Topology Books
American Mathematical Society Geometry Revisited
Book SynopsisAmong the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations.
£51.30
MP-AMM American Mathematical Computational Topology An Introduction
Book SynopsisTrade Review“This book is a very welcome, untraditional, thorough and well-organized introduction to a young and quickly developing discipline on the crossroads between mathematics, computer science, and engineering.” —DMV NewsletterTable of Contents Computational geometric topology: Graphs Surfaces Complexes Computational algebraic topology: Homology Duality Morse functions Computational persistent topology: Persistence Stability Applications References Index
£59.40
MP-AMM American Mathematical SYZ Geometry for CalabiYau 3folds TaubNUT and
Book Synopsis
£68.40
MP-AMM American Mathematical Eulerian Spaces
Book Synopsis
£67.50
MP-AMM American Mathematical The Wild World of 4Manifolds
Book SynopsisOffers a panorama of the topology of simply connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but small enough so that there is no room to undo the wildness.Trade ReviewThe book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it. -- Robion C. Kirby, University of California, Berkeley What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds."" —MAA Reviews""The author records many spectacular results in the subject ... (the author) gives the reader a taste of the techniques involved in the proofs, geometric topology, gauge theory and complex and symplectic structures. The book has a large and up-to-date collection of references for the reader wishing to get a more detailed or rigorous knowledge of a specific topic. The exposition is user-friendly, with a large number of illustrations and examples."" —Mathematical ReviewsTable of Contents Introduction Front matter Part I: Background scenery: Introduction Contents of part I Chapter 1: Higher dimensions and the $h$-cobordism theorem Chapter 2: Topological 4-manifolds and $h$-cobordisms Part II: Smooth 4-manifolds and intersection forms: Introduction Contents of part II Chapter 3: Getting acquainted with intersection forms Chapter 4: Intersection forms and topology Chapter 5: Classifications and counterclassifications Part III: A survey of complex surfaces: Introduction Contents of part III Chapter 6: Running through complex geometry Chapter 7: The Enriques-Kodaira classification Chapter 8: Elliptic surfaces Part IV: Gauge theory on 4-manifolds: Introduction Contents of part IV Chapter 9: Prelude, and the Donaldson invariants Chapter 10: The Seiberg-Witten invariants Chapter 11: The minimum genus of embedded surfaces Chapter 12: Wildness unleashed: The Fintushel-Stern surgery Epilogue List of figures and tables Bibliography Index Errata
£74.70
American Mathematical Society Differential Geometry of Plane Curves
Book SynopsisFeatures plane curves to illustrate many deep and inspiring results in the field in an elementary and accessible way. After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number, rotation index, Jordan curve theorem, and isoperimetric inequality.Table of Contents Plane curves Winding number Rotation index Jordan curve theorem Isoperimetric inequality Convex curves The four-vertex theorem Curve-shortening flow Appendix A: The class $\mathcal{C}^\infty$ convergence of the curvature function under the curve-shortening flow Appendix B: Answers to selected exercises Bibliography Index
£46.80
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
MP-AMM American Mathematical Compactifications Configurations and Cohomology
Book SynopsisFocuses on new and existing connections between three types of compactifications, thereby setting the stage for further research. The book draws on the discipline-specific expertise of all contributors, and at the same time gives a unified, self-contained reference for compactifications and related constructions in different contexts.Table of ContentsA. Balibanu, A quasi-Poisson structure on the multiplicative Grothendieck-Springer resolution; P. Brosnan, Volumes of definable sets in o-minimal expansions and affine GAGA theorems; P. Crooks and R. Roser, Hessenberg varieties and Poisson slices; G. Denham and A. Steiner, Geometry of logarithmic derivations of hyperplane arrangements; I. Halacheva, Shift of argument algebras and de Concini-Procesi spaces; B. Knudsen, Projection spaces and twisted Lie algebras; A. I. Suciu, Cohomology, Bocksteins, and resonance varieties in characteristic 2.
£103.50
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 Multidimensional Residue Theory and Applications
Book SynopsisDefines and studies multidimensional residues via analytic continuation for holomorphic bundle-valued current maps. This point of view offers versatility and flexibility to the tools and constructions proposed, allowing these residues to be defined and studied outside the classical case of complete intersection.Table of ContentsResidue calculus in one variable; Residue currents: A multiplicative approach; Residue currents: A bundle approach; Bochner-Martinelli kernels and weights; Integral closure, Briancon-Skoda type theorems; Residue calculus and trace formulae; Miscellaneous applications: Intersection, division; Complex manifolds and analytic spaces; Holomorphic bundles over complex analytic spaces; Positivity on complex analytic spaces; Various concepts in algebraic or analytic geometry; Bibliography; Index.
