Geometry Books
LAP Lambert Academic Publishing To Get Real Shapes and New Data of 120-Cell and 600-Cell
£34.57
Arnoldsche Mandala – Auf der Suche nach Erleuchtung: Heilige
Book SynopsisHailing from the cultural realm of India, the mandala signifies in its original sense a sacred circle. It serves as a meditation aid and at the same time reflects an ancient symbolism of strictly geometric basic forms accompanied by an interpretation of its sacred content. As an expression of the awareness of higher affinities, the symmetrically arranged geometry can be found in a variety of pictorial works and the architecture of various epochs and cultural realms, for example in medieval book illumination, the floor plan of the Blue Mosque in Istanbul, in Kazimir Malevich’s Black Square, or in various objects of the indigenous peoples of Africa, Asia, Australia, and the Americas. Based on these and other masterpieces from renowned museums and private collections and illustrated in fascinating photographs of unique buildings and rituals, this publication offers an impressive first analysis of the phenomenon of sacred geometry in art and architecture and their underlying ideologies. Text in German.
£999.99
Taylor & Francis Ltd Conical Approach to Linear Programming
Book SynopsisThe conical approach provides a geometrical understanding of optimization and is a powerful research tool and useful problem-solving technique (for example, in decision support and real time control applications). Conical optimality conditions are first stated in a very general optimization framework, and then applied to linear programming. A complete theory along with primal and dual algorithms is given, and solutions and algorithms are also provided for vector and robust linear optimization. The advantages of parameter dependence of conical methods are fully discussed. In addition to numerical results, the book provides source codes and detailed documentation of a Modula-2 implementation for the main algorithms.Table of ContentsPart I: General Theory Part II: Further Advanced Results Part III: Implementations and Numerical Results
£237.50
The University of Chicago Press Geometry of Nonpositively Curved Manifolds
Book SynopsisStarting from the foundations, this text presents an almost entirely self-contained treatment of differentiable spaces of nonpositive curvature, focusing on the symmetric spaces in which every geodesic lies in a flat Euclidean space of dimension at least two.
£117.80
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
The University of Chicago Press The Topological Classification of Stratified
Book SynopsisThis text provides topologists with a new way of looking at the classification theory of singular spaces. Divided into three parts, the book begins with an overview of high-dimensional manifold theory. It then offers the parallel theory for stratified spaces. Applications are also included.Table of ContentsPart 1 Manifold theory: algebraic K-theory and topology; surgery theory; spacification and functoriality; applications. Part 2 General theory: definitions and examples; classification of stratified spaces; transverse stratified classification; PT category; controlled topology; proof of main theorems in topology. Part 3 Applications and illustrations: manifolds and embedding theory revisited; supernormal spaces and varieties; group actions; rigidity conjectures.
£30.00
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
John Wiley & Sons Inc Dr. Math Presents More Geometry
Book SynopsisYou, too, can understand geometry just ask Dr. Math! Are things starting to get tougher in geometry class? Don''t panic. Dr. Maththe popular online math resourceis here to help you figure out even the trickiest of your geometry problems. Students just like you have been turning to Dr. Math for years asking questions about math problems, and the math doctors at The Math Forum have helped them find the answers with lots of clear explanations and helpful hints. Now, with Dr. Math Presents More Geometry, you''ll learn just what it takes to succeed in this subject. You''ll find the answers to dozens of real questions from students in a typical geometry class. You''ll also find plenty of hints and shortcuts for using coordinate geometry, finding angle relationships, and working with circles. Pretty soon, everything from the Pythagorean theorem to logic and proofs will make more sense. Plus, you''ll get plenty of tips for working with all kinds of real-life problems.<Table of ContentsIntroduction. PART 1. POINTS, LINES, PLANES, ANGLES, AND THEIR RELATIONSHIPS. 1. Angle relationships and perpendicular and parallel lines. 2. Proving lines parallel. 3. The parallel postulate. 4. Coordinates and distance. Resources on the Web. PART 2. LOGIC AND PROOF. 1. Introduction to logic. 2. Direct proof. 3. Indirect proof. Resources on the Web. PART 3. TRIANGLES: PROPERTIES, CONGRUENCE, AND SIMILARITY. 1. Triangle Inequality Property. 2. Centers of triangles. 3. Isosceles and equilateral triangles. 4. Congruence in triangles-SSS, SAS, ASA, and SSA. 5. Similarity in triangles. 6. Congruence proofs. Resources on the Web. PART 4. QUADRILATERALS AND OTHER POLYGONS. 1. Properties of Polygons. 2. Properties of Quadrilaterals. 3. Area and Perimeter of Quadrilaterals. Resources on the Web. PART 5. CIRCLES AND THEIR PARTS. 1. Tangents. 2. Arcs and Angles. 3. Chords. Resources on the Web.
