Topology Books
John Wiley & Sons Inc Fractals Random Shapes and Point Fields
Book SynopsisIn Part I the reader is introduced to the methods of measuring the fractal dimension of irregular geometric structures. Part II demonstrates important modern methods for the statistical analysis of random shapes. The statistical theory of point fields, with and without marks, is introduced in Part III. Each of the three sections concentrates on the mathematical ideas, rather than detailed proofs, and can be read independently.Table of ContentsFRACTALS AND METHODS FOR THE DETERMINATION OF FRACTALDIMENSIONS. Hausdorff Measure and Dimension. Deterministic Fractals. Random Fractals. Methods for the Empirical Determination of Fractal Dimension. THE STATISTICS OF SHAPES AND FORMS. Fundamental Concepts. Representation of Contours. Set Theoretic Analysis. Point Description of Figures. Examples. POINT FIELD STATISTICS. Fundamentals. Finite Point Fields. Poisson Point Fields. Fundamentals of the Theory of Point Fields. Statistics for Homogeneous Point Fields. Point Field Models. Appendices. References. Index.
£209.66
John Wiley & Sons Inc Techniques in Fractal Geometry
Book SynopsisFollowing on from the success of Fractal Geometry: Mathematical Foundations and Applications, this new sequel presents a variety of techniques in current use for studying the mathematics of fractals. Much of the material presented in this book has come to the fore in recent years.Table of ContentsMathematical Background. Review of Fractal Geometry. Some Techniques for Studying Dimension. Cookie-cutters and Bounded Distortion. The Thermodynamic Formalism. The Ergodic Theorem and Fractals. The Renewal Theorem and Fractals. Martingales and Fractals. Tangent Measures. Dimensions of Measures. Some Multifractal Analysis. Fractals and Differential Equations. References. Index.
£99.86
Dover Publications Introduction to Topology
Book SynopsisThis volume explains nontrivial applications of metric space topology to analysis, clearly establishing their relationship. Also, topics from elementary algebraic topology focus on concrete results with minimal algebraic formalism. Two chapters consider metric space and point-set topology; the other 2 chapters discuss algebraic topological material. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
£15.29
Dover Publications Inc. Croom F Principles of Topology
Book SynopsisDesigned for a one-semester introduction to topology at the undergraduate and beginning graduate levels, this text is accessible to students who have studied multivariate calculus. Topics include metric spaces, general topological spaces, continuity, topological equivalence, basis and subbasis, connectedness and compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces.
£18.69
Cambridge University Press Topology via Logic
Book SynopsisThis is an advanced textbook on topology for computer scientists. It is based on a course given by the author to postgraduate students of computer science at Imperial College.Table of Contents1. Introduction; 2. Affirmative and refutative assertions; 3. Frames; 4. Frames as algebras; 5. Topology: the definitions; 6. New topologies for old; 7. Point logic; 8. Compactness; 9. Spectral algebraic locales; 10. Domain theory; 11. Power domains; 12. Spectra of rings; Bibliography.
£47.99
Cambridge University Press Geometry and Topology
Book SynopsisGeometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. This book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The discussion moves from Euclidean to non-Euclidean geometries, including spherical and hyperbolic geometry, and then on to affine and projective linear geometries. Group theory is introduced to treat geometric symmetries, leading to the unification of geometry and group theory in the Erlangen program. An introduction to basic topology follows, with the MÃbius strip, the Klein bottle and the surface with g handles exemplifying quotient topologies and the homeomorphism problem. Topology combines with group theory to yield the geometry of transformation groups,having applications to relativity theory and quantum mechTrade ReviewA welcome addition to the undergraduate library. Highly recommended. --ChoiceTable of ContentsIntroduction; 1. Euclidean geometry; 2. Composing maps; 3. Non-Euclidean; 4. Affine geometry; 5. Projective geometry; 6. Geometry and group theory; 7. Topology; 8. Geometry of transformation groups; 9. Concluding remarks; A. Metrics; B. Linear algebra; References; Index.
£49.39
Cambridge University Press When Topology Meets Chemistry
Book SynopsisIn this topology text, the reader will learn about knot theory, 3-dimensional manifolds, and the topology of embedded graphs, and the role these play in understanding molecular structures. All the relevant background is provided. For advanced undergraduate mathematics students, and researchers in chemistry and biology.Trade Review'If you are a chemist … looking for applications of low dimensional topology in the natural sciences, this is a book you should own … serves as an excellent introduction to the field for a topologist looking for interesting applications of topology in science. The book is well produced with many useful diagrams and with exercises that range from easy to intriguing. This book is definitely on my 'buy list'.' Stuart Whittington, SIAM ReviewTable of Contents1. Stereochemical topology; 2. Detecting chirality; 3. Chiral moebius ladders and related molecular graphs; 4. Different types of chirality and achirality; 5. Embeddings of complete graphs in 3-space; 6. Rigid and non-rigid symmetries of graphs in 3-space; 7. Topology of DNA.
£34.99
Cambridge University Press Lectures on the Ricci Flow 325 London Mathematical Society Lecture Note Series Series Number 325
Book SynopsisHamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincaré conjecture and Thurston's geometrization conjecture. This book gives a concise introduction to the subject with the hindsight of Perelman's breakthroughs from 2002/2003.Trade Review"... The freedom to skip some of the proofs, and the lucid presentation, this small book is pleasant to read." Peng Lu, Mathematical ReviewsTable of Contents1. Introduction; 2. Riemannian geometry background; 3. The maximum principle; 4. Comments on existence theory for parabolic PDE; 5. Existence theory for the Ricci flow; 6. Ricci flow as a gradient flow; 7. Compactness of Riemannian manifolds and flows; 8. Perelman's W entropy functional; 9. Curvature pinching and preserved curvature properties under Ricci flow; 10. Three-manifolds with positive Ricci curvature and beyond.
