characteristic Images 33 2.3 Circular Diagrams at a Surface Point 42 2.4 One More Useful Characteristic Curve 53 Part II GEOMETRY OF CONTACT OF PART SURFACES 55 3 Early Works in the Field of Contact Geometry 57 3.1 Order of Contact 57 3.2 Contact Geometry of Part Surfaces 59 3.3 Local Relative Orientation of the Contacting Part Surfaces 59 3.4 First-Order Analysis: Common Tangent Plane 64 3.5 Second-Order Analysis 65 3.6 A Characteristic Curve Irk (R ) of Novel Kind 75 4 An Analytical Method Based on Second Fundamental Forms of the Contacting Part Surfaces 79 5 Indicatrix of Conformity of Two Smooth Regular Surfaces in the First Order of Tangency 83 5.1 Preliminary Remarks 83 5.2 Indicatrix of Conformity for Two Smooth Regular Part Surfaces in the First Order of Tangency 87 5.3 Directions of Extremum Degree of Conformity of Two Part Surfaces in Contact 94 5.4 Asymptotes of the Indicatrix of Conformity CnfR (P1/P2) 97 5.5 Comparison of Capabilities of Indicatrix of Conformity Cnf R(P1/P2) and of Dupin Indicatrix of the Surface of Relative Curvature Dup (R) 98 5.6 Important Properties of Indicatrix of Conformity Cnf R(P/T ) of Two Smooth Regular Part Surfaces 99 5.7 The Converse Indicatrix of Conformity of Two Regular Part Surfaces in the First Order of Tangency 99 6 Plücker Conoid: More Characteristic Curves 101 6.1 Plücker Conoid 101 6.2 On Analytical Description of Local Geometry of a Smooth Regular Part Surface 105 6.3 Relative Characteristic Curve 112 7 Feasible Kinds of Contact of Two Smooth Regular Part Surfaces in the First Order of Tangency 117 7.1 On the Possibility of Implementation of the Indicatrix of Conformity for the Purposes of Identification of the Actual Kind of Contact of Two Smooth Regular Part Surfaces 117 7.2 Impact of Accuracy of the Computation on the Parameters of the Indicatrices of Conformity Cnf R(P1/P2) 121 7.3 Classification of Possible Kinds of Contact of Two Smooth Regular Part Surfaces 122 Part III MAPPING OF THE CONTACTING PART SURFACES 131 8 R-Mapping of the Interacting Part Surfaces 133 8.1 Preliminary Remarks 133 8.2 On the Concept of R-Mapping of the Interacting Part Surfaces 134 8.3 R-mapping of a Part Surface P1 onto Another Part Surface P2 136 8.4 Reconstruction of the Mapped Part Surface 140 8.5 Illustrative Examples of the Calculation of the Design Parameters of the Mapped Part Surface 141 9 Generation of Enveloping Surfaces: General Consideration 145 9.1 Envelope for Successive Positions of a Moving Planar Curve 145 9.2 Envelope for Successive Positions of a Moving Surface 149 9.3 Kinematic Method for Determining Enveloping Surfaces 154 9.4 Peculiarities of Implementation of the Kinematic Method in Cases of Multi-parametric Relative Motion of the Surfaces 164 10 Generation of Enveloping Surfaces: Special Cases 167 10.1 Part Surfaces that Allow for Sliding Over Themselves 167 10.2 Reversibly Enveloping Surfaces: Introductory Remarks 169 10.3 Generation of Reversibly Enveloping Surfaces 180 10.4 On the Looseness of Two Olivier Principles 197 Conclusion 203 APPENDICES 205 Appendix A: Elements of Vector Calculus 207 A.1 Fundamental Properties of Vectors 207 A.2 Mathematical Operations over Vectors 207 Appendix B: Elements of Coordinate System Transformations 211 B.1 Coordinate System Transformation 211 B.2 Conversion of the Coordinate System Orientation 222 B.3 Transformation of Surface Fundamental Forms 223 Appendix C: Change of Surface Parameters 225 References 227 Bibliography 229 Index 233
£115.16
Taylor & Francis Inc An Illustrated Introduction to Topology and
Book SynopsisAn Illustrated Introduction to Topology and Homotopy explores the beauty of topology and homotopy theory in a direct and engaging manner while illustrating the power of the theory through many, often surprising, applications. This self-contained book takes a visual and rigorous approach that incorporates both extensive illustrations and full proofs.The first part of the text covers basic topology, ranging from metric spaces and the axioms of topology through subspaces, product spaces, connectedness, compactness, and separation axioms to Urysohn's lemma, Tietze's theorems, and Stone-Cech compactification. Focusing on homotopy, the second part starts with the notions of ambient isotopy, homotopy, and the fundamental group. The book then covers basic combinatorial group theory, the Seifert-van Kampen theorem, knots, and low-dimensional manifolds. The last three chapters discuss the theory of covering spaces, the Borsuk-Ulam theorem, and applications in grTrade Review"… reflects interesting aspects and will find its readers."—Zentralblatt MATH, 1323"… an ideal college or university textbook and an invaluable addition to academic library mathematical studies reference collections."—Library Bookwatch, May 2015Table of ContentsTOPOLOGY: Sets, Numbers, Cardinals, and Ordinals. Metric Spaces: Definition, Examples, and Basics. Topological Spaces: Definition and Examples. Subspaces, Quotient Spaces, Manifolds, and CW-Complexes. Products of Spaces. Connected Spaces and Path Connected Spaces. Compactness and Related Matters. Separation Properties. Urysohn, Tietze, and Stone-Čech. HOMOTOPY: Isotopy and Homotopy. The Fundamental Group of a Circle and Applications. Combinatorial Group Theory. Seifert-van Kampen Theorem and Applications. On Classifying Manifolds and Related Topics. Covering Spaces, Part 1. Covering Spaces, Part 2. Applications. Applications in Group Theory. Bibliography.