£101.70
MP-AMM American Mathematical Groups and Topological Dynamics
Book SynopsisFocuses on group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using group theory to study symbolic dynamics, and other connections between group theory and dynamical systems.Table of Contents Dynamical systems Group actions Groupoids Iterated monodromy groups Groups from groupoids Growth and amenability Bibliography Index
£67.50
MP-AMM American Mathematical Geometric Structures on Manifolds
Book SynopsisFocuses on several successful classification problems. Namely, fix a geometry in the sense of Klein and a topological manifold. Then the different ways of locally putting the geometry on the manifold lead to a moduli space'.Table of Contents Part 1. Affine and projective geometry: Affine geometry Projective geometry Duality and non-Euclidean geometry Convexity Part 2. Geometric manifolds: Locally homogeneous geometric structures Examples of geometric structures Classification Completeness Part 3. Affine and projective structures: Affine structures on surfaces and the Euler characteristic Affine Lie groups Parallel volume and completeness Hyperbolicity Projective structures on surfaces Complex-projective structures Geometric structures on 3-manifolds Appendices: Appendix A. Transformation groups Appendix B. Affine connections Appendix C. Representations of nilpotent groups Appendix D. 4-dimensional filiform nilpotent Lie algebras Appendix E. Semicontinuous functions Appendix F. $\mathsf{SL}(2,\mathbb{C})$ and $O(3,1)$ Appendix G. Lagrangian foliations of symplectic manifolds Bibliography Index
£68.40
MP-AMM American Mathematical Spaces of Constant Curvature
Book SynopsisThis book is the sixth edition of the classic Spaces of Constant Curvature, first published in 1967, with the previous (fifth) edition published in 1984. It illustrates the high degree of interplay between group theory and geometry. The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds and their curvatures, of the representation theory of finite groups, and of indications of recent progress in discrete subgroups of Lie groups. Part I is a brief introduction to differentiable manifolds, covering spaces, and riemannian and pseudo-riemannian geometry. It also contains a certain amount of introductory material on symmetry groups and space forms, indicating the direction of the later chapters. Part II is an updated treatment of euclidean space form. Part III is Wolf's classic solution to the Clifford-Klein Spherical Space Form Problem. It starts with an exposition of the representation theory of finite groups. Part IV introduces riemannian symmetric spaces and extends considerations of spherical space forms to space forms of riemannian symmetric spaces. Finally, Part V examines space form problems on pseudo-riemannian symmetric spaces. At the end of Chapter 12 there is a new appendix describing some of the recent work on discrete subgroups of Lie groups with application to space forms of pseudo-riemannian symmetric spaces. Additional references have been added to this sixth edition as well.Table of Contents Riemannian geometry: Affine differential geometry Riemannian curvature The Euclidean space form problem: Flat Riemannian manifolds The spherical space form problem: Representations of finite groups Vincent's work on the spherical space form problem The classification of fixed point free groups The solution to the spherical space form problem Space form problems on symmetric spaces: Riemannian symmetric spaces Space forms of irreducible symmetric spaces Locally symmetric spaces of non-negative curvature Space form problems on indefinite metric manifolds: Spaces of constant curvature Locally isotropic manifolds Appendix to Chapter 12 References Additional references Index
£48.60
MP-AMM American Mathematical Hamiltons Ricci Flow
Book SynopsisRicci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty. The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible. Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions. A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincare conjecture and Thurston's geometrization conjecture.Trade Review“The style of the book is very pleasant, including lots of motivations and background material, course outlines and exercises (with solutions), the bibliography is rather comprehensive. This work is certain to become one of the main references in this field of great current interest.” - M. Kunzinger“This book is a very well written introduction to and resource for study of the Ricci flow. It is quite self-contained, but relevant references are provided at appropriate points. The style of the book renders it accessible to graduate students (suggested course outlines and many relevant further references are provided), while its substance provides an essential resource for background, key concepts and fundamental ideas for further study in the area.” - James McCoy, Mathematical Reviews Table of Contents Riemannian geometry Fundamentals of the Ricci flow equation Closed 3-manifolds with positive Ricci curvature Ricci solitons and special solutions Isoperimetric estimates and no local collapsing Preparation for singularity analysis High-dimensional and noncompact Ricci flow Singularity analysis Ancient solutions Differential Harnack estimates Space-time geometry Appendix A. Geometric analysis related to Ricci flow Appendix B. Analytic techniques for geometric flows Appendix S. Solutions to selected exercises Bibliography Index
£73.80
MP-AMM American Mathematical Ricci Solitons in Low Dimensions
Book SynopsisFocuses on Ricci solitons, shedding light on their role in understanding singularity formation in Ricci flow and formulating surgery-based Ricci flow, which holds potential applications in topology.Table of Contents Ricci flow singularity formation The Ricci soliton equation The $2$-dimensional classification Estimates for shrinking Ricci solitons Classification of $3$-dimensional shrinkers The Bryant soliton Expanding and steady GRS and the flying wing Brendle's theorem on the uniqueness of $3$-dimensional steadies Geometric preliminaries Analytic preliminaries Bibliography Index
£100.80
MP-AMM American Mathematical Discrete Differential Geometry Integrable Structure
Book SynopsisAn emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systems. One of the main goals of this book is to reveal this integrable structure of discrete differential geometry. For a given smooth geometry one can suggest many different discretizations. Which one is the best? This book answers this question by providing fundamental discretization principles and applying them to numerous concrete problems. It turns out that intelligent theoretical discretizations are distinguished also by their good performance in applications. The intended audience of this book is threefold. It is a textbook on discrete differential geometry and integrable systems suitable for a one semester graduate course. On the other hand, it is addressed to specialists in geometry and mathematical physics. It reflects the recent progress in discrete differential geometry and contains many original results. The third group of readers at which this book is targeted is formed by specialists in geometry processing, computer graphics, architectural design, numerical simulations, and animation. They may find here answers to the question ""How do we discretize differential geometry?"" arising in their specific field. Prerequisites for reading this book include standard undergraduate background (calculus and linear algebra). No knowledge of differential geometry is expected, although some familiarity with curves and surfaces can be helpful.Trade Review“This book gives new life to old concepts of classical differential geometry, and a beautiful introduction to new notions of discrete integrable systems. It should be of interest to researchers in several areas of mathematics (integrable systems, differential geometry, numerical approximation of special surfaces), but also to advanced students interested in a good introduction to several classical areas of mathematics. Parts of it could well be used for graduate or possibly advanced undergraduate courses in mathematics.” - Mathematical Reviews“It can serve as a very good introduction into contemporary research and it seems to be the first book devoted to the topic. ... The book is well and clearly written.” - EMS Newsletter Table of Contents Classical differential geometry Discretization principles. Multidimensional nets Discretization principles. Nets in quadrics Special classes of discrete surfaces Approximation Consistency as integrability Discrete complex analysis. Linear theory Discrete complex analysis. Integrable circle patterns Foundations Solutions of selected exercises Bibliography Notations Index
£63.90
American Mathematical Society The Slice Spectral Sequence of a C4Equivariant
Book Synopsis
£67.45
American Mathematical Society Collected Works of William P. Thurston with
Book SynopsisWilliam Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. This four-part collection brings together Thurston's major writings.
£93.60
MP-AMM American Mathematical Collected Works of William P. Thurston with Comm
Book SynopsisWilliam Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. This four-part collection brings together Thurston's major writings.
