Topology Books
New Academic Science Ltd Metric Spaces and Complex Analysis
Book Synopsis
£30.00
World Scientific Publishing Co Pte Ltd Virtual Knots: The State Of The Art
Book SynopsisThe book is the first systematic research completely devoted to a comprehensive study of virtual knots and classical knots as its integral part. The book is self-contained and contains up-to-date exposition of the key aspects of virtual (and classical) knot theory.Virtual knots were discovered by Louis Kauffman in 1996. When virtual knot theory arose, it became clear that classical knot theory was a small integral part of a larger theory, and studying properties of virtual knots helped one understand better some aspects of classical knot theory and encouraged the study of further problems. Virtual knot theory finds its applications in classical knot theory. Virtual knot theory occupies an intermediate position between the theory of knots in arbitrary three-manifold and classical knot theory.In this book we present the latest achievements in virtual knot theory including Khovanov homology theory and parity theory due to V O Manturov and graph-link theory due to both authors. By means of parity, one can construct functorial mappings from knots to knots, filtrations on the space of knots, refine many invariants and prove minimality of many series of knot diagrams.Graph-links can be treated as “diagramless knot theory”: such “links” have crossings, but they do not have arcs connecting these crossings. It turns out, however, that to graph-links one can extend many methods of classical and virtual knot theories, in particular, the Khovanov homology and the parity theory.Table of ContentsBasic Definitions and Notions; Virtual Knots and Three-Dimensional Topology; Quandles (Distributive Groupoids) in Virtual Knot Theory; The Jones Polynomial. Atoms; Khovanov Homology; Virtual Braids; Vassiliev's Invariants; Parity in Knot Theory. Free-Knots. Cobordisms; Theory of Graph-Links.
£999.99
Clarendon Press Projective Geometries Over Finite Fields Oxford Mathematical Monographs
Book SynopsisThis is a complete reworking of the out-of-print first volume of a three-volume treatise on finite projective spaces. There are numerous articles in journals, but this is the only extended work in the area. It also includes a comprehensive bibliography of more than 3000 items.Trade ReviewThe first edition of this work appeared in 1979, and was immediately recognized as an outstanding contribution to the field of finite geometry; the present volume is a complete revision of the earlier work...The book can serve as the text for a basic course...or as a detailed reference work for all topics in spaces of dimension two...The work is an indispensable aid to all workers in finite geometry, from beginning students to advanced researchers. * Short Book Reviews *...A complete reworking [of the first edition]. As before, the volume is concisely but clearly written, and contains a wealth of interesting material...the new trilogy, comprising the 1998, 1986 and 1991 volumes, looks set to be the standard reference work on projective spaces over finite fields for many years to come. * Bulletin of the London Mathematical Society *'Snap it up !' Bulletin London mathematical SocietyTable of Contents1. Finite fields ; 2. Projective spaces and algebraic varieties ; 3. Subspaces ; 4. Partitions ; 5. Canonical forms for varieties and polarities ; 6. The line ; 7. First properties of the plane ; 8. Ovals ; 9. Arithmetic of arcs of degree two ; 10. Arcs in ovals ; 11. Cubic curves ; 12. Arcs of higher degree ; 13. Blocking sets ; 14. Small planes ; Appendix ; Notation ; References
£227.25
Oxford University Press Groups and Geometry
Book SynopsisAvailable for the first time in published form, Groups and Geometry presents the Oxford Mathematical Institute notes for undergraduates and first year postgraduates. The content is guided by the Oxford syllabus but includes much more material than is included on the syllabus. This book is about the measurement of symmetry: covering groups and geometry with the symbiotic relationship between the two more than justifying the union. A number of exercises are included in this sylish text to help the reader gain a full understanding of this branch of mathematics.Trade Review'develops a comprehensive group-theoretic approach to affine, projective and inversive geometry ... It ends with a fascinating chapter on the group theory behind the Rubik cube.' Ian Stewart, New Scientist'Both parts contain a number of exercises that will be invaluable to any reader wishing to gain a fuller understanding of this area of mathematics.' Extrait de L'Enseignement Mathematique, T. 40 1994The book can be recommended warmly for any interested reader. "Monatshefte fur Mathematik No.3 1996.delightful book ... The group theory is directed towards group actions, but all the basic material is there. * Mathematika, 41 (1994) *Table of Contents1. A survey of some group theory ; 2. A menagerie of groups ; 3. Actions of groups ; 4. A garden of G-spaces ; 5. Transitivity and orbits ; 6. The classification of transitive G-spaces ; 7. G-morphisms ; 8. Group actions in group theory ; 9. Actions count ; 10. Geometry: an introduction ; 11. The axiomatisation of geometry ; 12. Affine geometry ; 13. Projective geometry ; 14. Euclidean geometry ; 15. Finite groups of isometries ; 16. Complex numbers and quaternions ; 17. Inversive geometry ; 18. Topological considerations ; 19. The groups theory of Rubik's magic cube ; Index