£130.06
Lulu Press Euclid Transmogrified
Book Synopsis
£52.40
Taylor & Francis Inc Transformational Plane Geometry
Book SynopsisDesigned for a one-semester course at the junior undergraduate level, Transformational Plane Geometry takes a hands-on, interactive approach to teaching plane geometry. The book is self-contained, defining basic concepts from linear and abstract algebra gradually as needed.The text adheres to the National Council of Teachers of Mathematics Principles and Standards for School Mathematics and the Common Core State Standards Initiative Standards for Mathematical Practice. Future teachers will acquire the skills needed to effectively apply these standards in their classrooms. Following Felix Klein's Erlangen Program, the book provides students in pure mathematics and students in teacher training programs with a concrete visual alternative to Euclid's purely axiomatic approach to plane geometry. It enables geometrical visualization in three ways: Key concepts are motivated with explorTrade Review"This book is designed for a one-semester course at the junior undergraduate level and turns especially to future educators in the USA. … The arrangement and clarity of the text meet the most demanding pedagogical and mathematical requirements. Highlights of the book are the classification of isometries and similarities of the Euclidean plane. … a wonderful first step into transformational plane geometry …"—Zentralblatt MATH 1311 Table of ContentsAxioms of Euclidean Plane Geometry. Theorems of Euclidean Plane Geometry. Introduction to Transformations, Isometries, and Similarities. Translations, Rotations, and Reflections. Compositions of Translations, Rotations, and Reflections. Classification of Isometries. Symmetry of Plane Figures. Similarity. Appendix. Bibliography. Index.
£84.99
Taylor & Francis Inc Analytic Hyperbolic Geometry in N Dimensions
Book SynopsisThe concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language that sheds natural light on hyperbolic geometry and special relativity. Several authors have successfully employed the author's gyroalgebra in their exploration for novel results. Françoise Chatelin noted in her book, and elsewhere, that the computation language of Einstein described in this book plays a universal computational role, which extends far beyond the domain of special relativity. This book will encourage researchers to use the author's novel techniques to formulate their own results. The book provides new mathematical tools, such as hyperbolic simplexes, for the study of hyperbolic geometry Trade Review"Anyone who is concerned with hyperbolic geometry should use this wonderful and comprehensive book as a helpful compendium."—Zentralblatt MATH 1312Table of ContentsList of Figures. Preface. Author’s Biography. Introduction. Einstein Gyrogroups and Gyrovector Spaces. Einstein Gyrogroups. Problems. Einstein Gyrovector Spaces. Problems. Relativistic Mass Meets Hyperbolic Geometry. Problems. Mathematical Tools for Hyperbolic Geometry. Barycentric and Gyrobarycentric Coordinates. Problems. Gyroparallelograms and Gyroparallelotopes. Problems. Gyrotrigonometry. Problems. Hyperbolic Triangles and Circles. Gyrotriangles and Gyrocircles. Problems. Gyrocircle Theorems. Problems. Hyperbolic Simplices, Hyperplanes and Hyperspheres in N Dimensions. Gyrosimplices. Problems. Gyrosimplex Gyrovolume. Problems. Hyperbolic Ellipses and Hyperbolas. Gyroellipses and Gyrohyperbolas. Problems. VI Thomas Precession. Thomas Precession. Problems. Bibliography. Index.
