Series: Frontiers in Mathematics, Vol. 28
1st Edition., 2011, XXIV, 274 p.
Softcover, ISBN 978-3-0348-0153-9
Due: August 2011
Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set exploited since the twenties offered an expression of the geometric intuition of a "realistic" place (spot, grain) of non-trivial extent.
Imitating the behaviour of open sets and their relations led to a new approach to topology flourishing since the end of the fifties.It has proved to be beneficial in many respects. Neglecting points, only little information was lost, while deeper insights have been gained; moreover, many results previously dependent on choice principles became constructive. The result is often a smoother, rather than a more entangled, theory
No monograph of this nature has appeared since Johnstone's celebrated Stone Spaces in 1983. The present book is intended as a bridge from that time to the present. Most of the material appears here in book form for the first time or is presented from new points of view. Two appendices provide an introduction to some requisite concepts from order and category theories.
Preface.- Introduction.- I. Spaces and lattices of open sets.- II. Frames and locales. Spectra.- III. Sublocales.- IV. Structure of localic morphisms. The categories Loc and Frm.- V. Separation axioms.- VI. More on sublocales.-VII. Compactness and local compactness.- VIII. (Symmetric) uniformity and nearness.- IX. Paracompactness.- X. More about completion.- XI. Metric frames.- XII. Entourages, non-symmetric uniformity.- XIII. Connectedness.- XIV. The frame of reals and real functions.- XV. Localic groups.- Appendix I: Posets.- Appendix II: Categories.- Bibliography.- Index of Notation.- Index.
1st Edition., 2011, 400 p.
Hardcover, ISBN 978-3-642-19224-1
Due: September 16, 2011
This book is about modern algebraic geometry. The title A Royal Road to Algebraic Geometry is inspired by the famous anecdote about the king asking Euclid if there really existed no simpler way for learning geometry, than to read all of his work Elements. Euclid is said to have answered: gThere is no royal road to geometry!h The book starts by explaining this enigmatic answer, the aim of the book being to ague that indeed, in some sense there is a royal road to algebraic geometry. From a point of departure in algebraic curves, the exposition moves on to the present shape of the field, culminating with Alexander Grothendieckfs theory of schemes. Contemporary homological tools are explained. The reader will follow a directed path leading up to the main elements of modern algebraic geometry. When the road is completed, the reader is empowered to start navigating in this immense field, and to open up the door to a wonderful field of research. The greatest scientific experience of a lifetime!
Content Level ā Graduate
Keywords ā Algebraic curves - Algebraic geometry - Category theory - Homological algebra
Related subjects ā Algebra - Geometry & Topology - History of Mathematical Sciences
Series: Graduate Texts in Mathematics, Vol. 218
2nd Edition., 2012, XX, 730 p. 200 illus.
Hardcover, ISBN 978-1-4419-9981-8
Due: October 27, 2012
.This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer.
This second edition has been extensively revised and clarified. The topics have been substantially rearranged. The book now introduces the two most important analytic tools (the rank theorem and the fundamental theorem on flows) much earlier, so that they can be used throughout the book. A few new topics have been added, notably Sardfs theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, and a brief treatment of degree theory for smooth maps between compact manifolds.
The book is aimed at students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.
Preface.- 1 Smooth Manifolds.- 2 Smooth Maps.- 3 Tangent Vectors.- 4 Submersions, Immersions, and Embeddings.- 5 Submanifolds.- 6 Lie Groups.- 7 Vector Fields.- 8 Integral Curves and Flows.- 9 Vector Bundles.- 10 Sard's Theorem.- 11 Cotangent Bundle.- 12 Tensors.- 13 Riemannian Metrics.- 14 Differential Forms.- 15 Orientations.- 16 Integration on Manifolds.- 17 Distributions and Foliations.- 18 The Exponential Map of a Lie Group.- 19 Quotient Manifolds.- 20 De Rham Cohomology.- 21 The de Rham Theorem.- 22 Symplectic Manifolds.- Appendix A: Review of Topology.- Appendix B: Review of Linear Algebra.- Appendix C: Review of Calculus.- Appendix D: Review of Differential Equations.- References.- Notation Index.- Subject Index
Published 15th December 2010 228 pages
Series: Statistics: A Series of Textbooks and Monographs
For surveys involving sensitive questions, randomized response techniques (RRTs) and other indirect questions are helpful in obtaining survey responses while maintaining the privacy of the respondents. Written by one of the leading experts in the world on RR, Randomized Response and Indirect Questioning Techniques in Surveys describes the current state of RR as well as emerging developments in the field. The author also explains how to extend RR to situations employing unequal probability sampling.
While the theory of RR has grown phenomenally, the area has not kept pace in practice. Covering both theory and practice, the book first discusses replacing a direct response (DR) with an RR in a simple random sample with replacement (SRSWR). It then emphasizes how the application of RRTs in the estimation of attribute or quantitative features is valid for selecting respondents in a general manner. The author examines different ways to treat maximum likelihood estimation; covers optional RR devices, which provide alternatives to compulsory randomized response theory; and presents RR techniques that encompass quantitative variables, including those related to stigmatizing characteristics. He also gives his viewpoint on alternative RR techniques, including the item count technique, nominative technique, and three-card method.
312pp (approx.) Pub. date: May 2011
ISBN: 978-1-84816-642-4
This volume focuses on the interactions between mathematics, physics, biology and neuroscience by exploring new geometrical and topological modelling in these fields. Among the highlights are the central roles played by multilevel and scale-change approaches in these disciplines.
The integration of mathematics with physics, as well as molecular and cell biology and the neurosciences, will constitute the new frontier of 21st century science, where breakthroughs are more likely to span across traditional disciplines.
Geometry and Theoretical Physics:
The Emergence of Algebraic Geometry in Contemporary Physics
Quantum Gravity and Quantum Geometry
The de Sitter and anti-de Sitter Universes
Geometry and Topology in Relativistic Cosmology
The Problem of Space in Neurosciences:
Space in the Cerebral Cortex
Action and Space Representation
The Space Representations in the Brain
The Enactive Constitution of Space
Geometrical Methods in Biological Sciences:
Causes and Symmetries in Natural Sciences
Topological Invariants of Geometrical Surfaces and the Protein Folding Problem
The Geometry of Dense Packing and Biological Structures
When Topology Meets Biology eFor Lifef ? Remarks on how Topological Form Modulates Biological Function
Readership: Students and researchers in mathematical sciences at graduate level.