£12.59
John Wiley & Sons Inc Geometric Data Analysis An Empirical Approach to
Book SynopsisThis book addresses the most efficient methods of pattern analysis using wavelet decomposition. Readers will learn to analyze data in order to emphasize the differences between closely related patterns and then categorize them in a way that is useful to system users.Trade Review"...provides a valuable summary of data reduction." (Technometrics, May 2002) "...effectively describes and summarizes an emerging new field, namely, scientific data modeling and analysis." (Mathematical Reviews, 2003h)Table of ContentsPreface. Acknowledgments. INTRODUCTION. Pattern Analysis as Data Reduction. Vector Spaces and Linear Transformations. OPTIMAL ORTHOGONAL PATTERN REPRESENTATIONS. The Karhunen-Loève Expansion. Additional Theory, Algorithms and Applications. TIME, FREQUENCY AND SCALE ANALYSIS. Fourier Analysis. Wavelet Expansions. ADAPTIVE NONLINEAR MAPPINGS. Radial Basis Functions. Neural Networks. Nonlinear Reduction Architectures. Appendix A Mathemetical Preliminaries. References. Index.
£107.06
John Wiley & Sons Inc Introduction to Geometry
Book SynopsisThis classic work is now available in an unabridged paperback edition. The Second Edition retains all the characterisitcs that made the first edition so popular: brilliant exposition, the flexibility permitted by relatively self-contained chapters, and broad coverage ranging from topics in the Euclidean plane, to affine geometry, projective geometry, differential geometry, and topology. The Second Edition incorporates improvements in the text and in some proofs, takes note of the solution of the 4-color map problem, and provides answers to most of the exercises.Table of ContentsPart I Triangles 3 Regular Polygons 26 Isometry in the Euclidean Plane 39 Two-Dimensional Crystallography 50 Similarity in the Euclidean Plane 67 Circles and Spheres 77 Isometry and Similarity in Euclidean Space 96 Part II Coordinates 107 Complex Numbers 135 The Five Platonic Solids 148 The Golden Section and Phyllotaxis 160 Part III Ordered Geometry 175 Affine Geometry 191 Projective Geometry 229 Absolute Geometry 263 Hyperbolic Geometry 287 Part IV Differential Geometry of Curves 307 The Tensor Notation 328 Differential Geometry of Surfaces 342 Geodesics 366 Topology of Surfaces 379 Four-Dimensional Geometry 396 Tables 413 References 415 Answers to Exercises 419 Index 459
£146.66
John Wiley & Sons Inc The Finite Element Method in the Static and
Book SynopsisThe Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media Second Edition Roland W. Lewis, University of Wales Swansea, UK Bernard A.Table of ContentsMechanics of Saturated and Partially Saturated Porous Media. Numerical Solution for Isothermal Consolidation. Solid-Phase Constitutive Relationships, Variable Permeabilities and Solution Procedures. Verification of Elastic and Elastoplastic Consolidation Programs. Modelling Subsidence: Numerical Aspects and Problems of Regional Scale. Modelling Subsidence: Case Studies. Modelling Three-Phase Flow in Deforming Saturated Oil Reservoirs. Fractured Reservoir Simulation. Heat and Fluid Flow in Deforming Porous Media. Secondary Consolidation Creep in Solids. Soil-Structure Interaction. Back Analysis in Consolidation. Large-Strain Quasi-Static and Dynamic Soil Behaviour. Subject Index.
£228.56
John Wiley & Sons Inc Thermal Quadrupoles
Book SynopsisThis superb text describes a novel and powerful method for allowing design engineers to firstly model a linear problem in heat conduction, then build a solution in an explicit form and finally obtain a numerical solution. It constitutes a modelling and calculation tool based on a very efficient and systemic methodological approach. Solving the heat equations through integral transforms does not constitute a new subject. However, finding a solution generally constitutes only one part of the problem. In design problems, an initial thermal design has to be tested through the calculation of the temperature or flux field, followed by an analysis of this field in terms of constraints. A modified design is then proposed, followed by a new thermal field calculation, and so on until the right design is found. The thermal quadrupole method allows this often painful iterative procedure to be removed by allowing only one calculation. The chapters in this book increase in complexiTrade Review"The book can be highly recommended to anyone who works in the area of integral transforms and heat transfer". (Zentralblatt MATH, Vol.964, No.14, 2001)Table of ContentsInterest in the Quadrupole Approach. Linear Conduction and Simple Geometries. One-Dimensional Quadrupoles. Multidimensional Transfers. Time-Dependent Periodic Regimes. Advanced Quadrupoles. Mass Transfer in a Porous Medium. The Quadrupole Approach Applied to Heat Transfer in Semi-Transparent Materials. Inverse Laplace Transform. Appendices. Index.
£182.66
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
£69.70
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 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
£42.50
Princeton University Press A Course on Surgery Theory
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£999.99
Princeton University Press Whats Next The Mathematical Legacy of William P.
Book Synopsis
£130.40
Princeton University Press Whats Next The Mathematical Legacy of William P.