£74.10
Oxford University Press Topology A Geometric Approach
Book SynopsisThis new-in-paperback introduction to topology emphasizes a geometric approach with a focus on surfaces. A primary feature is a large collection of exercises and projects, which fosters a teaching style that encourages the student to be an active class participant. A wide range of material at different levels supports flexible use of the book for a variety of students. Part I is appropriate for a one-semester or two-quarter course, and Part II (which is problem based) allows the book to be used for a year-long course which supports a variety of syllabuses.The over 750 exercises range from simple checks of omitted details in arguments, to reinforce the material and increase student involvement, to the development of substantial theorems that have been broken into many steps. The style encourages an active student role. Solutions to selected exercises are included as an appendix, with solutions to all exercises available to the instructor on a companion website.Trade ReviewIdeas are introduced in a geometric context and development of material always maintains its excitement. Long live mathematics! * Peter Ruane, MAA Reviews *Table of ContentsPART I: A GEOMETRIC INTRODUCTION TO TOPOLOGY; PART II: COVERING SPACES, CW COMPLEXES AND HOMOLOGY
£79.80
Springer Topology of Gauge Fields and Condensed Matter
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£123.49
Springer New York Foundations of Hyperbolic Manifolds
Book SynopsisThis heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds.Trade ReviewFrom the reviews of the second edition: "Designed to be useful as both textbook and a reference, this book renders a real service to the mathematical community by putting together the tools and prerequisites needed to enter the territory of Thurston’s formidable theory of hyperbolic 3-mainfolds … . Every chapter is followed by historical notes, with attributions to the relevant literature, both of the originators of the idea present in the chapter and of modern presentation thereof. The bibliography contains 463 entries." (Victor V. Pambuccian, Zentralblatt MATH, Vol. 1106 (8), 2007)Table of ContentsEuclidean Geometry.- Spherical Geometry.- Hyperbolic Geometry.- Inversive Geometry.- Isometries of Hyperbolic Space.- Geometry of Discrete Groups.- Classical Discrete Groups.- Geometric Manifolds.- Geometric Surfaces.- Hyperbolic 3-Manifolds.- Hyperbolic n-Manifolds.- Geometrically Finite n-Manifolds.- Geometric Orbifolds.
£49.99
Springer A Topological Picturebook
Book SynopsisAims to encourage mathematicians to illustrate their work and to help artists understand the ideas expressed by such drawings. This book explains the graphic design of illustrations from Thurston's world of low-dimensional geometry and topology. It presents the principles of linear and aerial perspective from the viewpoint of projective geometry.Trade ReviewFrom the reviews: "I was very pleasantly surprised when I opened the book. … this is really a much richer book. Indeed, the approach it offers to drawing can have a significant impact on how we teach and think about mathematics. … If you are good at visualization and illustration, this book can help you become better yet. … this will give you concrete and specific suggestions for developing your skills. If you just appreciate skillful drawing and illustration, this book deserves a look." (William J. Satzer, MathDL, December, 2006) "This book is a drawing manual for mathematicians. It is written by a great expert in the subject … . The author explained his techniques of drawing and of shading pictures, he explains when to use perspective and when not to use it, and so on. The numerous illustrations that are contained in this book as examples for drawing of mathematical objects are delightful … . This book is unique in the mathematical literature, and the present second printing is most welcome." (Athanase Papadopoulos, Zentralblatt MATH, Vol. 1105 (7), 2007)Table of Contents1 Descriptive Topology.- 2 Methods and Media.- 3 Pictures in Perspective.- 4 The Impossible Tribar.- 5 Shadows from Higher Dimension.- 6 Sphere Eversions.- 7 Group Pictures.- 8 The Figure Eight Knot.- Postscript.