£175.75
Taylor & Francis Inc Blowup for HigherOrder Parabolic Hyperbolic
Book SynopsisBlow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrödinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book first studies the particular self-similar singularity solutions (patterns) of the equations. This approach allows four different classes of nonlinear PDEs to be treated simultaneously to establish their striking common features. The book describes many properties of the equations and examines traditional questions of existence/nonexistence, uniqueness/nonuniqueness, global asymptotics, regularizations, shock-wave theory, and various blow-up singularities.Preparing readers for more advanced mathematical PDE analysis, the book demonstrates that quasilinear degenerate higher-order PDEs, even exoticTrade Review"This volume gives a collection of results on self-similar singular solutions for nonlinear partial differential equations (PDEs), with special emphasis on ‘exotic’ equations of higher order …"—Zentralblatt MATH 1320Table of ContentsIntroduction. Complicated Self-Similar Blow-Up, Compacton, and Standing Wave Patterns for Four Nonlinear PDEs: A Unified Variational Approach to Elliptic Equations. Classification of Global Sign-Changing Solutions of Semilinear Heat Equations in the Subcritical Fujita Range: Second- and Higher-Order Diffusion. Global and Blow-Up Solutions for Kuramoto–Sivashinsky, Navier–Stokes, and Burnett Equations. Regional, Single-Point, and Global Blow-Up for a Fourth-Order Porous Medium-Type Equation with Source. Semilinear Fourth-Order Hyperbolic Equation: Two Types of Blow-Up Patterns. Quasilinear Fourth-Order Hyperbolic Boussinesq Equation: Shock, Rarefaction, and Fundamental Solutions. Blow-Up and Global Solutions for Korteweg–de Vries-Type Equations. Higher-Order Nonlinear Dispersion PDEs: Shock, Rarefaction, and Blow-Up Waves. Higher-Order Schrödinger Equations: From "Blow-Up" Zero Structures to Quasilinear Operators. References.
£155.00
Taylor & Francis Inc Reconstruction from Integral Data
Book SynopsisReconstruction of a function from data of integrals is used for problems arising in diagnostics, including x-ray, positron radiography, ultrasound, scattering, sonar, seismic, impedance, wave tomography, crystallography, photo-thermo-acoustics, photoelastics, and strain tomography. Reconstruction from Integral Data presents both long-standing and recent mathematical results from this field in a uniform way. The book focuses on exact analytic formulas for reconstructing a function or a vector field from data of integrals over lines, rays, circles, arcs, parabolas, hyperbolas, planes, hyperplanes, spheres, and paraboloids. It also addresses range characterizations. Coverage is motivated by both applications and pure mathematics.The book first presents known facts on the classical and attenuated Radon transform. It then deals with reconstructions from data of ray (circle) integrals. The author goes on to cover reconstructions in classical and new gTable of ContentsRadon Transform. Ray and Line Integral Transforms. Factorization Method. General Method of Reconstruction. Applications to Classical Geometries. Applications to the Spherical Mean Transform. Appendix.
£147.25
Taylor & Francis Inc Handbook of Discrete and Computational Geometry
Book SynopsisThe Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic worldas researchers in mathematics and computer scienceand in the professional worldas practitioners in ?elds as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed signi?cantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young ?eld of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided Trade Review"Discrete and computational geometry is a thriving field, and the collective knowledge represented in this third edition of the Handbook is evidence of this. Twenty years have passed since the publication of the first edition [Handbook of discrete and compu-tational geometry, CRC Press Ser. Discrete Math. Appl., CRC, Boca Raton, FL, 1997; MR1730156], and since then, the area has seen a tremendous growth due in part to the influence of both the first and second editions [Handbook of discrete and computational geometry, Discrete Math. Appl. (Boca Raton), Chapman & Hall/CRC, Boca Raton, FL, 2004; MR2082993] of the Handbook. The new edition can be expected to serve a similar purpose for future generations of researchers and practitioners.The third edition has a new co-editor, Csaba D. T´oth, who joins the two editors of the previous editions, Jacob E. Goodman and Joseph O’Rourke.The third edition of the Handbook has been substantially revised. The addition of almost 400 pages has resulted in a volume of well over 1900 pages. Fifty-eight out of the sixty-five chapters of the second edition have been updated (sometimes with a slightly revised title), many of them by the original authors, others in collaboration with new co-authors. Ten new chapters have been added, for an overall count of sixty-eight chapters.Five new chapters on computational topology and its applications have been added, including four in a new section on “Combinatorial and Computational Topology”. These deal with random simplicial complexes, computational topology of graphs on surfaces, persistent homology, high-dimensional topological data analysis, and geometry and topology of genomic, respectively. A new chapter on proximity algorithms, added to the section on “Algorithms and Complexity of Fundamental Geometric Objects”, provides a comprehensive treatment of relative neighborhood graphs and geometric spanners. There also are two new chapters in the section on “Computational Techniques”: on epsilon-approximations and epsilon-nets and on coresets and sketches, respectively. Finally, two more new chapters in the section on “Applications of Discrete and Compu-tational Geometry” describe recent advances in rigidity theory and concern rigidity of symmetric frameworks and global rigidity, respectively.The new version remains an invaluable resource for anyone interested in discrete and computational geometry and in related areas, including specialists and non-specialists. The Handbook continues to be an attractive one-stop reference book."