£93.60
Birkhauser Boston Infinite Dimensional Lie Algebras An Introduction Progress in Mathematics 44
Table of Contents1. Basic definitions.- 2. The invariant bilinear form and the generalized Casimir operator.- 3. Integrable representations and the Weyl group of a Kac-Moody algebra.- 4. Some properties of generalized Cartan matrices.- 5. Real and imaginary roots.- 6. Affine Lie algebras: the normalized invariant bilinear form, the root system and the Weyl group.- 7. Affine Lie algebras: the realization (case k = 1).- 8. Affine Lie algebras: the realization (case k = 2 or 3). Application to the classification of finite order automorphisms.- 9. Highest weight modules over the Lie algebra g(A).- 10. Integrable highest weight modules: the character formula.- 11. Integrable highest weight modules: the weight system, the contravariant Hermitian form and the restriction problem.- 12. Integrable highest weight modules over affine Lie algebras. Application to ?-function identities.- 13. Affine Lie algebras, theta functions and modular forms.- 14. The principal realization of the basic representation. Application to the KdV-type hierarchies of non-linear partial differential equations.- Index of notations and definitions.- References.
£85.49
Taylor & Francis Inc Nonlinear Functional Analysis in Banach Spaces
Book SynopsisUncover the Useful Interactions of Fixed Point Theory with Topological StructuresNonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and Banach algebras. The book provides researchers and graduate students with a unified survey of the fundamental principles of fixed point theory in Banach spaces and algebras. The authors present several extensions of Schauder's and Krasnosel'skii's fixed point theorems to the class of weakly compact operators acting on Banach spaces and algebras, particularly on spaces satisfying the DunfordPettis property. They also address under which conditions a 2×2 block operator matrix with single- and multi-valued nonlinear entries will have a fixed point.Table of ContentsFixed Point Theory: Fundamentals. Fixed Point Theory under Weak Topology. Fixed Point Theory in Banach Algebras. Fixed Point Theory for BOM on Banach Spaces and Banach Algebras. Applications in Mathematical Physics and Biology: Existence of Solutions for Transport Equations. Exsistence of Solutions for Nonlinear Integral Equations. Two-Dimensional Boundary Value Problems.
£147.25
Nova Science Publishers Inc Chaos for Linear Operators and Abstract
Book SynopsisThe theory of linear topological dynamics is a rapidly growing field of research over the last three decades or so. This book presents a survey of recent results of the author obtained in this field during the period 2016-2019. Without any doubt, this is the first research monograph concerning the topological dynamics of multivalued operators and binary relations, especially, multivalued linear woperators, simple graphs, digraphs and tournaments (we feel duty bound to say that multivalued topological dynamics is still a very undeveloped field of investigation, full of open problems and possible for further expansion). Asiede from that, the main purpose of this monograph is to consider topologically dynamical properties of linear single-valued operators in Frechet spaces and abstract fractional differential equations in Frechet spaces, which could be degenerate or non-degenerate in time variable. In this monograph, we use only two types of fractional derivatives, namely the Caputo time-fractional derivatives and Weyl time-fractional derivatives. However, most results on dynamics of differential equations are given to the abstract differential equations with integer order derivatives, especially those of first and second order in time. The monograph is consistsed of two chapters; the first chapter is further broken down into nine sections, while the second chapter is broken down into seven sections. It is not of introductory character to linear topological dynamics and it is not written in a traditional manner. As in all my previously published monographs, the numbering of definitions, theorems, propositions, remarks, lemmas, corollaries, definitions, etc., are by chapter and section; the bibliography is by author in alphabetic order. Concerning target audience, wWe deeply believe that the book could be of invaluable help to experts in linear topological dynamics, researchers in abstract partial differential equations but and also to PhD students and advanced graduate students in mathematics as well. A potential reader should be familiar with backgrounds including elementary functional analysis, measure and integration theory as well as the basic theory of abstract (degenerate) Volterra integro-differential equations. At some places, the knowledge of graph theory is preferable but not demandedable. This monograph is not intended to be a comprehensive review of current trends; albeit includes several recent results from the field of linear topological dynamics and has more than 450 titles, our reference list is far from being exhaustively complete.Table of ContentsPrefaceIntroductionDynamical Properties of Linear Operators and Abstract Differential EquationsDisjoint Dynamical Properties of Linear Operators and Abstract Differential EquationsBibliography.
£163.19
Nova Science Publishers Inc Topological, Projective & Combinatorial
Book SynopsisTopological, Projective & Combinatorial Properties Of Spaces
£123.99
Prometheus Books The Circle: A Mathematical Exploration beyond the
Book SynopsisThe circle has fascinated mathematicians since ancient times. This entertaining book describes in layperson's terms the many intriguing properties of this fundamental shape. If math has intimidated you, this may be the ideal book to help you appreciate the discipline through one of its most important elements. The authors begin with a brief review of the basic properties of the circle and related figures. They then show the many ways in which the circle manifests itself in the field of geometry--leading to some amazing relationships and truly important geometric theorems. In addition, they explore remarkable circle constructions and demonstrate how all constructions in geometry that usually require an unmarked straightedge and a compass can also be done with the compass alone. Among other things, the reader will learn that circles can generate some unusual curves - many even quite artistic. Finally, the role of circles in art and architecture and a discussion of the circle's place on the sphere bring "full circle" this presentation of a key element of geometry.