£61.19
Cambridge University Press Frobenius Manifolds and Moduli Spaces for Singularities 151 Cambridge Tracts in Mathematics Series Number 151
Book SynopsisThe relations between Frobenius manifolds and singularity theory are treated here in a rigorous yet accessible manner. For those working in singularity theory or other areas of complex geometry, this book will open the door to the study of Frobenius manifolds. This class of manifolds are now known to be relevant for the study of singularity theory, quantum cohomology, mirror symmetry, symplectic geometry and integrable systems. The first part of the book explains the theory of manifolds with a multiplication on the tangent bundle. The second presents a simplified explanation of the role of Frobenius manifolds in singularity theory along with all the necessary tools and several applications. Readers will find here a careful and sound study of the fundamental structures and results in this exciting branch of maths. This book will serve as an excellent resource for researchers and graduate students who wish to work in this area.Trade Review'… a nice introduction to the theory of Frobenius manifolds …' Zentralblatt für Mathematik'The book under review gives a very detailed analysis of the category of F-manifolds … the book is clean, rigorous and readable. the researchers in the areas of singularity theory, complex geometry, integrable systems, quantum cohomology, mirror symmetry and sympathetic geometry will find in this book a lot of useful information which has never been given in such detail before.' Proceedings of the Edinburgh Mathematical Society'… one can say this book is a must for workers in the field of singularity theory.' Duco van Straten, Department of Mathematics, University of MainzTable of ContentsPart I. Multiplication on the Tangent Bundle: 1. Introduction to part 1; 2. Definition and first properties of F-manifolds; 3. Massive F-manifolds and Lagrange maps; 4. Discriminants and modality of F-manifolds; 5. Singularities and Coxeter groups; Part II. Frobenius Manifolds, Gauss-Manin Connections, and Moduli Spaces for Hypersurface Singularities: 6. Introduction to part 2; 7. Connections on the punctured plane; 8. Meromorphic connections; 9. Frobenius manifolds ad second structure connections; 10. Gauss-Manin connections for hypersurface singularities; 11. Frobenius manifolds for hypersurface singularities; 12. ∴μυ-constant stratum; 13. Moduli spaces for singularities; 14. Variance of the spectral numbers.
£105.45
Cambridge University Press The Life of Bach Musical Lives
Book SynopsisArising from a summer school course, this book develops the modern theory of rational varieties at a level that will particularly suit graduate students. The authors have written a state-of-the-art treatment with numerous exercises and solutions to help students reach the stage where they can begin to tackle contemporary research.Trade Review'… a beautiful and ample introduction to the interesting topic of rational and 'nearly rational' varieties and it will be a valuable reference for a wide audience.' Zentralblatt MATHTable of ContentsIntroduction; 1. Examples of rational varieties; 2. Cubic surfaces; 3. Rational surfaces; 4. Nonrationality and reduction modulo p; 5. The Noether-Fano method; 6. Singularities of pairs; 7. Solutions to exercises.
£105.45
Cambridge University Press The CubeA Window to Convex and Discrete Geometry
Book SynopsisThis tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them.Trade Review"Because this book is a love letter to the unity of mathematics, readers can hardly but come to share Zong's undisguised enthusiasm...Highly recommended." -- ChoiceTable of ContentsPreface; Basic notation; 0. Introduction; 1. Cross sections; 2. Projections; 3. Inscribed simplices; 4. Triangulations; 5. 0/1 polytopes; 6. Minkowski's conjecture; 7. Furtwangler's conjecture; 8. Keller's conjecture; Bibliography; Index.
£105.45
Cambridge University Press An Introduction to Contact Topology 109 Cambridge
Book SynopsisThis text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.Trade Review'… a fundamental monograph … can be strongly recommended for graduate students and is indispensable for specialists in the field.' EMS NewsletterTable of ContentsForeword; 1. Facets of Contact Geometry; 2. Contact Manifolds; 3. Knots in Contact 3-Manifolds; 4. Contact Structures on 3-Manifolds; 5. Symplectic Fillings and Convexity; 6. Contact Surgery; 7. Further Constructions of Contact Manifolds; 8. Contact Structures on 5-Manifolds; Appendix A. The generalised Poincaré lemma; Appendix B. Time-dependent vector fields; References; Notation Index; Author Index; Subject Index.
£77.89
Cambridge University Press Kazhdans Property T 11 New Mathematical Monographs Series Number 11
Book SynopsisProperty (T) is a rigidity property for topological groups, first formulated by D. Kazhdan in the mid 1960's with the aim of demonstrating that a large class of lattices are finitely generated. Later developments have shown that Property (T) plays an important role in an amazingly large variety of subjects, including discrete subgroups of Lie groups, ergodic theory, random walks, operator algebras, combinatorics, and theoretical computer science. This monograph offers a comprehensive introduction to the theory. It describes the two most important points of view on Property (T): the first uses a unitary group representation approach, and the second a fixed point property for affine isometric actions. Via these the authors discuss a range of important examples and applications to several domains of mathematics. A detailed appendix provides a systematic exposition of parts of the theory of group representations that are used to formulate and develop Property (T).Table of ContentsIntroduction; Part I. Kazhdan's Property (T): 1. Property (T); 2. Property (FH); 3. Reduced Cohomology; 4. Bounded generation; 5. A spectral criterion for Property (T); 6. Some applications of Property (T); 7. A short list of open questions; Part II. Background on Unitary Representations: A. Unitary group representations; B. Measures on homogeneous spaces; C. Functions of positive type; D. Representations of abelian groups; E. Induced representations; F. Weak containment and Fell topology; G. Amenability; Appendix; Bibliography; List of symbols; Index.
£133.95
Princeton University Press Combinatorics of Train Tracks
Book SynopsisMeasured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry, and dynamical systems. This book presents a treatment of the combinatorial structure of the space of measured geodesic laminations in a fixed surface.Trade Review"The book is beautifully written, with a clear path of theoretical development amid a wealth of detail for the technician... [T]his text provides a valuable reference work as well as a readable introduction for the student or newcomer to the area."--Zentralblatt for MathematikTable of ContentsPrefaceAcknowledgementsCh. 1The Basic Theory31.1Train Tracks41.2Multiple Curves and Dehn's Theorem101.3Recurrence and Transverse Recurrence181.4Genericity and Transverse Recurrence391.5Trainpaths and Transverse Recurrence601.6Laminations681.7Measured Laminations821.8Bounded Surfaces and Tracks with Stops102Ch. 2Combinatorial Equivalence1152.1Splitting, Shifting, and Carrying1162.2Equivalence of Birecurrent Train Tracks1242.3Splitting versus Shifting1272.4Equivalence versus Carrying1332.5Splitting and Efficiency1392.6The Standard Models1452.7Existence of the Standard Models1542.8Uniqueness of the Standard Models160Ch. 3The Structure of ML[subscript 0]1733.1The Topology of ML[subscript 0] and PL[subscript 0]1743.2The Symplectic Structure of ML[subscript 0]1823.3Topological Equivalence1883.4Duality and Tangential Coordinates191Epilogue204Addendum The Action of Mapping Classes on ML[subscript 0]210Bibliography214