Book Synopsis
£66.30
Princeton University Press The Structure of Groups with a Quasiconvex
Book Synopsis
£124.00
Princeton University Press The Structure of Groups with a Quasiconvex
Book Synopsis
£59.50
Princeton University Press How to Fall Slower Than Gravity
Book SynopsisTrade Review"This book is without a doubt the most enjoyable, stimulating book of mathematical physics (and occasionally more pure branches of maths) puzzles that I have ever read. It’s essentially a series of cleverly, and occasionally fiendishly put-together mathematics and physics challenge questions, each of which gets you thinking in a new and fascinating way."---Jonathan Shock, Mathemafrica"Reading Nahin is like reading through a select library of ancient Babylonian mathematical clay tablets. Surprises abound. . . . Nahin weaves much colorful history into his narrative."---Andrew Simoson, Mathematical Intelligencer"Engaging. . . . The book contains a wealth of original problems. . . . An enjoyable read."---Antonín Slavík, Zentralblatt MATH"This reviewer found himself being drawn to a variety of unfamiliar settings with much interest and even fascination." * Choice *"I certainly enjoyed [the book]!"---Alan Stevens, Mathematics Today"The potential audience for this book should be fairly large and go from highly talented high school students up through professionals in any STEM field."---Geoffrey Dietz, MAA Reviews
£19.80
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
£130.40
Princeton University Press Introductory Lectures on Equivariant Cohomology
Book Synopsis
£63.75
Princeton University Press Arithmetic and Geometry
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£124.00
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
£46.75
Princeton University Press How to Fall Slower Than Gravity
Book SynopsisTrade Review"This book is without a doubt the most enjoyable, stimulating book of mathematical physics (and occasionally more pure branches of maths) puzzles that I have ever read. It’s essentially a series of cleverly, and occasionally fiendishly put-together mathematics and physics challenge questions, each of which gets you thinking in a new and fascinating way."---Jonathan Shock, Mathemafrica"Reading Nahin is like reading through a select library of ancient Babylonian mathematical clay tablets. Surprises abound. . . . Nahin weaves much colorful history into his narrative."---Andrew Simoson, Mathematical Intelligencer"Engaging. . . . The book contains a wealth of original problems. . . . An enjoyable read."---Antonín Slavík, Zentralblatt MATH"This reviewer found himself being drawn to a variety of unfamiliar settings with much interest and even fascination." * Choice *"I certainly enjoyed [the book]!"---Alan Stevens, Mathematics Today"The potential audience for this book should be fairly large and go from highly talented high school students up through professionals in any STEM field."---Geoffrey Dietz, MAA Reviews
£15.29
Princeton University Press Intermittent Convex Integration for the 3D Euler
Book Synopsis
£52.70
Princeton University Press Intermittent Convex Integration for the 3D Euler
Book Synopsis
£110.40
Birkhauser Boston Inc Complex Numbers from A to ... Z
a huge range and FREE tracked UK delivery on ALL orders.
£46.74
MP-AMM American Mathematical Groups and Geometric Analysis Integral Geometry
Book SynopsisGroup-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group.Trade ReviewFrom reviews of the original edition:""The book is excellent both as a text and as a reference work; it will clearly become another instant classic."" —American Scientist""This volume makes an excellent companion to the author's Differential Geometry, Lie Groups, and Symmetric Spaces, putting to work many of the abstract concepts developed in the earlier volume. The introductory material and large number of exercises (with answers!) will make the book quite appropriate for students. Researchers will find numerous useful references on geometric analysis, along with proofs, connections with other parts of mathematics, and valuable historical remarks. This book, like the author's previous work on differential geometry, will no doubt inspire considerable further research and become the standard text on the subjects it covers."" —Mathematical Reviews""Few treatises today can lay claim to being ""aere perennius"", but all of Helgason's books certainly do with a vengeance ... [He] sets a model of style and clarity that has not been matched since Enriques's Geometria proiettiva. This is the kind of mathematics that will live forever."" —The Bulletin of Mathematics Books""A most valuable contribution to Lie theory and to the interplay between geometry and analysis. It is remarkable that the beautiful theory in Chapter IV can be presented in a textbook form with complete proofs."" —Bulletin of the London Mathematical Society""The diversity of subjects treated is great. Nevertheless the author has managed to achieve coherence of presentation by clearly putting forward a few main themes and basic problems. The first third of the book is suitable as a text for beginning graduate students; the book is also an excellent source of reference for experts. No doubt it will become a new standard in the field."" —CWI QuarterlyTable of Contents Geometric Fourier analysis on spaces of constant curvature Integral geometry and Radon transforms Invariant differential operators Invariants and harmonic polynomials Spherical functions and spherical transforms Analysis on compact symmetric spaces Appendix Some details Bibliography Symbols frequently used Index Errata
£101.70
MP-CTM National Council of T Developing Essential Understanding of Geometry
Book SynopsisFocuses on essential knowledge for teachers about geometry. It is organized around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers.