£18.04
ISTE Ltd and John Wiley & Sons Inc Topology Optimization Design of Heterogeneous
Book SynopsisThis book pursues optimal design from the perspective of mechanical properties and resistance to failure caused by cracks and fatigue. The book abandons the scale separation hypothesis and takes up phase-field modeling, which is at the cutting edge of research and is of high industrial and practical relevance. Part 1 starts by testing the limits of the homogenization-based approach when the size of the representative volume element is non-negligible compared to the structure. The book then introduces a non-local homogenization scheme to take into account the strain gradient effects. Using a phase field method, Part 2 offers three significant contributions concerning optimal placement of the inclusion phases. Respectively, these contributions take into account fractures in quasi-brittle materials, interface cracks and periodic composites. The topology optimization proposed has significantly increased the fracture resistance of the composites studied.Table of ContentsIntroduction ix Part 1. Multiscale Topology Optimization in the Context of Non-separated Scales 1 Chapter 1. Size Effect Analysis in Topology Optimization for Periodic Structures Using the Classical Homogenization 3 1.1. The classical homogenization method 4 1.1.1. Localization problem 4 1.1.2. Definition and computation of the effective material properties 7 1.1.3. Numerical implementation for the local problem with PER 9 1.2. Topology optimization model and procedure 10 1.2.1. Optimization model and sensitivity number 10 1.2.2. Finite element meshes and relocalization scheme 12 1.2.3. Optimization procedure 14 1.3. Numerical examples 16 1.3.1. Doubly clamped elastic domain 17 1.3.2. L-shaped structure 19 1.3.3. MBB beam 24 1.4. Concluding remarks 25 Chapter 2. Multiscale Topology Optimization of Periodic Structures Taking into Account Strain Gradient 29 2.1. Non-local filter-based homogenization for non-separated scales 30 2.1.1. Definition of local and mesoscopic fields through the filter 30 2.1.2. Microscopic unit cell calculations 33 2.1.3. Mesoscopic structure calculations 39 2.2. Topology optimization procedure 41 2.2.1. Model definition and sensitivity numbers 41 2.2.2. Overall optimization procedure 42 2.3. Validation of the non-local homogenization approach 43 2.4. Numerical examples 45 2.4.1. Cantilever beam with a concentrated load 46 2.4.2. Four-point bending lattice structure 52 2.5. Concluding remarks 55 Chapter 3. Topology Optimization of Meso-structures with Fixed Periodic Microstructures 57 3.1. Optimization model and procedure 58 3.2. Numerical examples 61 3.2.1. A double-clamped beam 61 3.2.2. A cantilever beam 64 3.3. Concluding remarks 66 Part 2. Topology Optimization for Maximizing the Fracture Resistance 67 Chapter 4. Topology Optimization for Optimal Fracture Resistance of Quasi-brittle Composites 69 4.1. Phase field modeling of crack propagation 71 4.1.1. Phase field approximation of cracks 71 4.1.2. Thermodynamics of the phase field crack evolution 72 4.1.3. Weak forms of displacement and phase field problems 75 4.1.4. Finite element discretization 76 4.2. Topology optimization model for fracture resistance 78 4.2.1. Model definitions 78 4.2.2. Sensitivity analysis 80 4.2.3. Extended BESO method 85 4.3. Numerical examples 87 4.3.1. Design of a 2D reinforced plate with one pre-existing crack notch 88 4.3.2. Design of a 2D reinforced plate with two pre-existing crack notches 93 4.3.3. Design of a 2D reinforced plate with multiple pre-existing cracks 96 4.3.4. Design of a 3D reinforced plate with a single pre-existing crack notch surface 98 4.4. Concluding remarks 101 Chapter 5. Topology Optimization for Optimal Fracture Resistance Taking into Account Interfacial Damage 103 5.1. Phase field modeling of bulk crack and cohesive interfaces 104 5.1.1. Regularized representation of a discontinuous field 104 5.1.2. Energy functional 106 5.1.3. Displacement and phase field problems 108 5.1.4. Finite element discretization and numerical implementation 111 5.2. Topology optimization method 114 5.2.1. Model definitions 114 5.2.2. Sensitivity analysis 116 5.3. Numerical examples 119 5.3.1. Design of a plate with one initial crack under traction 120 5.3.2. Design of a plate without initial cracks for traction loads 123 5.3.3. Design of a square plate without initial cracks in tensile loading 125 5.3.4. Design of a plate with a single initial crack under three-point bending 128 5.3.5. Design of a plate containing multiple inclusions 130 5.4. Concluding remarks 133 Chapter 6. Topology Optimization for Maximizing the Fracture Resistance of Periodic Composites 135 6.1. Topology optimization model 136 6.2. Numerical examples 138 6.2.1. Design of a periodic composite under three-point bending 138 6.2.2. Design of a periodic composite under non-symmetric three-point bending 146 6.3. Concluding remarks 151 Conclusion 153 References 157 Index 173
£125.06
Imperial College Press Introduction To Differential Manifolds, An
Book SynopsisThis invaluable book, based on the many years of teaching experience of both authors, introduces the reader to the basic ideas in differential topology. Among the topics covered are smooth manifolds and maps, the structure of the tangent bundle and its associates, the calculation of real cohomology groups using differential forms (de Rham theory), and applications such as the Poincaré-Hopf theorem relating the Euler number of a manifold and the index of a vector field. Each chapter contains exercises of varying difficulty for which solutions are provided. Special features include examples drawn from geometric manifolds in dimension 3 and Brieskorn varieties in dimensions 5 and 7, as well as detailed calculations for the cohomology groups of spheres and tori.Trade Review"This book is an excellent introductory text into the theory of differential manifolds with a carefully thought out and tested structure and a sufficient supply of exercises and their solutions. It does not only guide the reader gently into the depths of the theory of differential manifolds but also careful on giving advice how one can place the information in the right context. It is certainly written in the best traditions of great Cambridge mathematics." Acta Scientiarum MathematicarumTable of ContentsDifferential Manifolds and Differentiable Maps; The Derivatives of Differentiable Maps; Fibre Bundles; Differential Forms and Integration; The Exterior Derivative; de Rham Cohomology; Degrees, Indices and Related Topics; Lie Groups; A Rapid Course in Differential Analysis; Solutions to the Exercises; Guide to the Literature.
£57.95
Imperial College Press Introduction To Differential Manifolds, An
Book SynopsisThis invaluable book, based on the many years of teaching experience of both authors, introduces the reader to the basic ideas in differential topology. Among the topics covered are smooth manifolds and maps, the structure of the tangent bundle and its associates, the calculation of real cohomology groups using differential forms (de Rham theory), and applications such as the Poincaré-Hopf theorem relating the Euler number of a manifold and the index of a vector field. Each chapter contains exercises of varying difficulty for which solutions are provided. Special features include examples drawn from geometric manifolds in dimension 3 and Brieskorn varieties in dimensions 5 and 7, as well as detailed calculations for the cohomology groups of spheres and tori.Trade Review"This book is an excellent introductory text into the theory of differential manifolds with a carefully thought out and tested structure and a sufficient supply of exercises and their solutions. It does not only guide the reader gently into the depths of the theory of differential manifolds but also careful on giving advice how one can place the information in the right context. It is certainly written in the best traditions of great Cambridge mathematics." Acta Scientiarum MathematicarumTable of ContentsDifferential Manifolds and Differentiable Maps; The Derivatives of Differentiable Maps; Fibre Bundles; Differential Forms and Integration; The Exterior Derivative; de Rham Cohomology; Degrees, Indices and Related Topics; Lie Groups; A Rapid Course in Differential Analysis; Solutions to the Exercises; Guide to the Literature.