£54.99
Springer Semiparallel Submanifolds in Space Forms Envelopes of Symmetric Orbits Springer Monographs in Mathematics
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£85.49
Springer Measure Topology and Fractal Geometry
Book SynopsisFractal Examples.- Metric Topology.- Topological Dimension.- Self-Similarity.- Measure Theory.- Fractal Dimension.- Additional Topics.Trade ReviewFrom the reviews of the second edition: "As a non-specialist, I found this book very helpful. It gave me a better understanding of the nature of fractals, and of the technical issues involved in the theory. I think it will be valuable as a textbook for undergraduate students in mathematics, and also for researchers wanting to learn fractal geometry from scratch. The material is well-organized and the proofs are clear; the abundance of examples is an asset for a book on measure theory and topology." (Fabio Mainardi, MathDL, February, 2008) "This is the second edition of a well-known textbook in the field … . The book may serve as a textbook for a one-semester (advanced) undergraduate course in mathematics. … the book is also suitable for readers interested in theoretical fractal geometry coming from other disciplines (e.g. physics, computer sciences) with a basic knowledge of mathematics. The presentation of the material is appealing … and the style is clear and motivating. … the book will remain as a standard reference in the field." (José-Manuel Rey, Zentralblatt MATH, Vol. 1152, 2009)Table of ContentsFractal Examples.- Metric Topology.- Topological Dimension.- Self-Similarity.- Measure Theory.- Fractal Dimension.- Additional Topics.
£35.14
Springer New York Stable Mappings and Their Singularities 14 Graduate Texts in Mathematics
Book SynopsisThe study of stable singularities is based on the now classical theories of Hassler Whitney, who determined the generic singularities (or lack of them) of Rn ~ Rm (m ~ 2n - 1) and R2 ~ R2, and Marston Morse, for mappings who studied these singularities for Rn ~ R.Table of ContentsI: Preliminaries on Manifolds.- §1. Manifolds.- §2. Differentiable Mappings and Submanifolds.- §3. Tangent Spaces.- §4. Partitions of Unity.- §5. Vector Bundles.- §6. Integration of Vector Fields.- II: Transversality.- §1. Sard’s Theorem.- §2. Jet Bundles.- §3. The Whitney C? Topology.- §4. Transversality.- §5. The Whitney Embedding Theorem.- §6. Morse Theory.- §7. The Tubular Neighborhood Theorem.- III: Stable Mappings.- §1. Stable and Infinitesimally Stable Mappings.- §2. Examples.- §3. Immersions with Normal Crossings.- §4. Submersions with Folds.- IV: The Malgrange Preparation Theorem.- §1. The Weierstrass Preparation Theorem.- §2. The Malgrange Preparation Theorem.- §3. The Generalized Malgrange Preparation Theorem.- V: Various Equivalent Notions of Stability.- §1. Another Formulation of Infinitesimal Stability.- §2. Stability Under Deformations.- §3. A Characterization of Trivial Deformations.- §4. Infinitesimal Stability => Stability.- §5. Local Transverse Stability.- §6. Transverse Stability.- §7. Summary.- VI: Classification of Singularities, Part I: The Thom-Boardman Invariants.- §1. The Sr Classification.- §2. The Whitney Theory for Generic Mappings between 2-Manifolds.- §3. The Intrinsic Derivative.- §4. The Sr,s Singularities.- §5. The Thom-Boardman Stratification.- §6. Stable Maps Are Not Dense.- VII: Classification of Singularities, Part II: The Local Ring of a Singularity.- §1. Introduction.- §2. Finite Mappings.- §3. Contact Classes and Morin Singularities.- §4. Canonical Forms for Morin Singularities.- §5. Umbilics.- §6. Stable Mappings in Low Dimensions.- §A. Lie Groups.- Symbol Index.
£71.24
Springer New York Differential Topology
Book SynopsisPresents a comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology.Trade ReviewM.W. Hirsch Differential Topology "A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology. Newly introduced concepts are usually well motivated, and often the historical development of an idea is described. There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text. "—MATHEMATICAL REVIEWSTable of Contents1 : Manifolds and Maps.- 0. Submanifolds of ?n+k.- 1. Differential Structures.- 2. Differentiable Maps and the Tangent Bundle.- 3. Embeddings and Immersions.- 4. Manifolds with Boundary.- 5. A Convention.- 2 : Function Spaces.- 1. The Weak and Strong Topologies on Cr(M, N).- 2. Approximations.- 3. Approximations on ?-Manifolds and Manifold Pairs.- 4. Jets and the Baire Property.- 5. Analytic Approximations.- 3 : Transversality.- 1. The Morse-Sard Theorem.- 2. Transversality.- 4 : Vector Bundles and Tubular Neighborhoods.- 1. Vector Bundles.- 2. Constructions with Vector Bundles.- 3. The Classification of Vector Bundles.- 4. Oriented Vector Bundles.- 5. Tubular Neighborhoods.- 6. Collars and Tubular Neighborhoods of Neat Submanifolds.- 7. Analytic Differential Structures.- 5 : Degrees, Intersection Numbers, and the Euler Characteristic.- 1. Degrees of Maps.- 2. Intersection Numbers and the Euler Characteristic.- 3. Historical Remarks.- 6 : Morse Theory.- 1. Morse Functions.- 2. Differential Equations and Regular Level Surfaces.- 3. Passing Critical Levels and Attaching Cells.- 4. CW-Complexes.- 7 : Cobordism.- 1. Cobordism and Transversality.- 2. The Thorn Homomorphism.- 8 : Isotopy.- 1. Extending Isotopies.- 2. Gluing Manifolds Together.- 3. Isotopies of Disks.- 9 : Surfaces.- 1. Models of Surfaces.- 2. Characterization of the Disk.- 3. The Classification of Compact Surfaces.