£70.40
Princeton University Press ThreeDimensional Geometry and Topology Volume 1
Book SynopsisHyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning, but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty. This book develops some of the power of geometry in two and three dimensions, and the strong connection of geometry with topology.Trade ReviewWinner of the 2005 Book Prize, American Mathematical Society Winner of the 1997 for the Best Professional/Scholarly Book in Mathematics, Association of American Publishers "The present volume represents the culmination of nearly two decades of honoring his famous but difficult 1978 lecture notes. This beautifully produced, exquisitely organized volume now reads as easily as one could possibly hope given the profundity of the material. An instant classic."--ChoiceTable of ContentsPreface Reader's Advisory Ch. 1. What Is a Manifold? 3 Ch. 2. Hyperbolic Geometry and Its Friends 43 Ch. 3. Geometric Manifolds 109 Ch. 4. The Structure of Discrete Groups 209 Glossary 289 Bibliography 295 Index 301
£84.00
Princeton University Press Combinatorial Group Theory and Topology
Book SynopsisTable of Contents*Frontmatter, pg. i*CONTENTS, pg. v*PREFACE, pg. vii*PROBLEMS IN COMBINATORIAL GROUP THEORY, pg. 3*POINCARE DUALITY GROUPS OF DIMENSION TWO ARE SURFACE GROUPS, pg. 35*HOW TO GENERALIZE ONE-RELATOR GROUP THEORY, pg. 53*GRAPHICAL THEORY OF AUTOMORPHISMS OF FREE GROUPS, pg. 79*PEAK REDUCTION AND AUTOMORPHISMS OF FREE GROUPS AND FREE PRODUCTS, pg. 107*NONSINGULAR EQUATIONS OF SMALL WEIGHT OVER GROUPS, pg. 121*GRAPH-THEORETIC LEMMA AND GROUP-EMBEDDINGS, pg. 145*THE TODD-COXETER PROCESS, USING GRAPHS, pg. 157*A SUBGROUP THEOREM FOR PREGROUPS, pg. 163*GROUPS WITH A RATIONAL CROSS-SECTION, pg. 175*ON THE RATIONAL GROWTH OF VIRTUALLY NILPOTENT GROUPS, pg. 185*SJOGREN'S THEOREM FOR DIMENSION SUBGROUPS - THE METABELIAN CASE, pg. 197*ON GROUP PRESENTATIONS, COPRODUCTS AND INVERSES, pg. 213*ON COMPLEXES DOMINATED BY A TWO-COMPLEX, pg. 221*SUBCOMPLEXES OF TWO-COMPLEXES AND PROJECTIVE CROSSED MODULES, pg. 255*LENGTH FUNCTIONS OF GROUP ACTIONS ON A-TREES, pg. 265*RESIDUAL FINITENESS FOR 3-MANIFOLDS, pg. 379*THE NIELSEN-THURSTON THEORY OF SURFACE AUTOMORPHISMS, pg. 397*WHITEHEAD GROUPS OF CERTAIN HYPERBOLIC MANIFOLDS, II, pg. 415*CHARACTERIZATION OF FINITE SUBGROUPS OF THE MAPPING-CLASS GROUP, pg. 433*A SEQUENCE OF PSEUDO-ANOSOV DIFFEOMORPHISMS, pg. 443*DEHN'S ALGORITHM REVISITED, WITH APPLICATIONS TO SIMPLE CURVES ON SURFACES, pg. 451*PATHS OF GEODESICS AND GEOMETRIC INTERSECTION NUMBERS: I, pg. 479*PATHS OF GEODESICS AND GEOMETRIC INTERSECTION NUMBERS: II, pg. 501*SELECTED PROBLEMS, pg. 545*Backmatter, pg. 552
£113.60
Princeton University Press Computers Rigidity and Moduli
Book SynopsisPresents an area of mathematical research that combines topology, geometry, and logic. This book seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity.Trade Review"This is a terrific book. It does no less than introduce an entire new field of mathematics - a truly astounding development. It will be widely read, I think, as much because of the masterful exposition as for the beautiful mathematics. Weinberger gives very clear and accessible descriptions of all the relevant tools from computability, topology, and geometry, in a friendly and engaging style. He has done the mathematical community a great service indeed." - Robin Forman, Rice University; "This book represents a very exciting new area of research at the interface of topology and logic. Written in a quite readable style, and presenting the more accessible cases in detail while giving references for the more involved results, it is a book whose methods and ideas will surely have many more significant applications over the next several years." - Kevin M. Whtye, University of Illinois at Chicago"
£62.40
Princeton University Press NonArchimedean Tame Topology and Stably Dominated
Book SynopsisOver the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools. For non-archimedTrade Review"A major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry."---Anand Pillay, MathSciNetTable of Contents*Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Preliminaries, pg. 8*3. The space v of stably dominated types, pg. 37*4. Definable compactness, pg. 57*5. A closer look at the stable completion, pg. 70*6. GAMMA-internal spaces, pg. 76*7. Curves, pg. 92*8. Strongly stably dominated points, pg. 104*9. Specializations and ACV2F, pg. 119*10. Continuity of homotopies, pg. 142*11. The main theorem, pg. 154*12. The smooth case, pg. 177*13. An equivalence of categories, pg. 183*14. Applications to the topology of Berkovich spaces, pg. 187*Bibliography, pg. 207*Index, pg. 211*List of notations, pg. 215
£130.40
Princeton University Press NonArchimedean Tame Topology and Stably Dominated
Book SynopsisTrade Review"A major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry."---Anand Pillay, MathSciNetTable of Contents*Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Preliminaries, pg. 8*3. The space v of stably dominated types, pg. 37*4. Definable compactness, pg. 57*5. A closer look at the stable completion, pg. 70*6. GAMMA-internal spaces, pg. 76*7. Curves, pg. 92*8. Strongly stably dominated points, pg. 104*9. Specializations and ACV2F, pg. 119*10. Continuity of homotopies, pg. 142*11. The main theorem, pg. 154*12. The smooth case, pg. 177*13. An equivalence of categories, pg. 183*14. Applications to the topology of Berkovich spaces, pg. 187*Bibliography, pg. 207*Index, pg. 211*List of notations, pg. 215
£60.00
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
£56.00
Princeton University Press Fourier Restriction for Hypersurfaces in Three
Book SynopsisTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Chapter 1. Introduction, pg. 1*Chapter 2. Auxiliary Results, pg. 29*Chapter 3. Reduction to Restriction Estimates near the Principal Root Jet, pg. 50*Chapter 4. Restriction for Surfaces with Linear Height below 2, pg. 57*Chapter 5. Improved Estimates by Means of Airy-Type Analysis, pg. 75*Chapter 6. The Case When hlin(PHI) => 2: Preparatory Results, pg. 105*Chapter 7. How to Go beyond the Case hlin(PHI) => 5, pg. 131*Chapter 8. The Remaining Cases Where m = 2 and B = 3 or B = 4, pg. 181*Chapter 9. Proofs of Propositions 1.7 and 1.17, pg. 244*Bibliography, pg. 251*Index, pg. 257
£130.40
Princeton University Press The Norm Residue Theorem in Motivic Cohomology
Book Synopsis
£130.40
Princeton University Press The Norm Residue Theorem in Motivic Cohomology
Book Synopsis
£60.00
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
£60.00
Princeton University Press Visual Differential Geometry and Forms A