£35.15
New Academic Science Ltd Metric Spaces and Complex Analysis
Book Synopsis
£28.50
Bento Books, Inc. Math Girls 6: The Poincaré Conjecture
Book Synopsis
£21.80
Mathematical Association of America Geometry Illuminated: An Illustrated Introduction
Book SynopsisAn introduction to geometry in the plane, both Euclidean and hyperbolic, this book is designed for an undergraduate course in geometry. With its patient approach, and plentiful illustrations, it will also be a stimulating read for anyone comfortable with the language of mathematical proof. While the material within is classical, it brings together topics that are not generally found together in books at this level, such as: parametric equations for the pseudosphere and its geodesics; trilinear and barycentric coordinates; Euclidean and hyperbolic tilings; and theorems proved using inversion. The book is divided into four parts, and begins by developing neutral geometry in the spirit of Hilbert, leading to the Saccheri–Legendre Theorem. Subsequent sections explore classical Euclidean geometry, with an emphasis on concurrence results, followed by transformations in the Euclidean plane, and the geometry of the Poincaré disk model.Trade Review…The author succeeds in elevating Euclidean geometry in particular to the level of advanced undergraduate study and in so doing presents it as a counterpart to a first analysis course. At the same time, some readers may prefer to move on to new ideas and results more quickly; to that end, Harvey gives an indication of several paths through the book in his preface." - Choice"To my mind, this book stands out from the crowd partly because of the way in which its imaginatively devised illustrations are used to stage the introduction of basic concepts and to guide the reader through various steps in a proof. It's not just a matter of pretty pictures, however, because Matthew Harvey's written commentary is easy going and yet mathematically precise. He has written a truly lovely book, which is now top of my reading list as an introduction to geometry at this level." - Peter RuaneTable of ContentsAxioms and models; Part I. Neutral Geometry: 1. The axioms of incidence and order; 2. Angles and triangles; 3. Congruence verse I: SAS and ASA; 4. Congruence verse II: AAS; 5. Congruence verse III: SSS; 6. Distance, length and the axioms of continuity; 7. Angle measure; 8. Triangles in neutral geometry; 9. Polygons; 10. Quadrilateral congruence theorems; Part II. Euclidean Geometry: 11. The axiom on parallels; 12. Parallel projection; 13. Similarity; 14. Circles; 15. Circumference; 16. Euclidean constructions; 17. Concurrence I; 18. Concurrence II; 19. Concurrence III; 20. Trilinear coordinates; Part III. Euclidean Transformations: 21. Analytic geometry; 22. Isometries; 23. Reflections; 24. Translations and rotations; 25. Orientation; 26. Glide reflections; 27. Change of coordinates; 28. Dilation; 29. Applications of transformations; 30. Area I; 31. Area II; 32. Barycentric coordinates; 33. Inversion I; 34. Inversion II; 35. Applications of inversion; Part IV. Hyperbolic Geometry: 36. The search for a rectangle; 37. Non-Euclidean parallels; 38. The pseudosphere; 39. Geodesics on the pseudosphere; 40. The upper half-plane; 41. The Poincaré disk; 42. Hyperbolic reflections; 43. Orientation preserving hyperbolic isometries; 44. The six hyperbolic trigonometric functions; 45. Hyperbolic trigonometry; 46. Hyperbolic area; 47. Tiling; Bibliography; Index.
£59.40
Tomas Edwards Ethereum: Everything You Need to Know About It's
Book Synopsis
£15.16
Gordon & Breach Science Publishers SA Systolic Algorithms
Book SynopsisWhile the architecture of present-day parallel supercomputers is largely based on the concept of a shared memory, with its attendant limitations of common access, advances in semicoductor technology have led to the development of highly parellel computer architectures with decentralized storage and limited connections in which each processor possesses high bandwidth local memory connected to a small number of such architectures, enabling cost-effective high-speed parallel processing for large volumes of data, with ultra-high throughput rates. Algorithms suitable for implementation on systolic arrays find applications in areas such as signal and image processing, pattern matching, linear algebra, recurrence algorithms and graph problems. This book provides an insight into the implementation of systolic arrays and gives a comprehensive overview of the techniques and theories contributing to the design of systolic algorithms.Table of ContentsPREFACE 1. INTRODUCTION Systolic Algorithms 2. POLYNOMIAL AND ROOT FINDING METHODS 3. SYSTOLIC MATRIX OPERATIONS 4. QUADRATURE AND DIFFERENTIAL EQUATIONS 5 . SOLUTION OF LINEAR SYSTEMS 6. EIGENV ALOE-EIGENVECTOR COMPUTATIONS 7. LINEAR AND DYNAMIC PROGRAMMING
£65.54
Springer Nature Switzerland AG Hamiltonian Group Actions and Equivariant Cohomology
Book SynopsisThis monograph could be used for a graduate course on symplectic geometry as well as for independent study.The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions and the Darboux theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients are studied. The convexity theorem and toric manifolds come next and we give a comprehensive treatment of Equivariant cohomology. The monograph also contains detailed treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections on 2-manifolds. Finally, there is an appendix which provides background material on Lie groups. A course on differential topology is an essential prerequisite for this course. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry.Trade Review“The target audience is graduate students; ... this monograph could easily be used by researchers interested in learning the subject at a fast pace. It is a perfect text for a seminar course. ... the book's material is presented in a crisp and abridged manner. ... This makes the presentation short and highly valuable.” (Eduardo A. Gonzalez, Mathematical Reviews, December, 2020)Table of ContentsSymplectic vector spaces.- Hamiltonian group actions.- The Darboux-Weinstein Theorem.- Elementary properties of moment maps.- The symplectic structure on coadjoint orbits.- Symplectic Reduction.- Convexity.- Toric Manifolds.- Equivariant Cohomology.- The Duistermaat-Heckman Theorem.- Geometric Quantization.- Flat connections on 2-manifolds.
£49.49
Springer Nature Switzerland AG From Differential Geometry to Non-commutative
Book SynopsisThis book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.Trade Review“The present book is well written. It is very useful to researchers in differential geometry who are interested in non-commutative geometry. It provides motivations for tudying non commutative geometry.” (Ion Mihai, zbMATH 1458.58001, 2021)Table of Contents1. Part I Spaces, bundles and characteristic classes in differential geometry.- 2. Part II Non-commutative differential geometry.- 3. Part III Index Theorems.- 4. Part IV Prospects in Index Theory. Part V.- 5. Non-commutative topology.