£59.99
Springer New York Linear Topological Spaces 36 Graduate Texts in Mathematics
£27.99
Springer Lecture Notes on Elementary Topology and Geometry
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£54.99
Springer Counterexamples in Topology
Book SynopsisI Basic Definitions.- 1. General Introduction.- 2. Separation Axioms.- 3. Compactness.- 4. Connectedness.- 5. Metric Spaces.- II Counterexamples.- III Metrization Theory.- Conjectures and Counterexamples.- IV Appendices.- Special Reference Charts.- Separation Axiom Chart.- Compactness Chart.- Paracompactness Chart.- Connectedness Chart.- Disconnectedness Chart.- Metrizability Chart.- General Reference Chart.- Problems.- Notes.Table of ContentsI Basic Definitions.- 1. General Introduction.- Limit Points.- Closures and Interiors.- Countability Properties.- Functions.- Filters.- 2. Separation Axioms.- Regular and Normal Spaces.- Completely Hausdorff Spaces.- Completely Regular Spaces.- Functions, Products, and Subspaces.- Additional Separation Properties.- 3. Compactness.- Global Compactness Properties.- Localized Compactness Properties.- Countability Axioms and Separability.- Paracompactness.- Compactness Properties and Ti Axioms.- Invariance Properties.- 4. Connectedness.- Functions and Products.- Disconnectedness.- Biconnectedness and Continua.- 5. Metric Spaces.- Complete Metric Spaces.- Metrizability.- Uniformities.- Metric Uniformities.- II Counterexamples.- 1. Finite Discrete Topology.- 2. Countable Discrete Topology.- 3. Uncountable Discrete Topology.- 4. Indiscrete Topology.- 5. Partition Topology.- 6. Odd-Even Topology.- 7. Deleted Integer Topology.- 8. Finite Particular Point Topology.- 9. Countable Particular Point Topology.- 10. Uncountable Particular Point Topology.- 11. Sierpinski Space.- 12. Closed Extension Topology.- 13. Finite Excluded Point Topology.- 14. Countable Excluded Point Topology.- 15. Uncountable Excluded Point Topology.- 16. Open Extension Topology.- 17. Either-Or Topology.- 18. Finite Complement Topology on a Countable Space.- 19. Finite Complement Topology on an Uncountable Space.- 20. Countable Complement Topology.- 21. Double Pointed Countable Complement Topology.- 22. Compact Complement Topology.- 23. Countable Fort Space.- 24. Uncountable Fort Space.- 25. Fortissimo Space.- 26. Arens-Fort Space.- 27. Modified Fort Space.- 28. Euclidean Topology.- 29. The Cantor Set.- 30. The Rational Numbers.- 31. The Irrational Numbers.- 32. Special Subsets of the Real Line.- 33. Special Subsets of the Plane.- 34. One Point Compactification Topology.- 35. One Point Compactification of the Rationals.- 36. Hilbert Space.- 37. Fréchet Space.- 38. Hilbert Cube.- 39. Order Topology.- 40. Open Ordinal Space [0,?) (? < ?).- 41. Closed Ordinal Space [0,?] (? < ?).- 42. Open Ordinal Space [0,?).- 43. Closed Ordinal Space [0,?].- 44. Uncountable Discrete Ordinal Space.- 45. The Long Line.- 46. The Extended Long Line.- 47. An Altered Long Line.- 48. Lexicographic Ordering on the Unit Square.- 49. Right Order Topology.- 50. Right Order Topology on R.- 51. Right Half-Open Interval Topology.- 52. Nested Interval Topology.- 53. Overlapping Interval Topology.- 54. Interlocking Interval Topology.- 55. Hjalmar Ekdal Topology.- 56. Prime Ideal Topology.- 57. Divisor Topology.- 58. Evenly Spaced Integer Topology.- 59. The p-adic Topology on Z.- 60. Relatively Prime Integer Topology.- 61. Prime Integer Topology.- 62. Double Pointed Reals.- 63. Countable Complement Extension Topology.- 64. Smirnov’s Deleted Sequence Topology.- 65. Rational Sequence Topology.- 66. Indiscrete Rational Extension of R.- 67. Indiscrete Irrational Extension of R.- 68. Pointed Rational Extension of R.- 69. Pointed Irrational Extension of R.- 70. Discrete Rational Extension of R.- 71. Discrete Irrational Extension of R.- 72. Rational Extension in the Plane.