Book SynopsisTrade Review"Finalist for the PROSE Award in Mathematics, Association of American Publishers""Needham proposes to provide a truly geometric 'visual' explication of differential geometry, and he succeeds brilliantly. I know nothing like it in the literature."---Frank Morgan, EMS Magazine"[The] book offers a truly unique and original take on differential geometry, and it amply deserves inclusion within the pantheon of textbook deities."---Eric Poisson, Notices of the AMS"This is a valuable and beautifully created guide to what can at first seem a confusing area of mathematical physics. There are other contenders that try to teach this subject, but this is the best that I have come across so far and I will continue to enjoy learning from it (and almost certainly teaching from it) over the coming years, I am sure."---Jonathan Shock, Mathemafrica"[Proactively] rethinks the way this important area of mathematics should be considered and taught." * MathSciNet *"The book is a remarkable and highly original approach to the basic stem of differential geometry. And that mathematical trunk has roots and branches in so many other unexpected yet related subjects, each of which can be equally well approached from the same geometrical point of view."---Adhemar Bultheel, MAA Reviews"[Visual Differential Geometry and Forms] its peers. It is fun to read and provides a unique and intuitive approach to differential geometry. The author’s passion for the subject is evident throughout the book. Although Needham’s approach is unorthodox, it is rewarding, and complements the exposition found in standard textbooks."---Sean M. Eli & Krešmir Josić, SIAM Review
£100.30
Springer Exercises in Basic Ring Theory 20 Texts in the
Book SynopsisOur intention was to provide a collection of exercises which cover only the easy part of ring theory, what we have named the "Basics of Ring Theory". The book is divided in two parts each consisting of seventeen chapters, the first part containing the exercises and the second part the solutions.Table of ContentsPreface. List of Symbols. I: Exercises. 1. Fundamentals. 2. Ideals. 3. Zero Divisors. 4. Ring Homomorphisms. 5. Characteristics. 6. Divisibility in Integral Domains. 7. Division Rings. 8. Automorphisms. 9. The Tensor Product. 10. Artinian and Noetherian Rings. 11. Socle and Radical. 12. Semisimple Rings. 13. Prime Ideals, Local Rings. 14. Polynomial Rings. 15. Rings of Quotients. 16. Rings of Continuous Functions. 17. Special Problems. II: Solutions. 1. Fundamentals. 2. Ideals. 3. Zero Divisors. 4. Ring Homomorphisms. 5. Characteristics. 6. Divisibility in Integral Domains. 7. Division Rings. 8. Automorphisms. 9. The Tensor Product. 10. Artinian and Noetherian Rings. 11. Socle and Radical. 12. Semisimple Rings. 13. Prime Ideals, Local Rings. 14. Polynomial Rings. 15. Rings of Quotients. 16. Rings of Continuous Functions. 17. Special Problems. Bibliography. Index.
£42.74
MP-AMM American Mathematical Lectures on Hilbert Schemes of Points on Surfaces
Book SynopsisIt has been realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory - even theoretical physics. This book reflects this feature of Hilbert schemes.Table of ContentsIntroduction Hilbert scheme of points Framed moduli space of torsion free sheaves on $\mathbb{P}^2$ Hyper-Kahler metric on $(\mathbb{C}^2)^{[n]}$ Resolution of simple singularities Poincare polynomials of the Hilbert schemes (1) Poincare polynomials of Hilbert schemes (2) Hilbert scheme on the cotangent bundle of a Riemann surface Homology group of the Hilbert schemes and the Heisenberg algebra Symmetric products of an embedded curve, symmetric functions and vertex operators Bibliography Index.
£55.10
MP-AMM American Mathematical Trends in Mathematical Physics
Book SynopsisPresents the proceedings of the conference on 'Trends in Mathematical Physics' held at the University of Tennessee. The conference drew international experts from mathematical and computational physics. The following topics were addressed: superstrings and quantum gravity, pattern formation, and crystallographic topology.Table of ContentsBerry's connection in a quantum relativistic description of the curved space analogue of development by R. R. Aldinger Heat-kernel asymptotics of the Gilkey-Smith boundary-value problem by I. G. Avramidi and G. Esposito On ellipticity and gauge invariance in Euclidean quantum gravity by I. G. Avramidi and G. Esposito Undercompressive waves in driven thin film flow: Theory, computation, and experiment by A. L. Bertozzi, A. Munch, and M. Shearer Internal time peculiarities as a cause of bifurcations arising in classical trajectory problem and quantum chaos creation in three-body systems by A. V. Bogdanov, A. S. Gevorkyan, and A. G. Grigoryan Random motion of quantum harmonic oscillator-Thermodynamics of nonrelativistic vacuum by A. V. Bogdanov, A. S. Gevorkyan, and A. G. Grigoryan A new formulation of Lax pairs for generalized Calogero-Moser models by A. J. Bordner Four-point correlation functions in the AdS/CFT correspondence by G. Chalmers and K. Schalm Gravitational instantons and moduli spaces by S. A. Cherkis Superdualities and twisted self-duality by E. Cremmer, B. Julia, H. Lu, and C. N. Pope Boomerons in field theory by I. Dasgupta A layman's guide to $M$-theory by M. J. Duff Family symmetry, the anomalous $U(1)$, and neutrino mixing by J. K. Elwood Stochastic quantization approach to $c \leq 1$ open-closed string field theories by D. Ennyu, H. Kawabe, and N. Nakazawa Gauge invariance and effective actions at finite temperature by C. D. Fosco Superconformal deformations and space-time symmetries by I. Giannakis Nonlinear patterns in microstructures by M. E. Glicksman Non-thermalizability of a quantum field theory by C. R. Hagen Field theory for chemical spaces by R. A. Hefferlin From functions to matrices by J. Hoppe Duality and construction of quantum integrable systems by E. Horozov and A. Kasman Geometric concepts for the mass in general relativity by G. Huisken Crystallographic topology 2: Overview and work in progress by C. K. Johnson Gravitationally dressed RG flows, zigzag symmetry and zero-tension strings by I. I. Kogan and O. A. Soloviev Einstein metrics and the Yamabe problem by C. LeBrun Numerical evolution in time of curvature perturbations in Kerr black holes by R. Lopez-Aleman Nonlinearity and self-similarity: Wavelets and compactons on a physical background by A. Ludu and J. P. Draayer On analytic approach to perturbative quantum chromodynamics by B. A. Magradze Lattice gauge theory by C. Michael Integrable models with boundary by R. I. Nepomechie Mathematical aspects of chiral gauge theories on the lattice by H. Neuberger The statistical entropy of black holes and the $AdS_3$ geometry by L. A. Pando Zayas Canonical treatment of regular Lagrangians with holonomic constraints as singular systems by E. M. Rabei Algebraic shape invariant models by C. Rasinariu, U. P. Sukhatme, and A. Gangopadhyaya Molecular configurations and Euclidean distance matrices by W. Rivera-Gallego Derivative expansion of the one-loop effective action in QED by I. A. Shovkovy Nonlinear generalizations of a 3-manifold's Dirac operator by C. H. Taubes Dynamical symmetry approach to quantum many-body problems by C.-L. Wu.