£104.49
Springer Nature Switzerland AG Set Function T: An Account on F. B. Jones'
Book SynopsisThis book presents, in a clear and structured way, the set function \mathcal{T} and how it evolved since its inception by Professor F. Burton Jones in the 1940s. It starts with a very solid introductory chapter, with all the prerequisite material for navigating through the rest of the book. It then gradually advances towards the main properties, Decomposition theorems, \mathcal{T}-closed sets, continuity and images, to modern applications.The set function \mathcal{T} has been used by many mathematicians as a tool to prove results about the semigroup structure of the continua, and about the existence of a metric continuum that cannot be mapped onto its cone or to characterize spheres. Nowadays, it has been used by topologists worldwide to investigate open problems in continuum theory.This book can be of interest to both advanced undergraduate and graduate students, and to experienced researchers as well. Its well-defined structure make this book suitable not only for self-study but also as support material to seminars on the subject. Its many open problems can potentially encourage mathematicians to contribute with further advancements in the field.Table of ContentsPreliminaries.- The Set Function T.- Decomposition Theorems.- T-Closed Sets.- Continuity of T.- Images of T.- Applications.- Questions.- References.- Index.
£82.49
Springer Nature Switzerland AG Extrinsic Geometry of Foliations
Book SynopsisThis book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem of the Ricci curvature for the case of mixed curvature of foliations is examined. The book is divided into five chapters that deal with integral and variation formulas and curvature and dynamics of foliations. Different approaches and methods (local and global, regular and singular) in solving the problems are described using integral and variation formulas, extrinsic geometric flows, generalizations of the Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and 'computable' Finsler metrics.The book presents the state of the art in geometric and analytical theory of foliations as a continuation of the authors' life-long work in extrinsic geometry. It is designed for newcomers to the field as well as experienced geometers working in Riemannian geometry, foliation theory, differential topology, and a wide range of researchers in differential equations and their applications. It may also be a useful supplement to postgraduate level work and can inspire new interesting topics to explore.Trade Review“The reader is assumed to have some background in topology and differential geometry. The book is a continuation of the authors’ work in extrinsic geometry and thus provides a useful reference for researchers in this field.” (Emanuel-Ciprian Cismaş, zbMATH 1479.53002, 2022)Table of ContentsPreface.- 1. Preliminaries.- 2. Integral formulas.- 3. Prescribing the mean curvature.- 4. Variational formulae.- 5. Extrinsic Geometric flows.- References.- Index.
£66.49
Springer Nature Switzerland AG Equivariant Cohomology of Configuration Spaces
Book SynopsisThis book gives a brief treatment of the equivariant cohomology of the classical configuration space F(ℝ^d,n) from its beginnings to recent developments. This subject has been studied intensively, starting with the classical papers of Artin (1925/1947) on the theory of braids, and progressing through the work of Fox and Neuwirth (1962), Fadell and Neuwirth (1962), and Arnol'd (1969). The focus of this book is on the mod 2 equivariant cohomology algebras of F(ℝ^d,n), whose additive structure was described by Cohen (1976) and whose algebra structure was studied in an influential paper by Hung (1990). A detailed new proof of Hung's main theorem is given, however it is shown that some of the arguments given by him on the way to his result are incorrect, as are some of the intermediate results in his paper.This invalidates a paper by three of the authors, Blagojević, Lück and Ziegler (2016), who used a claimed intermediate result in order to derive lower bounds for the existence of k-regular and ℓ-skew embeddings. Using the new proof of Hung's main theorem, new lower bounds for the existence of highly regular embeddings are obtained: Some of them agree with the previously claimed bounds, some are weaker.Assuming only a standard graduate background in algebraic topology, this book carefully guides the reader on the way into the subject. It is aimed at graduate students and researchers interested in the development of algebraic topology in its applications in geometry.Trade Review“The book is well written. … The book will be important for those who study the cohomology rings of configuration spaces.” (Shintarô Kuroki, Mathematical Reviews, November, 2022)Table of Contents- 1. Snapshots from the History. - Part I Mod 2 Cohomology of Configuration Spaces. - 2. The Ptolemaic Epicycles Embedding. - 3. The Equivariant Cohomology of Pe(Rd, 2m). - 4. Hu’ng’s Injectivity Theorem. - Part II Applications to the (Non-)Existence of Regular and SkewEmbeddings. - 5. On Highly Regular Embeddings: Revised. - 6. More Bounds for Highly Regular Embeddings. - Part III Technical Tools. - 7. Operads. - 8. The Dickson Algebra. - 9. The Stiefel–Whitney Classes of the Wreath Square of a Vector Bundle. - 10. Miscellaneous Calculations.
£42.74
Springer International Publishing AG Fixed Point Theory in Generalized Metric Spaces
Book SynopsisThis book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.Table of ContentsMetric Spaces.- Extension of Metric Spaces.- Fixed Point Theorems on Extended Metric Spaces.
£44.99
Springer International Publishing AG Dialogues Between Physics and Mathematics: C. N.