- 73. Telophase Topology.- 74. Double Origin Topology.- 75. Irrational Slope Topology.- 76. Deleted Diameter Topology.- 77. Deleted Radius Topology.- 78. Half-Disc Topology.- 79. Irregular Lattice Topology.- 80. Arens Square.- 81. Simplified Arens Square.- 82. Niemytzki’s Tangent Disc Topology.- 83. Metrizable Tangent Disc Topology.- 84. Sorgenfrey’s Half-Open Square Topology.- 85. Michael’s Product Topology.- 86. Tychonoff Plank.- 87. Deleted Tychonoff Plank.- 88. Alexandroff Plank.- 89. Dieudonne Plank.- 90. Tychonoff Corkscrew.- 91. Deleted Tychonoff Corkscrew.- 92. Hewitt’s Condensed Corkscrew.- 93. Thomas’ Plank.- 94. Thomas’ Corkscrew.- 95. Weak Parallel Line Topology.- 96. Strong Parallel Line Topology.- 97. Concentric Circles.- 98. Appert Space.- 99. Maximal Compact Topology.- 100. Minimal Hausdorff Topology.- 101. Alexandroff Square.- 102. ZZ.- 103. Uncountable Products of Z+.- 104. Baire Product Metric on Rw.- 105. II.- 106. [0,?) × II.- 107. Helly Space.- 108. C[0,1].- 109. Box Product Topology on Rw.- 110. Stone-?ech Compactification.- 111. Stone-?ech Compactification of the Integers.- 112. Novak Space.- 113. Strong Ultrafilter Topology.- 114. Single Ultrafilter Topology.- 115. Nested Rectangles.- 116. Topologist’s Sine Curve.- 117. Closed Topologist’s Sine Curve.- 118. Extended Topologist’s Sine Curve.- 119. The Infinite Broom.- 120. The Closed Infinite Broom.- 121. The Integer Broom.- 122. Nested Angles.- 123. The Infinite Cage.- 124. Bernstein’s Connected Sets.- 125. Gustin’s Sequence Space.- 126. Roy’s Lattice Space.- 127. Roy’s Lattice Subspace.- 128. Cantor’s Leaky Tent.- 129. Cantor’s Teepee.- 130. A Pseudo-Arc.- 131. Miller’s Biconnected Set.- 132. Wheel without Its Hub.- 133. Tangora’s Connected Space.- 134. Bounded Metrics.- 135. Sierpinski’s Metric Space.- 136. Duncan’s Space.- 137. Cauchy Completion.- 138. Hausdorff’s Metric Topology.- 139. The Post Office Metric.- 140. The Radial Metric.- 141. Radial Interval Topology.- 142. Bing’s Discrete Extension Space.- 143. Michael’s Closed Subspace.- III Metrization Theory.- Conjectures and Counterexamples.- IV Appendices.- Special Reference Charts.- Separation Axiom Chart.- Compactness Chart.- Paracompactness Chart.- Connectedness Chart.- Disconnectedness Chart.- Metrizability Chart.- General Reference Chart.- Problems.- Notes.
£85.49
Springer Basic Topology
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£43.99
Springer New York Foundations of Differentiable Manifolds and Lie Groups 94 Graduate Texts in Mathematics
Book SynopsisFoundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. Coverage includes differentiable manifolds, tensors and differentiable forms, Lie groups and homogenous spaces, and integration on manifolds.Table of Contents1 Manifolds.- 2 Tensors and Differential Forms.- 3 Lie Groups.- 4 Integration on Manifolds.- 5 Sheaves, Cohomology, and the de Rham Theorem.- 6 The Hodge Theorem.- Supplement to the Bibliography.- Index of Notation.
£49.99
Springer General Topology
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£49.99
Springer Topology of Surfaces
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£50.99
Springer New York Homology Theory
Book Synopsis1 Singular Homology Theory.- 2 Attaching Spaces with Maps.- 3 The Eilenberg-Steenrod Axioms.- 4 Covering Spaces.- 5 Products.- 6 Manifolds and Poincaré Duality.- 7 Fixed-Point Theory.- Appendix I.- Appendix II.- References.- Books and Historical Articles Since 1973.- Books and Notes.- Survey and Expository Articles.Table of Contents1 Singular Homology Theory.- 2 Attaching Spaces with Maps.- 3 The Eilenberg-Steenrod Axioms.- 4 Covering Spaces.- 5 Products.- 6 Manifolds and Poincaré Duality.- 7 Fixed-Point Theory.- Appendix I.- Appendix II.- References.- Books and Historical Articles Since 1973.- Books and Notes.- Survey and Expository Articles.