£70.30
MP-AMM American Mathematical An Invitation to Operator Theory
Book SynopsisPresents a comprehensive exposition of the theory of linear operators on Banach spaces and Banach lattices. This book offers a presentation that includes various developments in operator theory and draws together results that are spread over the vast literature. It contains over 600 exercises to help students master the material developed.Table of ContentsOdds and ends Basic operator theory Operators on $AL$- and $AM$-spaces Special classes of operators Integral operators Spectral properties Some special spectra Positive matrices Irreducible operators Invariant subspaces The Daugavet equation Bibliography Index.
£108.00
MP-AMM American Mathematical Geometry of Manifolds
Book SynopsisPresents the study of Riemannian manifolds through specializing the theory of connections on principle bundles and affine connections. This work emphasizes the geometry of Riemannian manifolds, so that the theorems of Hopf-Rinow, Hadamard-Cartan, and Cartan's local isometry theorem are included, but no elliptic operator theory.Table of ContentsManifolds Lie groups Fibre bundles Differential forms Connexions Affine connexions Riemannian manifolds Geodesics and complete Riemannian manifolds Riemannian curvature Immersions and the second fundamental form Second variation of arc length Theorems on differential equations Bibliography Subject index.
£54.90
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-AMM American Mathematical Modern Spherical Functions
Book SynopsisPresents an exposition of spherical functions on compact symmetric spaces, from the viewpoint of Cartan-Selberg. This title treats compact symmetric pairs, spherical representations for compact symmetric pairs, the fundamental groups of compact symmetric spaces, and the radial part of an invariant differential operator.Table of ContentsIntroduction Spherical functions Compact symmetric pairs Spherical functions on spheres and on complex projective spaces Appendix References Subject index Notation index.
£129.60
MP-AMM American Mathematical The Geometrization Conjecture
Book SynopsisTrade ReviewIn the introduction the authors give a good outline of the proof so the reader can catch the spirit of such a complex proof. In the course of proving the conjecture, the authors apply very difficult tools reviewed in the book. They give a good survey on Ricci flows with surgery on 3-dimensional manifolds and they discuss in details the properties of the Hausdorff–Gromov distance and the theory of Alexandrov spaces." - János Kincses, Acta Sci. Math.Table of Contents Introduction Geometric and analytic results for Ricci flow with surgery Ricci flow with surger Limits as t?? Local results valid for large time Proofs of the three propositions Locally volume collapsed 3-manifolds Introduction to part II The collapsing theorem Overview of the rest of the argument Basics of Gromov-Hausdorff convergence Basics of Alexandrov spaces 2-dimensional Alexandrov spaces 3-dimensional analogues The global result The equivariant case The equivariant case Bibliography Glossary of symbols Index
£72.90
MP-AMM American Mathematical Fixed Points
Book SynopsisPresents an exposition of fixed point theory. This work focuses on the problem of whether a closed interval, square, disk, or sphere has the fixed point property. It aims to show how fixed point theory uses combinatorial ideas related to decomposition of figures into distinct parts called faces, which adjoin each other in a regular fashion.Table of ContentsContinuous mappings of a closed interval and a square First combinatorial lemma Second combinatorial lemma, or walks through the rooms in a house Sperner's lemma Continuous mappings, homeomorphisms, and the fixed point property Compactness Proof of Brouwer's Theorem for a closed interval, the intermediate value theorem, and applications Proof of Brouwer's Theorem for a square The iteration method Retraction Continuous mappings of a circle, homotopy, and degree of a mapping Second definition of the degree of a mapping Continuous mappings of a sphere Lemma on equality of degrees.
£35.96
Taylor & Francis Ltd Topics on Continua Chapman HallCRC Pure and
Book SynopsisSpecialized as it might be, continuum theory is one of the most intriguing areas in mathematics. However, despite being popular journal fare, few books have thoroughly explored this interesting aspect of topology. In Topics on Continua, Sergio Macías, one of the field's leading scholars, presents four of his favorite continuum topics: inverse limits, Jones's set function T, homogenous continua, and n-fold hyperspaces, and in doing so, presents the most complete set of theorems and proofs ever contained in a single topology volume. Many of the results presented have previously appeared only in research papers, and some appear here for the first time. After building the requisite background and exploring the inverse limits of continua, the discussions focus on Professor Jones''s set function T and continua for which T is continuous. An introduction to topological groups and group actions lead to a proof of Effros''s Theorem, followed by a presentTable of ContentsPreliminaries, including an introduction to Product Topology. Inverse Limits and Related Topics. Jones Set Function T. A Theorem of E.G. Effros. Decomposition Theorems. n-Fold Hyperspaces. Questions.
£166.25
Cambridge University Press Lectures on Lagrangian Torus Fibrations
Book SynopsisThis book explains how to use simple 2-dimensional pictures to understand the geometry and topology of 4-dimensional spaces. These spaces are of relevance in Hamiltonian dynamics, in algebraic geometry, and in mathematical string theory. It is suitable for graduate students and researchers in geometry and topology.Trade Review'Lagrangian torus fibrations are an interesting source of examples in symplectic geometry, since their symplectic features are encoded by the geometry of certain half-dimensional base diagrams. Enriched by many pictures and exercises with solutions, this book provides an accessible and well-written introduction to this topic, which is of interest to a broad audience through its connections with integrable systems and algebraic geometry. This work will be appreciated by students and experts alike, since it fills a crucial gap in the literature by giving an excellent discussion of almost toric fibrations, which have attracted a lot of attention in recent years.' Felix Schlenk, Université de Neuchatel'This is a lucid and engaging introduction to the fascinating world of (almost) toric geometry, in which one can understand the properties of Lagrangian and symplectic submanifolds in four dimensions simply by drawing suitable two-dimensional diagrams. The book has many illustrations and intricate examples.' Dusa McDuff, Barnard College, Columbia UniversityTable of Contents1. The Arnold–Liouville theorem; 2. Lagrangian fibrations; 3. Global action-angle coordinates and torus actions; 4. Symplectic reduction; 5. Visible Lagrangian submanifolds; 6. Focus-focus singularities; 7. Examples of focus-focus systems; 8. Almost toric manifolds; 9. Surgery; 10. Elliptic and cusp singularities; A. Symplectic linear algebra; B. Lie derivatives; C. Complex projective spaces; D. Cotangent bundles; E. Moser's argument; F. Toric varieties revisited; G. Visible contact hypersurfaces and Reeb flows; H. Tropical Lagrangian submanifolds; I. Markov triples; J. Open problems; References; Index.