£999.99
John Wiley & Sons Inc Introduction to Topology and Geometry
Book SynopsisAn easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition . . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained. CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible,Table of ContentsPreface ix Acknowledgments xiii 1 Informal Topology 1 2 Graphs 13 2.1 Nodes and Arcs 13 2.2 Traversability 16 2.3 Colorings 21 2.4 Planarity 25 2.5 Graph Homeomorphisms 31 3 Surfaces 41 3.1 Polygonal Presentations 42 3.2 Closed Surfaces 50 3.3 Operations on Surfaces 71 3.4 Bordered Surfaces 79 3.5 Riemann Surfaces 94 4 Graphs and Surfaces 103 4.1 Embeddings and Their Regions 103 4.2 Polygonal Embeddings 113 4.3 Embedding a Fixed Graph 118 4.4 Voltage Graphs and Their Coverings 128 Appendix: 141 5 Knots and Links 143 5.1 Preliminaries 144 5.2 Labelings 147 5.3 From Graphs to Links and on to Surfaces 158 5.4 The Jones Polynomial 169 5.5 The Jones Polynomial and Alternating Diagrams 187 5.6 Knots and surfaces 194 6 The Differential Geometry of Surfaces 205 6.1 Surfaces, Normals, and Tangent Planes 205 6.2 The Gaussian Curvature 212 6.3 The First Fundamental Form 219 6.4 Normal Curvatures 229 6.5 The Geodesic Polar Parametrization 236 6.6 Polyhedral Surfaces I 242 6.7 Gauss’s Total Curvature Theorem 247 6.8 Polyhedral Surfaces II 252 7 Riemann Geometries 259 8 Hyperbolic Geometry 275 8.1 Neutral Geometry 275 8.2 The Upper Half Plane 287 8.3 The HalfPlane Theorem of Pythagoras 295 8.4 HalfPlane Isometries 305 9 The Fundamental Group 317 9.1 Definitions and the Punctured Plane 317 9.2 Surfaces 325 9.3 3Manifolds 332 9.4 The Poincar´e Conjecture 357 10 General Topology 361 10.1 Metric and Topological Spaces 361 10.2 Continuity and Homeomorphisms 367 10.3 Connectedness 377 10.4 Compactness 379 11 Polytopes 387 11.1 Introduction to Polytopes 387 11.2 Graphs of Polytopes 401 11.3 Regular Polytopes 405 11.4 Enumerating Faces 415 Appendix A Curves 429 A.1 Parametrization of Curves and Arclength 429 Appendix B A Brief Survey of Groups 441 B.1 The General Background 441 B.2 Abelian Groups 446 B.3 Group Presentations 447 Appendix C Permutations 457 Appendix D Modular Arithmetic 461 Appendix E Solutions and Hints to Selected Exercises 465 References and Resources 497
£99.86
John Wiley & Sons Inc Geometry 1001 Practice Problems For Dummies Free
Book SynopsisTable of ContentsIntroduction 1 Part 1: The Questions 3 Chapter 1: Diving into Geometry 5 Chapter 2: Constructions 13 Chapter 3: Geometric Proofs with Triangles 17 Chapter 4: Classifying Triangles 31 Chapter 5: Investigating the Centers of a Triangle 41 Chapter 6: Similar Triangles 49 Chapter 7: The Right Triangle 59 Chapter 8: Triangle Inequalities 67 Chapter 9: Polygons 75 Chapter 10: Properties of Parallel Lines 81 Chapter 11: Properties of Quadrilaterals 89 Chapter 12: Coordinate Geometry 97 Chapter 13: Transformational Geometry 105 Chapter 14: Exploring Circles 121 Chapter 15: Circle Theorems 127 Chapter 16: Three-Dimensional Geometry 141 Chapter 17: Locus Problems 149 Part 2: The Answers 155 Chapter 18: Answers and Explanations 157 Index 439
£18.69
Springer-Verlag New York Inc. Mathematics and Its History
Book SynopsisThe Theorem of Pythagoras.- Greek Geometry.- Greek Number Theory.- Infinity in Greek Mathematics.- Number Theory in Asia.- Polynomial Equations.- Analytic Geometry.- Projective Geometry.- Calculus.- Infinite Series.- The Number Theory Revival.- Elliptic Functions.- Mechanics.- Complex Numbers in Algebra.- Complex Numbers and Curves.- Complex Numbers and Functions.- Differential Geometry.- Non-Euclidean Geometry.- Group Theory.- Hypercomplex Numbers.- Algebraic Number Theory.- Topology.- Simple Groups.- Sets, Logic, and Computation.- Combinatorics.Trade Review“Mathematics and Its History is an original, engaging and effective book, which I think would be enjoyed by students, lay readers with the right background, or indeed mathematicians themselves.” (Danny Yee, Danny Yee's Book Reviews, dannyreviews.com, March, 2019)From the reviews of the third edition:"The author’s goal for Mathematics and its History is to provide a “bird’s-eye view of undergraduate mathematics.” (p. vii) In that regard it succeeds admirably. ... Mathematics and its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. ... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics. ... While Stillwell does a wonderful job of tying together seemingly unrelated areas of mathematics, it is possible to read each chapter independently. I would recommend this fine book for anyone who has an interest in the history of mathematics. For those who teach mathematics, it provides lots of information which could easily be used to enrich an opening lecture in most any undergraduate course. It would be an ideal gift for a department’s outstanding major or for the math club president. Pick it up at your peril — it is hard to put down!"(Richard Wilders, MAA Reviews)“I appreciate and recommend Stillwell’s presentation of mathematics and history written in a lively style. The author’s concept (history mostly as the means of approaching mathematics) remains a matter of interest for both the mathematician and the historian … .” (Rüdiger Thiele, Zentralblatt MATH, Vol. 1207, 2011)From the reviews of the second edition:"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."