£71.24
Springer New York Algebraic Topology
Book SynopsisRather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet.Table of ContentsI Calculus in the Plane.- 1 Path Integrals.- 1a. Differential Forms and Path Integrals.- 1b. When Are Path Integrals Independent of Path?.- 1c. A Criterion for Exactness.- 2 Angles and Deformations.- 2a. Angle Functions and Winding Numbers.- 2b. Reparametrizing and Deforming Paths.- 2c. Vector Fields and Fluid Flow.- II Winding Numbers.- 3 The Winding Number.- 3a. Definition of the Winding Number.- 3b. Homotopy and Reparametrization.- 3c. Varying the Point.- 3d. Degrees and Local Degrees.- 4 Applications of Winding Numbers.- 4a. The Fundamental Theorem of Algebra.- 4b. Fixed Points and Retractions.- 4c. Antipodes.- 4d. Sandwiches.- III Cohomology and Homology, I.- 5 De Rham Cohomology and the Jordan Curve Theorem.- 5a. Definitions of the De Rham Groups.- 5b. The Coboundary Map.- 5c. The Jordan Curve Theorem.- 5d. Applications and Variations.- 6 Homology.- 6a. Chains, Cycles, and H0U.- 6b. Boundaries, H1U, and Winding Numbers.- 6c. Chains on Grids.- 6d. Maps and Homology.- 6e. The First Homology Group for General Spaces.- IV Vector Fields.- 7 Indices of Vector Fields.- 7a. Vector Fields in the Plane.- 7b. Changing Coordinates.- 7c. Vector Fields on a Sphere.- 8 Vector Fields on Surfaces.- 8a. Vector Fields on a Torus and Other Surfaces.- 8b. The Euler Characteristic.- V Cohomology and Homology, II.- 9 Holes and Integrals.- 9a. Multiply Connected Regions.- 9b. Integration over Continuous Paths and Chains.- 9c. Periods of Integrals.- 9d. Complex Integration.- 10 Mayer—Vietoris.- 10a. The Boundary Map.- 10b. Mayer—Vietoris for Homology.- 10c. Variations and Applications.- 10d. Mayer—Vietoris for Cohomology.- VI Covering Spaces and Fundamental Groups, I.- 11 Covering Spaces.- 11a. Definitions.- 11b. Lifting Paths and Homotopies.- 11c. G-Coverings.- 11d. Covering Transformations.- 12 The Fundamental Group.- 12a. Definitions and Basic Properties.- 12b. Homotopy.- 12c. Fundamental Group and Homology.- VII Covering Spaces and Fundamental Groups, II.- 13 The Fundamental Group and Covering Spaces.- 13a. Fundamental Group and Coverings.- 13b. Automorphisms of Coverings.- 13c. The Universal Covering.- 13d. Coverings and Subgroups of the Fundamental Group.- 14 The Van Kampen Theorem.- 14a. G-Coverings from the Universal Covering.- 14b. Patching Coverings Together.- 14c. The Van Kampen Theorem.- 14d. Applications: Graphs and Free Groups.- VIII Cohomology and Homology, III.- 15 Cohomology.- 15a. Patching Coverings and ?ech Cohomology.- 15b. ?ech Cohomology and Homology.- 15c. De Rham Cohomology and Homology.- 15d. Proof of Mayer—Vietoris for De Rham Cohomology.- 16 Variations.- 16a. The Orientation Covering.- 16b. Coverings from 1-Forms.- 16c. Another Cohomology Group.- 16d. G-Sets and Coverings.- 16e. Coverings and Group Homomorphisms.- 16f. G-Coverings and Cocycles.- IX Topology of Surfaces.- 17 The Topology of Surfaces.- 17a. Triangulation and Polygons with Sides Identified.- 17b. Classification of Compact Oriented Surfaces.- 17c. The Fundamental Group of a Surface.- 18 Cohomology on Surfaces.- 18a. 1-Forms and Homology.- 18b. Integrals of 2-Forms.- 18c. Wedges and the Intersection Pairing.- 18d. De Rham Theory on Surfaces.- X Riemann Surfaces.- 19 Riemann Surfaces.- 19a. Riemann Surfaces and Analytic Mappings.- 19b. Branched Coverings.- 19c. The Riemann—Hurwitz Formula.- 20 Riemann Surfaces and Algebraic Curves.- 20a. The Riemann Surface of an Algebraic Curve.- 20b. Meromorphic Functions on a Riemann Surface.- 20c. Holomorphic and Meromorphic 1-Forms.- 20d. Riemann’s Bilinear Relations and the Jacobian.- 20e. Elliptic and Hyperelliptic Curves.- 21 The Riemann—Roch Theorem.- 21a. Spaces of Functions and 1-Forms.- 21b. Adeles.- 21c. Riemann—Roch.- 21d. The Abel—Jacobi Theorem.- XI Higher Dimensions.- 22 Toward Higher Dimensions.- 22a. Holes and Forms in 3-Space.- 22b. Knots.- 22c. Higher Homotopy Groups.- 22d. Higher De Rham Cohomology.- 22e. Cohomology with Compact Supports.- 23 Higher Homology.- 23a. Homology Groups.- 23b. Mayer—Vietoris for Homology.- 23c. Spheres and Degree.- 23d. Generalized Jordan Curve Theorem.- 24 Duality.- 24a. Two Lemmas from Homological Algebra.- 24b. Homology and De Rham Cohomology.- 24c. Cohomology and Cohomology with Compact Supports.- 24d. Simplicial Complexes.- Appendices.- Appendix A Point Set Topology.- A1. Some Basic Notions in Topology.- A2. Connected Components.- A3. Patching.- A4. Lebesgue Lemma.- Appendix B Analysis.- B1. Results from Plane Calculus.- B2. Partition of Unity.- Appendix C Algebra.- C1. Linear Algebra.- C2. Groups; Free Abelian Groups.- C3. Polynomials; Gauss’s Lemma.- Appendix D On Surfaces.- D1. Vector Fields on Plane Domains.- D2. Charts and Vector Fields.- D3. Differential Forms on a Surface.- Appendix E Proof of Borsuk’s Theorem.- Hints and Answers.- References.- Index of Symbols.