£28.49
CRC Press Map of the World
Book SynopsisCarl Friedrich Gauss, the foremost of mathematicians, was a land surveyor. Measuring and calculating geodetic networks on the curved Earth was the inspiration for some of his greatest mathematical discoveries. This is just one example of how mathematics and geodesy, the science and art of measuring and mapping our world, have evolved together throughout history.This text is for students and professionals in geodesy, land surveying, and geospatial science who need to understand the mathematics of describing the Earth and capturing her in maps and geospatial data: the discipline known as mathematical geodesy. Map of the World: An Introduction to Mathematical Geodesy aims to provide an accessible introduction to this area, presenting and developing the mathematics relating to maps, mapping, and the production of geospatial data. Described are the theory and its fundamental concepts, its application for processing, analyzing, transforming, and projecting geospatial data, and how these are used in producing charts and atlases. Also touched upon are the multitude of cross-overs into other sciences sharing in the adventure of discovering what our world really looks like.FEATURESâ Written in a fluid and accessible style, replete with exercises; adaptable for courses on different levels.â Suitable for students and professionals in the mapping sciences, but also for lovers of maps and map making.Trade Review"Map of the World: An Introduction to Mathematical Geodesy is organized, written and presented in an impressively accessible style that is replete with exercises -- making it highly adaptable textbook for curriculum courses on different levels. Especially and unreservedly recommended for students and professionals in the mapping sciences, Map of the World will prove to be an ideal and instructive source for non-specialist readers with an interest in maps and map making. While a critically important addition to college and university library collections, it should be noted for personal reading lists that Maps of the World is also available in a digital book format."—Midwest Book Review"This is a textbook covering mathematics applied to geodesy: the measuring and mapping of our ellipsoid spheroid earth that includes an overview of earth measurement and mapping back to remote times. The mathematics of describing the Earth through maps and geospatial data is covered from underpinnings to application. [. . .] This textbook, including some exercises (without solutions), is aimed at students and practitioners in geodesy, land surveying, and geospatial science. It is easy to see this as a reference work. [. . .] this is a concise review of the theory and development of coordinate reference systems."—Tom Schulte, MAA Reviews ". . .(T)his text, by a geodesist (Vermeer) and a mathematician (Rasila), focuses primarily on the mathematics enabling map projections, coordinate systems, and transformation of three-dimensional coordinate representations, ranging from Euclidean to Reimannian geometries. Although the geometry is beyond what most geography students would need to address, the detailed mathematics offers a bridge for integration of collaborative teaching appropriate for upper-level mathematics and physics students, with applications to both cartography and geophysics. Each chapter concludes with exercises that provide an opportunity for learning the explicit mathematics behind the calculation presented. Interesting historical anecdotes about mathematicians and the evolution of geodesy are also included throughout. Students and readers of mathematics and geophysics as well as scientists working in the interdisciplinary area of geodesy will appreciate this book."– Choice Review, C. A. Badurek, SUNY Cortland"Map of the World: An Introduction to Mathematical Geodesy is organized, written and presented in an impressively accessible style that is replete with exercises -- making it highly adaptable textbook for curriculum courses on different levels. Especially and unreservedly recommended for students and professionals in the mapping sciences, Map of the World will prove to be an ideal and instructive source for non-specialist readers with an interest in maps and map making. While a critically important addition to college and university library collections, it should be noted for personal reading lists that Maps of the World is also available in a digital book format."—Midwest Book Review"This is a textbook covering mathematics applied to geodesy: the measuring and mapping of our ellipsoid spheroid earth that includes an overview of earth measurement and mapping back to remote times. The mathematics of describing the Earth through maps and geospatial data is covered from underpinnings to application. [. . .] This textbook, including some exercises (without solutions), is aimed at students and practitioners in geodesy, land surveying, and geospatial science. It is easy to see this as a reference work. [. . .] this is a concise review of the theory and development of coordinate reference systems."—Tom Schulte, MAA Reviews Table of Contents1. A Brief History of Mapping. 2. Popular Conformal Map Projections. 3. The Complex Plane and Conformal Mappings. 4. Complex Analysis. 5. Conformal Mappings. 6. Transversal Mercator Projections. 7. Sperical Trigonometry. 8. The Geometry of the Ellipsoid of Revolution. 9. Three-dimensional Co-ordinates and Transformations. 10. Co-ordinate Reference Systems. 11. Co-ordinates of Heaven and Earth. 12. The Orbital Motion of Satellites. 13. The Surface Theory of Gauss. 14. Riemann Surfaces and Charts. 15. Map Projections in the Light of Surface Theory. 16. Appendices
£37.99
Taylor & Francis Ltd Differential Geometry and Its Visualization
Book SynopsisDifferential Geometry and Its Visualization is suitable for graduate level courses in differential geometry, serving both students and teachers. It can also be used as a supplementary reference for research in mathematics and the natural and engineering sciences.Differential geometry is the study of geometric objects and their properties using the methods of mathematical analysis. The classical theory of curves and surfaces in three-dimensional Euclidean space is presented in the first three chapters. The abstract and modern topics of tensor algebra, Riemannian spaces and tensor analysis are studied in the last two chapters. A great number of illustrating examples, visualizations and genuine figures created by the authors' own software are included to support the understanding of the presented concepts and results, and to develop an adequate perception of the shapes of geometric objects, their properties and the relations between them.FeatuTable of Contents1. Curves in Three–dimensional Euclidean Space. 1.1. Points and Vectors. 1.2. Vector–valued Functions of a Real Variable. 1.3. The General Concept of Curves. 1.4. Some Examples of Planar Curves. 1.5. The Arc Length of a Curve. 1.6. The Vectors of the Trihedron of a Curve. 1.7. Frenet’s Formulae. 1.8. The Geometric Significance of Curvature and Torsion. 1.9. Osculating Circles and Spheres. 1.10. Involutes and Evolutes. 1.11. The Fundamental Theorem of Curves. 1.12. Lines of Constant Slope. 1.13. Spherical Images of a Curve. 2. Surfaces in Three–dimensional Euclidean Space. 2.1. Surfaces and Curves on Surfaces. 2.2. The Tangent Planes and Normal Vectors of a Surface. 2.3. The Arc Length, Angles and Gauss’s First Fundamental Coefficients. 2.4. the Curvature of Curves on Surfaces, Geodesic and Normal Curvature. 2.5. The Normal, Principal, Gaussian and Mean Curvature. 2.6. The Shape of a Surface in the Neighbourhood of a Point. 2.7. Dupin’s Indicatrix. 2.8. Lines of Curvature and Asymptotic Lines. 2.9. Triple Orthogonal Systems. 2.10. the Weingarten Equations. 3. The Intrinsic Geometry of Surfaces. 3.1. the Christoffel Symbols. 3.2. Geodesic Lines. 3.3. Geodesic Lines on Surfaces with Orthogonal Parameters. 3.4. Geodesic Lines on Surfaces of Revolution. 3.5. the Minimum Property of Geodesic Lines. 3.6. Orthogonal and Geodesic Parameters. 3.7. Levi–civitá Parallelism. 3.8. Theorema Egregium. 3.9. Maps Between Surfaces. 3.10. the Gauss–bonnet Theorem. 3.11. Minimal Surfaces. 4. Tensor Algebra and Riemannian Geometry. 4.1. Differentiable Manifolds. 4.2. Transformation of Bases. 4.3. Linear Functionals and Dual Spaces. 4.4. Tensors of Second Order. 4.5. Symmetric Bilinear Forms and Inner Products. 4.6. Tensors of Arbitary Order. 4.7. Symmetric and Anti–symmetric Tensors. 4.8. Riemann Spaces. 4.9. the Christoffel Symbols. 5. Tensor Analysis. 5.1. Covariant Differentiation. 5.2. the Covariant Derivative of an (R, S)–tensor. 5.3. the Interchange of Order for Covariant Differentiation and Ricci’s Identity. 5.4. Bianchi’s Identities for the Covariant Derivative of the Tensors of Curvature. 5.5. Beltrami’s Differentiators. 5.6. a Geometric Meaning of the Covariant Differentiation, the Levi–civitá Parallelism. 5.7. The Fundamental Theorem for Surfaces. 5.8. A Geometric Meaning of the Riemann Tensor of Curvature. 5.9. Spaces With Vanishing Tensor of Curvature. 5.10. An Extension of Frenet’s Formulae. 5.11. Riemann Normal Coordinates and the Curvature of Spaces.