Book SynopsisThis volume celebrates the 100th birthday of Professor Chen-Ning Frank Yang (Nobel 1957), one of the giants of modern science and a living legend. Starting with reminiscences of Yang's time at the research centre for theoretical physics at Stonybrook (now named C. N. Yang Institute) by his successor Peter van Nieuwenhuizen, the book is a collection of articles by world-renowned mathematicians and theoretical physicists. This emphasizes the Dialogue Between Physics and Mathematics that has been a central theme of Professor Yang’s contributions to contemporary science. Fittingly, the contributions to this volume range from experimental physics to pure mathematics, via mathematical physics. On the physics side, the contributions are from Sir Anthony Leggett (Nobel 2003), Jian-Wei Pan (Willis E. Lamb Award 2018), Alexander Polyakov (Breakthrough Prize 2013), Gerard 't Hooft (Nobel 1999), Frank Wilczek (Nobel 2004), Qikun Xue (Fritz London Prize 2020), and Zhongxian Zhao (Bernd T. Matthias Prize 2015), covering an array of topics from superconductivity to the foundations of quantum mechanics. In mathematical physics there are contributions by Sir Roger Penrose (Nobel 2022) and Edward Witten (Fields Medal 1990) on quantum twistors and quantum field theory, respectively. On the mathematics side, the contributions by Vladimir Drinfeld (Fields Medal 1990), Louis Kauffman (Wiener Gold Medal 2014), and Yuri Manin (Cantor Medal 2002) offer novel ideas from knot theory to arithmetic geometry.Inspired by the original ideas of C. N. Yang, this unique collection of papers b masters of physics and mathematics provides, at the highest level, contemporary research directions for graduate students and experts alike.Table of Contents1 Frank Yang at Stony Brook and the Beginning of Supergravity.- 2. A Stacky Approach to Crystals.- 3 The Potts Model, the Jones Polynomial and Link Homology.- 4 The Penrose–Onsager–Yang Approach to Superconductivity and Superfluidity.- 5 Quantum Operads.- 6 Quantum computational complexity withphotons and linear optics.- 7 Quantized Twistors, G2*, and the Split Octonions.- 8 Kronecker Anomalies and Gravitational Striction.- 9 Projecting Local and Global Symmetries to the Planck Scale.- 10 Gauge Symmetry in Shape Dynamics.- 11 Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit?.- 12 Quantum Anomalous Hall Effect.- 13 Magic Superconducting States in Cuprates.
£98.99
Springer International Publishing AG Manifolds, Vector Fields, and Differential Forms:
Book SynopsisThis textbook serves as an introduction to modern differential geometry at a level accessible to advanced undergraduate and master's students. It places special emphasis on motivation and understanding, while developing a solid intuition for the more abstract concepts. In contrast to graduate level references, the text relies on a minimal set of prerequisites: a solid grounding in linear algebra and multivariable calculus, and ideally a course on ordinary differential equations. Manifolds are introduced intrinsically in terms of coordinate patches glued by transition functions. The theory is presented as a natural continuation of multivariable calculus; the role of point-set topology is kept to a minimum. Questions sprinkled throughout the text engage students in active learning, and encourage classroom participation. Answers to these questions are provided at the end of the book, thus making it ideal for independent study. Material is further reinforced with homework problems ranging from straightforward to challenging. The book contains more material than can be covered in a single semester, and detailed suggestions for instructors are provided in the Preface.Trade Review“This book is intended to be a modern introduction to the basics of differential geometry, accessible to undergraduate and master students. From my point of view, this goal is achieved, the book being very well structured and supported by illustrative examples and problems. … this book will be of great interest for undergraduate students, master students, and also helpful for instructors.” (Gabriel Eduard Vilc, zbMATH 1522.53001, 2023)Table of Contents1. Introduction2. Manifolds3. Smooth maps4. Submanifolds5. Tangent spaces6. Vector fields7. Differential forms8. Integration9. Vector bundlesNotions from set theoryNotions from algebraTopological properties of manifoldsHints and answers to in-text questionsReferencesList of SymbolsIndex
£35.99
Springer International Publishing AG A Course on Hopf Algebras
Book SynopsisThis textbook provides a concise, visual introduction to Hopf algebras and their application to knot theory, most notably the construction of solutions of the Yang–Baxter equations. Starting with a reformulation of the definition of a group in terms of structural maps as motivation for the definition of a Hopf algebra, the book introduces the related algebraic notions: algebras, coalgebras, bialgebras, convolution algebras, modules, comodules. Next, Drinfel’d’s quantum double construction is achieved through the important notion of the restricted (or finite) dual of a Hopf algebra, which allows one to work purely algebraically, without completions. As a result, in applications to knot theory, to any Hopf algebra with invertible antipode one can associate a universal invariant of long knots. These constructions are elucidated in detailed analyses of a few examples of Hopf algebras. The presentation of the material is mostly based on multilinear algebra, with all definitions carefully formulated and proofs self-contained. The general theory is illustrated with concrete examples, and many technicalities are handled with the help of visual aids, namely string diagrams. As a result, most of this text is accessible with minimal prerequisites and can serve as the basis of introductory courses to beginning graduate students.Table of Contents- 1. Groups and Hopf Algebras. - 2. Constructions of Algebras, Coalgebras, Bialgebras, and Hopf Algebras. - 3. The Restricted Dual of an Algebra. - 4. The Restricted Dual of Hopf Algebras: Examples of Calculations. - 5. The Quantum Double. - 6. Applications in Knot Theory.
£40.49
Springer International Publishing AG Partial Differential Equations I: Basic Theory
Book SynopsisThe first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. In includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds.Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC.Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.”(Peter Lax, SIAM review, June 1998)Table of ContentsContents of Volumes II and III.- Preface.- 1 Basic Theory of ODE and Vector Fields.- 2 The Laplace Equation and Wave Equation.- 3 Fourier Analysis, Distributions, and Constant-Coefficient Linear PDE.- 4 Sobolev Spaces.- 5 Linear Elliptic Equation.- 6 Linear Evolution Equations.- A Outline of Functional Analysis.- B Manifolds, Vector Bundles, and Lie Groups.- Index.
£58.49
Springer Nature Switzerland The Cohomology of Monoids
Book Synopsis
£103.99
Birkhäuser Morse Homology with Differential Graded
Book Synopsis
£118.35
Springer Continuum Theory
Book SynopsisChapter 1. Introduction.- Chapter 2. Locally Connected Continua.- Chapter 3. CuttingWires and Bumping Boundaries.- Chapter 4. Indecomposable Continua.- Chapter 5. Characterizing Arcs and Circles.- Chapter 6. Finite Graphs.- Chapter 7. Dendroids.- Chapter 8. The Cantor Set.- Chapter 9. Hyperspaces of Continua.- Chapter 10. Models of Hyperspaces.- Chapter 11. Irreducible Continua.- Chapter 12. Unicoherence.- Chapter 13. The Fixed Point Property.- Chapter 14. Inverse Limits.- Chapter 15. Homogeneity of the Hilbert Cube.- Chapter 16. Absolute Retracts.- Chapter 17. Stronger Properties of the Pseudo-Arc.