£33.99
Springer Mathematical Analysis
Book Synopsis1 Real Numbers.- 1.1 Sets, Relations, Functions.- 1.2 Numbers.- 1.3 Infinite Sets.- 1.4 Incommensurability.- 1.5 Ordered Fields.- 1.6 Functions on R.- 1.7 Intervals in R.- 1.8 Algebraic and Transcendental Numbers.- 1.9 Existence of R.- 1.10 Exercises.- 1.11 Notes.- 2 Sequences and Series.- 2.1 Sequences.- 2.2 Continued Fractions.- 2.3 Infinite Series.- 2.4 Rearrangements of Series.- 2.5 Unordered Series.- 2.6 Exercises.- 2.7 Notes.- 3 Continuous Functions on Intervals.- 3.1 Limits and Continuity.- 3.2 Two Fundamental Theorems.- 3.3 Uniform Continuity.- 3.4 Sequences of Functions.- 3.5 The Exponential function.- 3.6 Trigonometric Functions.- 3.7 Exercises.- 3.8 Notes.- 4 Differentiation.- 4.1 Derivatives.- 4.2 Derivatives of Some Elementary Functions.- 4.3 Convex Functions.- 4.4 The Differential Calculus.- 4.5 L'Hospital's Rule.- 4.6 Higher Order Derivatives.- 4.7 Analytic Functions.- 4.8 Exercises.- 4.9 Notes.- 5 The Riemann Integral.- 5.1 Riemann Sums.- 5.2 Existence Results.- 5.3 ProTrade ReviewThis is a very good textbook presenting a modern course in analysis both at the advanced undergraduate and at the beginning graduate level. It contains 14 chapters, a bibliography, and an index. At the end of each chapter interesting exercises and historical notes are enclosed.\par From the cover: ``The book begins with a brief discussion of sets and mappings, describes the real number field, and proceeds to a treatment of real-valued functions of a real variable. Separate chapters are devoted to the ideas of convergent sequences and series, continuous functions, differentiation, and the Riemann integral (of a real-valued function defined on a compact interval). The middle chapters cover general topology and a miscellany of applications: the Weierstrass and Stone-Weierstrass approximation theorems, the existence of geodesics in compact metric spaces, elements of Fourier analysis, and the Weyl equidistribution theorem. Next comes a discussion of differentiation of vector-valued functions of several real variables, followed by a brief treatment of measure and integration (in a general setting, but with emphasis on Lebesgue theory in Euclidean spaces). The final part of the book deals with manifolds, differential forms, and Stokes' theorem [in the spirit of M. Spivak's: ``Calculus on manifolds'' (1965; Zbl 141.05403)] which is applied to prove Brouwer's fixed point theorem and to derive the basic properties of harmonic functions, such as the Dirichlet principle''. ZENTRALBLATT MATH A. Browder Mathematical Analysis An Introduction "Everything needed is clearly defined and formulated, and there is a reasonable number of examples…. Anyone teaching a year course at this level to should seriously consider this carefully written book. In the reviewer's opinion, it would be a real pleasure to use this text with such a class."—MATHEMATICAL REVIEWSTable of Contents1 Real Functions 2 Sequences and Series 3 Continuous Functions on Intervals 4 Differentiation 5 The Riemann Integral 6 Topology 7 Function Spaces 8 Differentiable Maps 9 Measures 10 Integration 11 Manifolds 12 Multilinear Algebra 13 Differential Forms 14 Integration on Manifolds
£44.99
Springer The Fundamental Theorem of Algebra
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£66.49
Springer Topological Spaces
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£54.99
Springer New York An Introduction To Semiclassical And Microlocal Analysis Hb