- Egon Schulte - Mathematical Reviews Clippings - May 2019Table of ContentsFinite point configurations. Packing and covering. Tilings. Helly-type theorems and geometric transversals. Pseudoline arrangements. Oriented matroids.Lattice points and lattice polytopes. Low-distortion embeddings of finite metric spaces. Geometry and topology of polygonal linkages. Geometric graph theory. Euclidean Ramsey theory. Discrete aspects of stochastic geometry. Geometric discrepancy theory and uniform distribution. Polyominoes. Basic properties of convex polytopes. Subdivisions and triangulations of polytopes. Face numbers of polytopes and complexes. Symmetry of polytopes and polyhedra. Polytope skeletons and paths. Polyhedral maps.Topological methods in discrete geometry.Random simplicial complexes. Computational topology of graphs on surfaces. Persistent homology. High-dimensional topological data analysis. Convex hull computations. Voronoi diagrams and Delaunay triangulations. Arrangements.Triangulations and mesh generation. Polygons.Shortest paths and networks. Proximity algorithms. Visibility. Geometric reconstruction problems. Curve and surface reconstruction. Computational convexity. Computational and quantitative real algebraic geometry.Point location. Collision and proximity queries. Range searching. Ray shooting and lines in space. Geometric intersection. Nearest neighbors in high-dimensional spaces.Randomizaton and derandomization. Robust geometric computation. Parallel algorithms in geometry. Epsilon-nets and epsilon-approximations Coresets and sketches. Linear programming. Algorithmic motion planning. Robotics. Computer graphics. Modeling motion. Pattern recognition. Graph drawing.Splines and geometric modeling. Solid modeling. Computation of robust statistics: Depth, median, and related measures. Geographic information systems.Geometric applications of the Grassmann-Cayley algebra. Rigidity of symmetric frameworks. Global rigidity. Crystals, periodic and aperiodic..Applications to structural molecular biology. Geometry and topology of genomics. Software. Two computational geometry libraries: LEDA and CGAL
£237.50
Taylor & Francis Inc Introduction to Abelian Model Structures and
Book SynopsisIntroduction to Abelian Model Structures and Gorenstein Homological Dimensions provides a starting point to study the relationship between homological and homotopical algebra, a very active branch of mathematics. The book shows how to obtain new model structures in homological algebra by constructing a pair of compatible complete cotorsion pairs related to a specific homological dimension and then applying the Hovey Correspondence to generate an abelian model structure. The first part of the book introduces the definitions and notations of the universal constructions most often used in category theory. The next part presents a proof of the Eklof and Trlifaj theorem in Grothedieck categories and covers M. Hovey's work that connects the theories of cotorsion pairs and model categories. The final two parts study the relationship between model structures and classical and Gorenstein homological dimensions and explore special types of Grothendieck categorieTrade Review"This book is a worthy addition to the relative homological algebra literature. Graduate students can use it to introduce themselves in the topic and it is also a useful reference's book for specialists in the field of homological algebra." - Blas Torrecillas"The main goal of this book is to provide a multitude of model category structures for categories such as categories of chain complexes, categories of modules, and more specifically, Gorenstein categories (a Grothendieck category with extra properties). The author provides these model category structures by making use of the Hovey Correspondence, which allows one to associate a model category structure to a complete cotorsion pair in an abelian category […]This text is based on the thesis of the author and the majority of original results presented here are related to the model category structures coming from homological dimensions. The intended audience includes graduate students pursuing a degree in the field and researchers interested in the development of model category structures associated to Gorenstein homological dimensions. It is well written and is well suited for the target audience."- Bruce R. Corrigan-Salter, Mathematical Reviews, August 2017"The main goal of this book is to provide a multitude of model category structures for categories such as categories of chain complexes, categories of modules, and more specifically, Gorenstein categories (a Grothendieck category with extra properties). The author provides these model category structures by making use of the Hovey Correspondence, which allows one to associate a model category structure to a complete cotorsion pair in an abelian category […]This text is based on the thesis of the author and the majority of original results presented here are related to the model category structures coming from homological dimensions. The intended audience includes graduate students pursuing a degree in the field and researchers interested in the development of model category structures associated to Gorenstein homological dimensions. It is well written and is well suited for the target audience."- Bruce R. Corrigan-Salter, Mathematical Reviews, August 2017Table of ContentsCategorical and algebraic preliminaries. Interactions between homological algebra and homotopy theory. Classical homological dimensions and abelian model structures on chain complexes. Gorenstein homological dimensions and abelian model structures. Bibliography. Index.
£147.25