(David Parrott, Australian Mathematical Society)"The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." (European Mathematical Society)"Since Stillwell treats many topics, most mathematicians will learn a lot from this book as well as they will find pleasant and rather clear expositions of custom materials. The book is accessible to students that have already experienced calculus, algebra and geometry and will give them a good account of how the different branches of mathematics interact."(Denis Bonheure, Bulletin of the Belgian Society)Table of ContentsPreface to the Third Edition.- Preface to the Second Edition.- Preface to the First Edition.- The Theorem of Pythagoras.- Greek Geometry.- Greek Number Theory.- Infinity in Greek Mathematics.- Number Theory in Asia.- Polynomial Equations.- Analytic Geometry.- Projective Geometry.- Calculus.- Infinite Series.- The Number Theory Revival.- Elliptic Functions.- Mechanics.- Complex Numbers in Algebra.- Complex Numbers and Curves.- Complex Numbers and Functions.- Differential Geometry.- Non-Euclidean Geometry.- Group Theory.- Hypercomplex Numbers.- Algebraic Number Theory.- Topology.- Simple Groups.- Sets, Logic, and Computation.- Combinatorics.- Bibliography.- Index.-
£47.49
MP-AMM American Mathematical Polynomial Methods in Combinatorics
Book SynopsisExplains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields. The author also discusses in detail various problems in incidence geometry associated to Paul Erdos's distinct distances problem in the plane from the 1940s.Trade ReviewSome of the greatest advances in geometric combinatorics and harmonic analysis in recent years have been accomplished using the polynomial method. Larry Guth gives a readable and timely exposition of this important topic, which is destined to influence a variety of critical developments in combinatorics, harmonic analysis and other areas for many years to come." - Alex Iosevich, University of Rochester, author of The Erdos Distance Problem and A View from the Top"It is extremely challenging to present a current (and still very active) research area in a manner that a good mathematics undergraduate would be able to grasp after a reasonable effort, but the author is quite successful in this task, and this would be a book of value to both undergraduates and graduates." - Terence Tao, University of California, Los Angeles, author of An Epsilon of Room I, II and Hilbert's Fifth Problem and Related Topics"In the 273 page long book, a huge number of concepts are presented, and many results concerning them are formulated and proved. The book is a perfect presentation of the theme." - Béla Uhrin, Mathematical Reviews "One of the strengths that combinatorial problems have is that they are understandable to non-experts in the field...One of the strengths that polynomials have is that they are well understood by mathematicians in general. Larry Guth manages to exploit both of those strengths in this book and provide an accessible and enlightening drive through a selection of combinatorial problems for which polynomials have been used to great effect." - Simeon Ball, Jahresbericht der Deutschen Mathematiker-VereinigungTable of Contents Introduction Fundamental examples of the polynomial method Why polynomials? The polynomial method in error-correcting codes On polynomials and linear algebra in combinatorics The Bezout theorem Incidence geometry Incidence geometry in three dimensions Partial symmetries Polynomial partitioning Combinatorial structure, algebraic structure, and geometric structure An incidence bound for lines in three dimensions Ruled surfaces and projection theory The polynomial method in differential geometry Harmonic analysis and the Kakeya problem The polynomial method in number theory Bibliography
£54.90
MP-AMM American Mathematical Algebraic Geometry over Cinfty Rings
Book SynopsisExplains the foundations of a version of algebraic geometry in which rings or algebras are replaced by $C^\infty $-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are $C^\infty $-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps.Table of Contents Introduction $C^\infty$-rings The $C^\infty$-ring $C^\infty (X)$ of a manifold $X$ $C^\infty $-ringed spaces and $C^\infty $-schemes Modules over $C^\infty$-rings and $C^\infty $-schemes $C^\infty $-stacks Deligne-Mumford $C^\infty $-stacks Sheaves on Deligne-Mumford $C^\infty $-stacks Orbifold strata of $C^\infty $-stacks Appendix A. Background material on stacks Bibliography Glossary of Notation Index.
£64.80
MP-AMM American Mathematical Probabilistic Methods in Geometry Topology and
Book SynopsisContains the proceedings of the CRM Workshops on Probabilistic Methods in Spectral Geometry and PDE, held in 2016 at the Centre de Recherches Mathematiques. This volume covers developments in active research areas at the interface of Probability, Semiclassical Analysis, Mathematical Physics, Theory of Automorphic Forms and Graph Theory.Table of Contents L. Chen and N. Shu, A geometric treatment of log-correlated Gaussian free fields S. Eswarathasan, Tangent nodal sets for random spherical harmonics J. Friedman, Formal zeta function expansions and the frequency of Ramanujan graphs D. Jakobson, T. Langsetmo, I. Rivin, and L. Turner, Rank and Bollobas-Riordan polynomials: Coefficient measures and zeros V. Konakov, S. Menozzi, and S. Molchanov, The Brownian motion on $\mathrm{Aff}(\mathbb{R})$ and quasi-local theorems N. Laaksonen, Quantum limits of Eisenstein series in $\mathbb{H}^3$ F. Macia and G. Riviere, Observability amd quantum limits for the Schrodinger equation on $\mathbb{S}^d$ M. Rossi, Random nodal lengths and Wiener chaos L. Silberman and A. Venkatesh, Entropy bounds and quantum unique ergodity for Hecke eigenfunctions on division algebras.
