Series: Springer Proceedings in Mathematics, Vol. 8
1st Edition., 2011, X, 420 p. 5 illus.
Hardcover, ISBN 978-3-642-20299-5
Due: May 2011
.This volume contains the Proceedings of the conference "Complex and Differential Geometry 2009", held at Leibniz Universitat Hannover, September 14 - 18, 2009. It was the aim of this conference to bring specialists from differential geometry and (complex) algebraic geometry together and to discuss new developments in and the interaction between these fields. Correspondingly, the articles in this book cover a wide area of topics, ranging from topics in (classical) algebraic geometry through complex geometry, including (holomorphic) symplectic and poisson geometry, to differential geometry (with an emphasis on curvature flows) and topology.
Content Level ≫ Research
Keywords ≫ Algebraic Geometry - Complex Geometry - Diffential Geometry - Kahler Geometry - Symplectic Geometry
Related subjects ≫ Algebra - Analysis - Geometry & Topology
Participants.- Surfaces of general type with geometric genus zero: a survey.- Holomorphic symplectic geometry: a problem list.- Generalized Lagrangian mean curvature flow in Kahler manifolds that are almost Einstein.- Einstein metrics and preserved curvature conditions for the Ricci flow.- Differential Harnack Estimates for Parabolic Equations.- Euler characteristic of a complete intersection.- Cremona special sets of points in products of projective spaces.- Stable bundles and polyvector fields.- Buser-Sarnak invariant and projective normality of abelian varieties.- Complete K¨ahler-Einstein Manifolds.- Fixed point subalgebras of Weil algebras: from geometric to algebraic Questions.- Self-similar solutions and translating solutions.- Aspects of conformal holonomy.- Bifurcation braid monodromy of plane curves.- A survey of Torelli and monodromy results for holomorphic-symplectic Varieties.- On singularities of generically immersive holomorphic maps between complex hyperbolic space forms.- Generically nef vector bundles and geometric applications.- Dolbeault cohomology of nilmanifolds with left-invariant complex structure.- Smooth rationally connected threefolds contain all smooth curves.- Submanifolds in Poisson geometry: a survey.
Series: Springer Undergraduate Mathematics Series
1st Edition., 2011, VIII, 233 p. 49 illus.
Softcover, ISBN 978-0-85729-599-6
Due: May 2011
Written for students taking a second or third year undergraduate course in mathematics or computer science, this book is the ideal companion to a course in enumeration. Enumeration is a branch of combinatorics where the fundamental subject matter is numerous methods of pattern formation and counting. An Introduction to Enumeration provides a comprehensive and practical introduction to this subject giving a clear account of fundamental results and a thorough grounding in the use of powerful techniques and tools.
Two major themes run in parallel through the book, generating functions and group theory. The former theme takes enumerative sequences and then uses analytic tools to discover how they are made up. Group theory provides a concise introduction to groups and illustrates how the theory can be used to count the number of symmetries a particular object has. These enrich and extend basic group ideas and techniques.
The authors present their material through examples that are carefully chosen to establish key results in a natural setting. The aim is to progressively build fundamental theorems and techniques. This development is interspersed with exercises that consolidate ideas and build confidence. Some exercises are linked to particular sections while others range across a complete chapter. Throughout, there is an attempt to present key enumerative ideas in a graphic way, using diagrams to make them immediately accessible. The development assumes some basic group theory, a familiarity with analytic functions and their power series expansion along with some basic linear algebra.
Content Level ≫ Upper undergraduate
Keywords ≫ Counting - Enumeration - Generating functions - Group actions - Groups
Related subjects ≫ Algebra
What Is Enumeration?.- Generating Functions Count.- Working with Generating Functions.- Permutation Groups.- Matrices, Sequences and Sums.- Group Actions and Counting.- Exponential Generating Functions.- Graphs.- partitions and Paths.
1st Edition., 2011, IV, 150 p. 8 illus.
Softcover, ISBN 978-1-4419-9499-8
Due: July 29, 2011
.Written by the pre-eminent E. L Lehman
Examines the history of statistics through the personal and professional relationships of Neyman and Fisher, two of the discipline's most influential contributors
Creates a personal account of the creation of hypothesis testing, estimation, and the design of experiments and sample surveys
Classical statistical theory?hypothesis testing, estimation, and the design of experiments and sample surveys?is mainly the creation of two men: Ronald A. Fisher (1890-1962) and Jerzy Neyman (1894-1981). Their contributions sometimes complemented each other, sometimes occurred in parallel, and, particularly at later stages, often were in strong opposition. The two men would not be pleased to see their names linked in this way, since throughout most of their working lives they detested each other. Nevertheless, they worked on the same problems, and through their combined efforts created a new discipline.
This new book by E.L. Lehmann, himself a student of Neyman’s, explores the relationship between Neyman and Fisher, as well as their interactions with other influential statisticians, and the statistical history they helped create together. Lehmann uses direct correspondence and original papers to recreate an historical account of the creation of the Neyman-Pearson Theory as well as Fisher’s dissent, and other important statistical theories.