Book SynopsisThis book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical, way and is mainly addressed to non-specialists in the subject.Trade ReviewFrom the reviews: "The book is very clearly written, and is indeed much simpler than most of others. … this is an excellent book, suitable even for students with a poor background in the subject. In my opinion, every department offering courses on partial differential equations or asymptotic analysis should have it in the library. It will be very useful to all mathematicians working in semi-classical or microlocal analysis … ." (Yuri Safarov, Bulletin of the London Mathematical Society, Issue 35, 2003) "This is a concise and accessible book on the basic techniques of semiclassical and microlocal analysis. … An appendix provides a useful summary of the major formulas used in the text. Each chapter is followed by a collection of provocative and well chosen exercises. The exercises are essential for understanding the work and provide important applications. … the text does provide a very readable, clear, and concise introduction to semiclassical and microlocal analysis." (Peter D. Hislop, Mathematical Reviews, 2003 b) "The contents of the book correspond to a course at Ph. D. Level, given by the author at the Universities of Bologna and Paris-Nord. … the book collects in an original way standard results and new aspects of semi-classical microlocal analysis; the reading is suggested to non-specialists as well." (L. Rodino, Zentralblatt MATH, Vol. 994 (19), 2002) "This book presents most of the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics. … The originality lies in the fact that the main features of analytic microlocal analysis are derived from a single and elementary a priori estimate. Various exercises illustrate the chief results of each chapter while introducing the reader to further developments of the theory. Applications to the study of the Schrödinger operator are also discussed, to further the understanding of new notions … ." (L’ Enseignement Mathematique, Vol. 48 (1-2), 2002) "The book under review consists of lecture notes corresponding to a course taught for several years at the universities of Paris-Nord (France) and Bologna (Italy). It is addressed mainly to non-specialists in the subject, and the prerequisites are essentially reduced to the basic notions of the theory of distributions. … The author tries to make clear how the things work and show examples where they can be applied. It is nicely written … . the book can be highly recommended." (J. Synnatzschke, Zeitschrift für Analysis und ihre Anwendungen – ZAA, Vol. 21 (3), 2002)Table of ContentsIntroduction * Semiclassical Pseudodifferential Calculus * Microlocalization * Applications to the Solutions of Analytic Linear PDEs * Complements: Symplectic Aspects * Appendix: List of Formulae * Bibliography * Index * List of Notations
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Springer Dynamics of Evolutionary Equations
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Penguin Publishing Group Poincares Prize The HundredYear Quest to Solve One of Maths Greatest Puzzles
Book SynopsisThe amazing story of one of the greatest math problems of all time and the reclusive genius who solved itIn the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found.Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.
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Springer Topological Function Spaces 78 Mathematics and its Applications
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Springer Algebras and Orders Proceedings of the NATO Advanced Study Institute and Seminaire De Mathematiques Superieures Montreal Canada July 29August 9 1991 389 Nato Science Series C
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Springer Ordered Algebraic Structures Proceedings of the Curacao Conference Sponsored by the Caribbean Mathematics Foundation June 2630 1995 Proceedings Mathematics Foundation June 2630 1995
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Springer Algorithmic and Computer Methods for ThreeManifolds 425 Mathematics and Its Applications
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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.
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Springer Basic Topological Structures of Ordinary Differential Equations 432 Mathematics and Its Applications
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Springer New Developments in Differential Geometry Budapest 1996 Proceedings of the Conference on Differential Geometry Budapest Hungary July 2730 1996
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Springer Infinite Homotopy Theory 6 KMonographs in Mathematics
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