£84.99
Cambridge University Press Manifolds Tensors and Forms
Book SynopsisProviding a succinct yet comprehensive treatment of the essentials of modern differential geometry and topology, this book's clear prose and informal style make it accessible to advanced undergraduate and graduate students in mathematics and the physical sciences. It features over 250 detailed exercises and discusses a variety of applications.Table of ContentsPreface; 1. Linear algebra; 2. Multilinear algebra; 3. Differentiation on manifolds; 4. Homotopy and de Rham cohomology; 5. Elementary homology theory; 6. Integration on manifolds; 7. Vector bundles; 8. Geometric manifolds; 9. The degree of a smooth map; Appendixes; References; Index.
£64.99
Cambridge University Press Monoidal Topology A Categorical Approach to Order Metric and Topology 153 Encyclopedia of Mathematics and its Applications Series Number 153
Book SynopsisMonoidal Topology describes an active research area that, after various past proposals on how to axiomatize 'spaces' in terms of convergence, began to emerge at the beginning of the millennium. It combines Barr's relational presentation of topological spaces in terms of ultrafilter convergence with Lawvere's interpretation of metric spaces as small categories enriched over the extended real half-line. Hence, equipped with a quantale V (replacing the reals) and a monad T (replacing the ultrafilter monad) laxly extended from set maps to V-valued relations, the book develops a categorical theory of (T,V)-algebras that is inspired simultaneously by its metric and topological roots. The book highlights in particular the distinguished role of equationally defined structures within the given lax-algebraic context and presents numerous new results ranging from topology and approach theory to domain theory. All the necessary pre-requisites in order and category theory are presented in the book.Table of ContentsPreface; 1. Introduction Robert Lowen and Walter Tholen; 2. Monoidal structures Gavin J. Seal and Walter Tholen; 3. Lax algebras Dirk Hofmann, Gavin J. Seal and Walter Tholen; 4. Kleisli monoids Dirk Hofmann, Robert Lowen, Rory Lucyshyn-Wright and Gavin J. Seal; 5. Lax algebras as spaces Maria Manuel Clementino, Eva Colebunders and Walter Tholen; Bibliography; Tables; Index.
£133.95
Cambridge University Press Mathematical Methods for Physics
Book SynopsisThis detailed yet accessible text introduces the advanced mathematical methods at the core of theoretical physics. Based on a course for senior undergraduate students of physics, it is written in a clear, pedagogical style and would also be valuable to students in other areas of science and engineering.Trade Review'The recent explosive development of topological quantum matter requires a deep systematic understanding of modern mathematics. Quantum many-body entanglement in topological quantum matter is a new phenomenon that requires new mathematical language to describe. This is a rare book that provides systematic and in-depth coverage of some of the most important mathematical concepts, such as groups, geometry, topology and algebra, among others. Many abstract mathematical notions are explained in an easy, explicit fashion. This is an in-depth, friendly book on modern mathematics. Very timely and highly recommended.' Xiao-Gang Wen, Massachusetts Institute of TechnologyTable of Contents1. Introduction; 2. Group theory; 3. Representation theory of groups; 4. Differentiable manifolds; 5. Riemannian geometry; 6. Semisimple Lie algebras and their unitary representations; Appendix A; References; Index.
£44.99
Cambridge University Press Electricity and Magnetism for Mathematicians
Book SynopsisThis text is an introduction to some of the mathematical wonders of Maxwell''s equations. These equations led to the prediction of radio waves, the realization that light is a type of electromagnetic wave, and the discovery of the special theory of relativity. In fact, almost all current descriptions of the fundamental laws of the universe can be viewed as deep generalizations of Maxwell''s equations. Even more surprising is that these equations and their generalizations have led to some of the most important mathematical discoveries of the past thirty years. It seems that the mathematics behind Maxwell''s equations is endless. The goal of this book is to explain to mathematicians the underlying physics behind electricity and magnetism and to show their connections to mathematics. Starting with Maxwell''s equations, the reader is led to such topics as the special theory of relativity, differential forms, quantum mechanics, manifolds, tangent bundles, connections, and curvature.Table of Contents1. A brief history; 2. Maxwell's equations; 3. Electromagnetic waves; 4. Special relativity; 5. Mechanics and Maxwell's equations; 6. Mechanics, Lagrangians, and the calculus of variations; 7. Potentials; 8. Lagrangians and electromagnetic forces; 9. Differential forms; 10. The Hodge * operator; 11. The electromagnetic two-form; 12. Some mathematics needed for quantum mechanics; 13. Some quantum mechanical thinking; 14. Quantum mechanics of harmonic oscillators; 15. Quantizing Maxwell's equations; 16. Manifolds; 17. Vector bundles; 18. Connections; 19. Curvature; 20. Maxwell via connections and curvature; 21. The Lagrangian machine, Yang–Mills, and other forces.