£44.99
Birkhauser Verlag AG Frames and Locales: Topology without points
Book SynopsisUntil the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set exploited since the twenties offered an expression of the geometric intuition of a "realistic" place (spot, grain) of non-trivial extent.Imitating the behaviour of open sets and their relations led to a new approach to topology flourishing since the end of the fifties.It has proved to be beneficial in many respects. Neglecting points, only little information was lost, while deeper insights have been gained; moreover, many results previously dependent on choice principles became constructive. The result is often a smoother, rather than a more entangled, theory.No monograph of this nature has appeared since Johnstone's celebrated Stone Spaces in 1983. The present book is intended as a bridge from that time to the present. Most of the material appears here in book form for the first time or is presented from new points of view. Two appendices provide an introduction to some requisite concepts from order and category theories.Trade ReviewFrom the reviews:“The book covers, in a comprehensive and self-contained way, the development of point-free topology in the last 30 years … . The book ends with two short appendices containing those facts about partially ordered sets and categories needed in the book. In conclusion, this is a very good book; it is nicely written and is highly recommended for anyone wishing to gain an overview of point-free topology.” (Javier Gutiérrez García, Mathematical Reviews, Issue 2012 j)“The book starts with a recount of sobriety and the TD-axiom, which is then quickly followed by the definition of the category of locales, various facets of spectra, the usual adjunctions and several criteria for spatiality. … this book is an erudite account of the current status of pointfree topology, written beautifully in the authors’ inimitable style. It is both easily accessible to a complete beginner, and an excellent source of reference for the mature pointfree practitioner.” (Themba Dube, Zentralblatt MATH, Vol. 1231, 2012)“In a total of fifteen chapters the reader is taken from spaces and lattices of open sets, through a thorough discussion of the notions of frames and locales … . book ends (modulo its appendices) with a discussion of localic groups … together with frames, that’s what this entire book is ultimately all about. … is quite-well written: it’s a clear and thorough treatment of what is really rather an important subject, which is to say, a greatly underappreciated one.” (Michael Berg, The Mathematical Association of America, April, 2012)Table of ContentsPreface.- Introduction.- I. Spaces and lattices of open sets.- II. Frames and locales. Spectra.- III. Sublocales.- IV. Structure of localic morphisms. The categories Loc and Frm.- V. Separation axioms.- VI. More on sublocales.-VII. Compactness and local compactness.- VIII. (Symmetric) uniformity and nearness.- IX. Paracompactness.- X. More about completion.- XI. Metric frames.- XII. Entourages, non-symmetric uniformity.- XIII. Connectedness.- XIV. The frame of reals and real functions.- XV. Localic groups.- Appendix I: Posets.- Appendix II: Categories.- Bibliography.- Index of Notation.- Index.
£52.24
Birkhauser Verlag AG Foliations: Dynamics, Geometry and Topology
Book SynopsisThis book is an introduction to several active research topics in Foliation Theory and its connections with other areas. It contains expository lectures showing the diversity of ideas and methods converging in the study of foliations. The lectures by Aziz El Kacimi Alaoui provide an introduction to Foliation Theory with emphasis on examples and transverse structures. Steven Hurder's lectures apply ideas from smooth dynamical systems to develop useful concepts in the study of foliations: limit sets and cycles for leaves, leafwise geodesic flow, transverse exponents, Pesin Theory and hyperbolic, parabolic and elliptic types of foliations. The lectures by Masayuki Asaoka compute the leafwise cohomology of foliations given by actions of Lie groups, and apply it to describe deformation of those actions. In his lectures, Ken Richardson studies the properties of transverse Dirac operators for Riemannian foliations and compact Lie group actions, and explains a recently proved index formula. Besides students and researchers of Foliation Theory, this book will be interesting for mathematicians interested in the applications to foliations of subjects like Topology of Manifolds, Differential Geometry, Dynamics, Cohomology or Global Analysis.Trade Review“This book contains the lecture notes of four courses on several topics with rather different flavor, which are linked by their relation with Foliation Theory. … the courses will be very helpful for any reader that wants to get quickly introduced to any of these lines of research.” (Jesus A. Álvarez López, zbMATH 1318.57001, 2015)Table of ContentsFundamentals of Foliation Theory.- Foliation Dynamics.- Deformation of Locally Free Actions and Leafwise Cohomology.- Transversal Dirac Operators on Distributions, Foliations, and G-Manifolds.
£29.69
Springer International Publishing AG A Course in Point Set Topology
Book SynopsisThis textbook in point set topology is aimed at an upper-undergraduate audience. Its gentle pace will be useful to students who are still learning to write proofs. Prerequisites include calculus and at least one semester of analysis, where the student has been properly exposed to the ideas of basic set theory such as subsets, unions, intersections, and functions, as well as convergence and other topological notions in the real line. Appendices are included to bridge the gap between this new material and material found in an analysis course. Metric spaces are one of the more prevalent topological spaces used in other areas and are therefore introduced in the first chapter and emphasized throughout the text. This also conforms to the approach of the book to start with the particular and work toward the more general. Chapter 2 defines and develops abstract topological spaces, with metric spaces as the source of inspiration, and with a focus on Hausdorff spaces. The final chapter concentrates on continuous real-valued functions, culminating in a development of paracompact spaces.Trade ReviewFrom the book reviews:“This book by Conway (George Washington Univ.) provides the three stepping-stones for leading a successful practitioner of calculus to proficiency in point set topology, with one chapter devoted to each. … Summing Up: Recommended. Upper-division undergraduates and beginning graduate students.” (F. E. J. Linton, Choice, Vol. 51 (11), July, 2014)“The book under review is, as the title makes clear, an introduction to point set topology … . Conway wrote this book to give students ‘a set of tools’, discussing ‘material [that] is used in almost every part of mathematics.’ … this is a well-written book that I enjoyed reading. Assuming that your idea of what to teach in a first-semester course in topology is in line with the author’s, this book would make an excellent text for such a course.” (Mark Hunacek, MAA Reviews, January, 2014)“The author is a specialist in analysis with a life long love for point set topology. … There is a relatively large collection of well investigated biographies which appear as footnotes, which are interesting and helpful, espacially for young readers. … The book will be a success, a good introduction to point set topology and a valuable entrance … .” (Friedrich Wilhelm Bauer, zbMATH, Vol. 1284, 2014)Table of ContentsMetric Spaces.- Topological Spaces.- Continuous Real-Valued Functions.- Appendix.- Bibliography.- Terms.- Symbols.
£49.49