£103.50
MP-AMM American Mathematical Topology and Geometry of Biopolymers
Book SynopsisContains the proceedings of the AMS Special Session on Topology of Biopolymers, held April 2018, at Northeastern University. The papers cover recent results on the topology and geometry of DNA and protein knotting using techniques from knot theory, spatial graph theory, differential geometry, molecular simulations, and laboratory experimentation.Table of Contents The topology and geometry of DNA: J. M. Fogg and L. Zechiedrich, Beyond the static DNA model of Watson and Crick P. Liu, R. Polischuk, Y. Diao, and J. Arsuaga, Characterizing the topology of kinetoplast DNA using random knotting A. Kasman and B. LeMesurier, Did sequence dependent geometry influence the evolution of the genetic code? T. Deguchi and E. Uehara, Topological sum rules in the knotting probabilities of DNA D. Buck and D. O'Donnol, Knotting of replication intermediates is narrowly restricted A. H. Moore and M. Vazquez, Recent advances on the non-coherent band surgery model for site-specific recombination The topology and geometry of proteins: S. E. Jackson, Why are there knots in proteins? A. Nunes and P. F. N. Faisca, Knotted proteins: Tie etiquette in structural biology D. Goundaroulis, J. Dorier, and A. Stasiak, Knotoids and protein structure K. C. Millett, Topological linking and entanglement in proteins E. Panagiotou and K. W. Plaxco, A topological study of protein folding kinetics.
£96.30
MP-AMM American Mathematical Integrability Quantization and Geometry The Set
Book SynopsisOffers a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher.Table of Contents Part I. Integrable Systems: K. Aleshkin and K. Saito, Primitive forms without higher residue structure and integrable hierarchies (I) M. Alkadhem, G. Antoniou, and M, Feigin, Solutions of $BC_n$ type of WDVV equations P. P. Boalch, Topology of the Stokes phenomenon G. Cotti and A. Varchenko, Equivariant quantum differential equation and qKZ equations for a projective space: Stokes bases as exceptional collections, Stokes matrices as Gram matrices, and $\mathcyr{B}$-theorem L. David and C. Hertling, Meromorphic connections over F-manifolds G. Jorjadze and S. Theisen, Canonical maps and integrability in $T\bar{T}$ deformed 2d CFTs I. Krichever and A. Varchenko, Incarnations of XXX $\widehat{\mathfrak{sl}_N}$ Bethe ansatz equations and integrable hierarchies F. Magri, The Kowalewski separability conditions O. Mokhov and N. A. Strizhova, On the Liouville integrable reduction of the associativity equations in the case of three primary fields S. M. Natanzon and A. Yu. Orlov, Hurwitz numbers from matrix integrals over Guassian measure N. Reshetikhin, Spin Calogero-Moser models on symmetric spaces M. Semenov-Tian-Shansky, Quantum toda lattice: A challenge for representation theory A. O. Smirnov, M. V. Pavlov, V. B. Matveev, and V. S. Gerdjikov, Finite-gap solutions of the Mikhalev equation I. A. B. Strachan, Flat coordinates on orbit spaces: From Novikov algebras to cyclic quotient singularities K. Takasaki, Cubic Hodge integrals and integrable hierarchies of Volterra type G. Tian and G. Xu, Gauged Witten equation and adiabatic limit Part II. Quantum Theories and Algebraic Geometry: T. Bridgeland, Geometry from Donaldson-Thomas invariants V. M. Buchstaber and A. P. Veselov, Fricke identities, Frobenius $K$-characters and Markov equation I. Cherednik, On Harish-Chandra theory of global nonsymmetric functions N. C. Combe and Y. I. Manin, Symmetries of genus zero modular operad R. Coquereaux and J.-B. Zuber, On Schur problem and Kostka numbers P. Etingof, E. Frenkel, and D. Kazhdan, An analytic version of the Langlands correspondence for complex curves D. Gaiotto, T. Johnson-Freyd, and E. Witten, A note on some minimally supersymmetric models in two dimensions O. Garcia-Prada and D. Salamon, A moment map interpretation of the Ricci form, Kahler-Einstein structures, and Teichmuller spaces E. Getzler and S. W. Pohorence, Global gauge conditions in the Batalin-Vilkovisky formalism V. Golyshev and D. Zagier, Interpolated Apery numbers, quasiperiods of modular forms, and motivic gamma functions Y.-P. Lee, H.-W. Lin, and C.-L. Wang, Quantum flips I: Local model M. Marcolli, Aspects of $p$-adic geometry related to entanglement entropy S. Merkulov, Grothendieck-Teichmuller group, operads and graph complexes: A survey O. Ogievetsky and S. Shlosman, Platonic compounds of cylinders.
£195.30
MP-AMM American Mathematical Integrability Quantization and Geometry I.
Book SynopsisOffers a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher.Table of Contents K. Aleshkin and K. Saito, Primitive forms without higher residue structure and integrable hierarchies (I) M. Alkadhem, G. Antoniou, and M, Feigin, Solutions of $BC_n$ type of WDVV equations P. P. Boalch, Topology of the Stokes phenomenon G. Cotti and A. Varchenko, Equivariant quantum differential equation and qKZ equations for a projective space: Stokes bases as exceptional collections, Stokes matrices as Gram matrices, and $\mathcyr{B}$-theorem L. David and C. Hertling, Meromorphic connections over F-manifolds G. Jorjadze and S. Theisen, Canonical maps and integrability in $T\bar{T}$ deformed 2d CFTs I. Krichever and A. Varchenko, Incarnations of XXX $\widehat{\mathfrak{sl}_N}$ Bethe ansatz equations and integrable hierarchies F. Magri, The Kowalewski separability conditions O. Mokhov and N. A. Strizhova, On the Liouville integrable reduction of the associativity equations in the case of three primary fields S. M. Natanzon and A. Yu. Orlov, Hurwitz numbers from matrix integrals over Guassian measure N. Reshetikhin, Spin Calogero-Moser models on symmetric spaces M. Semenov-Tian-Shansky, Quantum toda lattice: A challenge for representation theory A. O. Smirnov, M. V. Pavlov, V. B. Matveev, and V. S. Gerdjikov, Finite-gap solutions of the Mikhalev equation I. A. B. Strachan, Flat coordinates on orbit spaces: From Novikov algebras to cyclic quotient singularities K. Takasaki, Cubic Hodge integrals and integrable hierarchies of Volterra type G. Tian and G. Xu, Gauged Witten equation and adiabatic limit.