£36.99
Cambridge University Press Geometry of Quantum States
Book SynopsisQuantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and KochenSpecker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings'' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers interTrade Review'True story: A few years ago my daughter took a break from her usual question, 'Dad, what is your favourite colour?' and asked instead, 'What is your favourite shape?' I was floored! 'What a wonderful question; my favourite shape is Hilbert space!' 'What does it look like?' she asked. My answer: 'I don't know! But every day when I go to work, that's what I think about.' What I was speaking of, of course, is the geometry of quantum-state space. It is as much a mystery today as it was those years ago, and maybe more so as we learn to focus on its most key and mysterious features. This book, the worn first-edition of which I've had on my shelf for 11 years, is the indispensable companion for anyone's journey into that exotic terrain. Beyond all else, I am thrilled about the inclusion of two new chapters in the new edition, one of which I believe goes to the very heart of the meaning of quantum theory.' Christopher A. Fuchs, University of Massachusetts, Boston'The quantum world is full of surprises as is the mathematical theory that describes it. Bengtsson and Życzkowski prove to be expert guides to the deep mathematical structure that underpins quantum information science. Key concepts such as multipartite entanglement and quantum contextuality are discussed with extraordinary clarity. A particular feature of this new edition is the treatment of SIC generalised measurements and the curious bridge they make between quantum physics and number theory.' Gerard J. Milburn, University of QueenslandPraise for the first edition: 'Geometry of Quantum States can be considered an indispensable item on a bookshelf of everyone interest in quantum information theory and its mathematical background.' Miłosz Michalski, editor of Open Systems and Information DynamicsPraise for the first edition: 'Bengtsson's and Zyczkowski's book is an artful presentation of the geometry that lies behind quantum theory … the authors collect, and artfully explain, many important results scattered throughout the literature on mathematical physics. The careful explication of statistical distinguishability metrics (Fubini-Study and Bures) is the best I have read.' Gerard Milburn, University of QueenslandTable of ContentsPreface; 1. Convexity, colours, and statistics; 2. Geometry of probability distributions; 3. Much ado about spheres; 4. Complex projective spaces; 5. Outline of quantum mechanics; 6. Coherent states and group actions; 7. The stellar representation; 8. The space of density matrices; 9. Purification of mixed quantum states; 10. Quantum operations; 11. Duality: maps versus states; 12. Discrete structures in Hilbert space; 13. Density matrices and entropies; 14. Distinguishability measures; 15. Monotone metrics and measures; 16. Quantum entanglement; 17. Multipartite entanglement; Appendix 1. Basic notions of differential geometry; Appendix 2. Basic notions of group theory; Appendix 3. Geometry – do it yourself; Appendix 4. Hints and answers to the exercises; Bibliography; Index.
£51.99
Cambridge University Press Topological Data Analysis with Applications
Book SynopsisThe continued and dramatic rise in the size of data sets has meant that new methods are required to model and analyze them. This timely account introduces topological data analysis (TDA), a method for modeling data by geometric objects, namely graphs and their higher-dimensional versions: simplicial complexes. The authors outline the necessary background material on topology and data philosophy for newcomers, while more complex concepts are highlighted for advanced learners. The book covers all the main TDA techniques, including persistent homology, cohomology, and Mapper. The final section focuses on the diverse applications of TDA, examining a number of case studies drawn from monitoring the progression of infectious diseases to the study of motion capture data. Mathematicians moving into data science, as well as data scientists or computer scientists seeking to understand this new area, will appreciate this self-contained resource which explains the underlying technology and how it can be used.Table of ContentsPart I. Background: 1. Introduction; 2. Data; Part II. Theory: 3. Topology; 4. Shape of data; 5. Structures on spaces of barcodes; Part III. Practice: 6. Case studies; References; Index.
£39.99
CRC Press The Shape of Space
Book SynopsisThe Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spacesâstretching studentsâ minds as they learn to visualize new possibilities for the shape of our universe.Written by a master expositor, leading researcher in the field, and MacArthur Fellow, its informal exposition and engaging exercises appeal to an exceptionally broad audience, from liberal arts students to math undergraduate and graduate students looking for a clear intuitive understanding to supplement more formal texts, and even to laypeople seeking an entertaining self-study book to expand their understanding of space.Features of the Third Edition: Full-color figures throughout Picture proofs have replaced algebraic proofs Simpler handles-and-crosscaps approach to surfaces Updated discussiTable of ContentsPart I Surfaces and Three-Manifolds Flatland Gluing Vocabulary Orientability Classification of Surfaces Products Flat Manifolds Orientability vs. Two-Sidedness Part II Geometries on Surfaces The Sphere The Hyperbolic Plane Geometries on Surfaces Gauss-Bonnet Formula and Euler Number Part III Geometries on Three-Manifolds Four-Dimensional Space The Hypersphere Hyperbolic Space Geometries on Three-Manifolds I Bundles Geometries on Three-Manifolds II Part IV The Universe The Universe The History of Space Appendix A: Answers Appendix B: Bibliography Appendix C: Conway’s ZIP Proof
£128.25
Springer New York Topological Methods in Group Theory
Book SynopsisThis book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field.Trade ReviewFrom the reviews:"The author of this book has done a great service to the geometric group theory community by writing a very useful and well-written book on many topics in geometric group theory that every neophyte and researcher in the field should know. … This book is suitable as a textbook for a graduate course, with many good examples and exercises. The reviewer highly recommends this book as a basic reference book for topological methods in group theory." (John G. Ratcliffe, Mathematical Reviews, Issue 2008 j)"This is an interesting book on the interplay between algebraic topology and the theory of infinite discrete groups written for graduate students and group theorists who need to learn more in geometric and homological group theory. … It is a beautiful text in algebraic topology, with modern topics and which points the reader towards new research directions." (Corina Mohorianu, Zentralblatt MATH, Vol. 1142, 2008)“This book is an invaluable resource for anyone wanting a deep understanding of topics related to the ends of groups. … there is a good deal of material in this book that does not appear anywhere else in the literature. … Geoghegan’s book provides a well-presented, concrete development of geometric group theory focused on a topological approach.” (John Meier, Bulletin of the American Mathematical Society, July, 2012)Table of ContentsAlgebraic Topology for Group Theory.- CW Complexes and Homotopy.- Cellular Homology.- Fundamental Group and Tietze Transformation.- Some Techniques in Homotopy Theory.- Elementary Geometric Topology.- Finiteness Properties of Groups.- The Borel Construction and Bass-Serre Theory.- Topological Finiteness Properties and Dimension of Groups.- Homological Finiteness Properties of Groups.- Finiteness Properties of Some Important Groups.- Locally Finite Algebraic Topology for Group Theory.- Locally Finite CW Complexes and Proper Homotopy.- Locally Finite Homology.- Cohomology of CW Complexes.- Topics in the Cohomology of Infinite Groups.- Cohomology of Groups and Ends of Covering Spaces.- Filtered Ends of Pairs of Groups.- Poincaré Duality in Manifolds and Groups.- Homotopical Group Theory.- The Fundamental Group At Infinity.- Higher homotopy theory of groups.- Three Essays.- Three Essays.
£52.24