Content Level ≫ Popular/general
Keywords ≫ History of Statistics
Related subjects ≫ Statistical Theory and Methods
Introduction.- Fisher’s Testing Methodology.- The Neyman-Pearson Theory.- Fisher’s Dissent.- The Design of Experiments and Sample Surveys.- Estimation.- Epilogue.
Series: Springer Monographs in Mathematics
1st Edition., 2011, X, 246 p.
Hardcover, ISBN 978-3-642-20971-0
Due: July 15, 2011
Incidence geometry is a central part of modern mathematics that has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polar spaces.
Embedded into the modern view of diagram geometry, projective and affine geometry including the fundamental theorems, polar geometry including the Theorem of Buekenhout-Shult and the classification of quadratic sets are presented in this volume. Incidence geometry is developed along the lines of the fascinating work of Jacques Tits and Francis Buekenhout.
The book is a clear and comprehensible introduction into a wonderful piece of mathematics. More than 200 figures make even complicated proofs accessible to the reader.
Content Level ≫ Research
Keywords ≫ - buildings - coxeter geometries - diagram geometry - polar spaces - projective and affine geometry
Related subjects ≫ Geometry & Topology
I Projective and Affine Geometries.- 1. Introduction.- 2. Geometries and Pregeometries.- 3. Projective and Affine Planes.- 4. Projective Spaces.- 5. Affine Spaces.- 6. A Characterization of Affine Spaces.- 7. Residues and Diagrams.- 8. Finite geometries.- II Isomorphisms and Collineations.- 1. Introduction.- 2. Morphisms.- 3. Projections.- 4. Collineations of projective and affine spaces.- 5. Central Collineations.- 6. The Theorem of Desargues.- III Projective Geometry over a Vector Space.- 1. Introduction.- 2. The Projective Space P(V).- 3. Homogeneous Coordinates of Projective Spaces.- 4. Automorphisms of P(V).- 5. The Affine Space AG(W).- 6. Automorphisms of A(W).- 7. The First Fundamental Theorem.- 8. The Second Fundamental Theorem.- IV Polar Spaces and Polarities.- 1. Introduction.- 2. The Theorem of Buekenhout-Shult.- 3. The diagram of a polar space.- 4. Polarities.- 5. Sesquilinear Forms.- 6. Pseudo-quadrics.- 7. The Kleinian Polar Space.- 8. The Theorem of Buekenhout and Parmentier.- V Quadrics and Quadratic Sets.- 1. Introduction.- 2. Quadratic Sets.- 3. Quadrics.- 4. Quadratic Sets in PG(3, K).- 5. Perspective Quadratic Sets.- 6. Classification of the Quadratic Sets.- 7. The Kleinian Quadric.- 8. The Theorem of Segre.- 9. Further Reading.- References.- Index.
Series: Texts in Applied Mathematics, Vol. 38
2011, X, 708 p. 20 illus.
Hardcover, ISBN 978-1-4419-9960-3
Due: July 28, 2011
More examples and references added
Chapters have been expanded
Offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups
This book is an introduction to the fundamental concepts and tools needed for solving problems of a geometric nature using a computer. It attempts to fill the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, robotics, or machine learning.
This book covers the following topics: affine geometry, projective geometry, Euclidean geometry, convex sets, SVD and principal component analysis, manifolds and Lie groups, quadratic optimization, basics of differential geometry, and a glimpse of computational geometry (Voronoi diagrams and Delaunay triangulations). Some practical applications of the concepts presented in this book include computer vision, more specifically contour grouping, motion interpolation, and robot kinematics.
Content Level ≫ Graduate
Keywords ≫ Affine Geometry - Convex Optimization - Euclidean Geometry - Projective geometry
Related subjects ≫ Geometry & Topology - Image Processing - Mathematics - Robotics
Introduction.- Basics of Affine Geometry.- Basic Properties of Convex Sets.- Embedding an Affine Space in a Vector Space.- Basics of Projective Geometry.- Basics of Euclidean Geometry.- Separating and Supporting Hyperplanes; Polar Duality.- Polytopes and Polyhedra.- The Cartan?Dieudonn´e Theorem.- The Quaternions and the Spaces S3, SU(2), SO(3), and RP3 .- Dirichlet?Voronoi Diagrams.- Basics of Hermitian Geometry.- Spectral Theorems.- Singular Value Decomposition (SVD) and Polar Form.- Applications of SVD and Pseudo-Inverses.- Quadratic Optimization Problems.- Schur Complements and Applications.- Quadratic Optimization and Contour Grouping.- Basics of Manifolds and Classical Lie Groups.- Basics of the Differential Geometry of Curves.- Basics of the Differential Geometry of Surfaces.- Appendix.- References.- Symbol Index.- IndexAppendix.- References.- Symbol Index.- Index