£108.00
MP-AMM American Mathematical Integrability Quantization and Geometry II.
Book SynopsisOffers a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher.Table of Contents T. Bridgeland, Geometry from Donaldson-Thomas invariants V. M. Buchstaber and A. P. Veselov, Fricke identities, Frobenius $K$-characters and Markov equation I. Cherednik, On Harish-Chandra theory of global nonsymmetric functions N. C. Combe and Y. I. Manin, Symmetries of genus zero modular operad R. Coquereaux and J.-B. Zuber, On Schur problem and Kostka numbers P. Etingof, E. Frenkel, and D. Kazhdan, An analytic version of the Langlands correspondence for complex curves D. Gaiotto, T. Johnson-Freyd, and E. Witten, A note on some minimally supersymmetric models in two dimensions O. Garcia-Prada and D. Salamon, A moment map interpretation of the Ricci form, Kahler-Einstein structures, and Teichmuller spaces E. Getzler and S. W. Pohorence, Global gauge conditions in the Batalin-Vilkovisky formalism V. Golyshev and D. Zagier, Interpolated Apery numbers, quasiperiods of modular forms, and motivic gamma functions Y.-P. Lee, H.-W. Lin, and C.-L. Wang, Quantum flips I: Local model M. Marcolli, Aspects of $p$-adic geometry related to entanglement entropy S. Merkulov, Grothendieck-Teichmuller group, operads and graph complexes: A survey O. Ogievetsky and S. Shlosman, Platonic compounds of cylinders.
£108.00
MP-AMM American Mathematical Algebra and Geometry
Book SynopsisThe second of three volumes that, together, give an exposition of the mathematics of grades 9-12 that is simultaneously mathematically correct and grade-level appropriate. The volumes are consistent with CCSSM (Common Core State Standards for Mathematics) and aim at presenting the mathematics of K-12 as a totally transparent subject.Table of Contents Linear functions. Quadratic functions and equations. Polynomial and rational functions. Exponential and logarithmic functions. Polynomial forms and complex numbers. Basic theorems of plane geometry. Ruler and compass constructions. Axiomatic systems. Facts from [Wu2020a]. Glossary of symbols. Bibliography. Index.
£39.56
American Mathematical Society Cyclic Cohomology at 40
Book SynopsisPresents survey articles providing a user-friendly introduction to applications of cyclic cohomology in such areas as higher categorical algebra, Hopf algebra symmetries, de Rham-Witt complex, quantum physics, etc, in which cyclic homology plays the role of a unifying theme.Table of Contents A. Baldare, M. Benameur, and V. Nistor, Chern-Connes-Karoubi character isomorphisms and algebras of symbols of pseudodifferential operators J. Block, N. Higson, and J. Sanchez Jr., On Perrot's index cocycles P. Carrillo Rouse, The Chern-Baum Connes assembly map for Lie groupoids A. Connes and C. Consani, Hochschild homology, trace map and $\zeta$-cycles A. Connes and C. Consani, Cyclic theory and the pericyclic category J. Cuntz, The image of Bott peridocity in cyclic homology B. I. Dundas, Applications of topological cyclic homology to algebraic $K$-theory D. Gepner, Algebraic $K$-theory and generalized stable homotopy theory A. Gorokhovsky and E. van Erp, Cyclic cohomology and the extended Heisenberg calculus of Epstein and Melrose L. Hesselholt, Topological cyclic homology and the Fargues-Fontaine curve M. Khalkhali and I. Shapiro, Hopf cyclic cohomology and beyond M. Lorentz, The Hochschild cohomology of uniform Roe algebras E. McDonald, F. Sukochev, and X. Xiong, Quantum differntiability-The analytical perspective R. Meyer and D. Mukherjee, Local cyclic homology for nonarchimedean Banach algebras H. Moscovici, On the van Est analogy in Hopf cyclic cohomology P. Piazza and X. Tang, Primary and secondary invariants of Dirac operators on $G$-proper manifolds M. J. Pflaum, Localization in Hochschild homology R. Ponge, Cyclic homology and group actions E. Prodan, Cyclic cocycles and quantized pairings in materials science M. Puschnigg, Periodic cyclic homology of crossed products A. Savin and E. Schrohe, Trace expansions and equivariant traces on an algebra of Fourier integral operators on $\mathbb{R}^n$ Y. Song and X. Tang, Carton motion group and orbital integrals B. Tsygan, On noncommutative crystalline cohomology T. D. H. Van Nuland and W. D. van Suijlekom, Cyclic cocycles and one-loop corrections in the spectral action J. Wang, Z. Xie, and G. Yu, $\ell^1$-higher index, $\ell^1$-higher rho invariant and cyclic cohomology.
£109.80
American Mathematical Society Teaching and Learning with Primary Source
Book SynopsisA collection of 24 classroom modules (PSPs) produced by TRIUMPHS that incorporate the reading of primary source excerpts to teach core mathematical topics. The selected excerpts are intertwined with thoughtfully designed student tasks that prompt students to actively engage with and explore the source material.Trade ReviewPrimary sources provide motivation in the words of the original discoverers of new mathematics, draw attention to subtleties, encourage reflection on today's paradigms, and enhance students' ability to participate equally, regardless of their background. These beautifully written primary source projects that adopt an ``inquiry'' approach are rich in features lacking in modern textbooks. Prompted by the study of historical sources, students will grapple with uncertainties, ask questions, interpret, conjecture, and compare multiple perspectives, resulting in a unique and vivid guided learning experience. -- David Pengelley, Oregon State UniversityTable of ContentsJ. H. Barnett, D. K. Ruch, and N. A. Scoville, Contents; Introduction: J. H. Barnett, D. K. Ruch, and N. A. Scoville, Teaching and Learning with Primary Source Projects; J. H. Barnett, D. K. Ruch, and N. A. Scoville, PSP Summaries: The Collection at a Glance; J. H. Barnett, Historical Overview; Real Analysis: J. H. Barnett, Why Be So Critical? Nineteenth-Century Mathematics and the Origins of Analysis; D. Ruch, Investigations into Bolzano's Bounded Set Theorem; M. P. Saclolo, Stitching Dedekind Cuts to Construct the Real Numbers; D. Ruch, Investigations into d'Alembert's Definition of Limit; D. Ruch, Bolzano on Continuity and the Intermediate Value Theorem; N. Somasunderam, Understanding Compactness: Early Work, Uniform Continuity to the Heine-Borel Theorem; D. Ruch, An Introduction to a Rigorous Definition of Derivative; J. H. Barnett, Rigorous Debates over Debatable Rigor: Monster Functions in Introductory Analysis; D. Ruch, The Mean Value Theorem; D. Ruch, Euler's Rediscovery of $e$; D. Ruch, Abel and Cauchy on a Rigorous Approach to Infinite Series; D. Ruch, The Definite Integrals of Cauchy and Riemann; J. H. Barnett, Henri Lebesgue and the Development of the Integral Concept; Topology: N. A. Scoville, The Cantor Set before Cantor; N. A. Scoville, Topology from Analysis; N. A. Scoville, Nearness without Distance; N. A. Scoville, Connectedness: Its Evolution and Applications; N. A. Scoville, Connecting Connectedness; N. A. Scoville, From Sets to Metric Spaces to Topological Spaces; N. A. Scoville, The Closure Operation as the Foundation of Topology; N. A. Scoville, A Compact Introduction to a Generalized Extreme Value Theorem; Complex Variables: D. Klyve, The Logarithm of $-1$; D. Ruch, Riemann's Development of the Cauchy-Riemann Equations; D. Ruch, Gauss and Cauchy on Complex Integration.
£51.30
American Mathematical Society Inverse Problems in Memory of Professor Zbigniew Oziewicz
£104.40
American Mathematical Society Amenability of Discrete Groups by Examples
Book SynopsisPuts together main approaches to study amenability. A novel feature of the book is that the exposition of the material starts with examples which introduce a method rather than illustrating it. This allows the reader to quickly move on to meaningful material without learning and remembering a lot of additional definitions and preparatory results.
£98.10
American Mathematical Society Cocycles de groupe pour mathrm GLn et
Book SynopsisCe livre constitue un expose detaille de la serie de cours donnes en 2020 par le Prof. Nicolas Bergeron, titulaire de la Chaire Aisenstadt au CRM de Montreal. L'objet de ce texte est une ample generalisation d'une famille d'identites classiques, notamment la formule d'addition de la fonction cotangente ou celle des series d'Eisenstein.Trade ReviewI think that the text ``Cocycles de groupe pour $\mathrm{GL}_n$ et arrangements d'hyperplans'' is terrific. I like how it begins in a leisurely, enticing way with an elementary example that neatly gets to the topic. The construction of these ``meromorphic function''-valued modular symbols are fundamental objects, and play (and will continue to) play an important role. -- Barry Mazur, Harvard UniversityTable of ContentsConstruction de cocycles : aspects topologiques; Enonces des principaux resultats : cocycles explicites; Cohomologie d'arrangements d'hyerplans : representants canoniques; Formes differentielles sur l'espace symetrique associe a $textrm{SL}_n(C)$; Compactifications de Satake, de Tits et symboles modulaires; Cocycles de $\textrm{GL}_n(C)$ explicites; Series d'Eisenstein associees a $\psi$; Cocycle multicatif du groupe rationnel $\textrm{GL}_n(Q)^+$; Cocycle elliptique du groupe rationnel $\textrm{GL}_n(Q)^+$; Annexe A. Cohomologie equivariante et complexe de de Rham simplicial; Annexe B. Classe d'Eisenstein affine et theorie de l'obstruction; Bibliographie.
£102.60
