Books about Generalization from Amazon.com

This book is designed to serve as an introduction to the fascinating world of maps. It explains how to use maps to obtain information about a wide variety of topics. Throughout the book, maps are viewed in a broad framework. Thus, the discussion includes mental maps, aerial photographs, remotely sensed images, computer-assisted cartography, and geographical information systems, in addition to traditional printed maps. The writing style is neither formalistic nor casual, with an emphasis on clarity of explanation. The discussions assume that the reader has no specific prior knowledge of the topic, so that even novice map users can understand and use the information and techniques presented..
Price: $86.12 [Notify me when price goes down.]

Using the sorts in this book, your students will acquire word pattern knowledge, learn spelling rules, and formulate generalizations through compare-and-contrast activities. They'll learn to sort groups of words according to spelling rules, meanings, endings, sound patterns, prefixes, suffixes, spelling generalizations, syllables, and other shared properties..
Price: $140.00 [Notify me when price goes down.]

From reviews of the first edition: "The important feature of the present book is that it starts from the beginning (with only a very modest knowledge assumed) and covers all important topics... The book is very carefully organized [and] ends with 20 pages of useful historic comments. Such a comprehensive and carefully written treatment of fundamentals of the theory will certainly be a basic reference and text book in the future." -- Newsletter of the EMS "This is a fundamental book and none, beginner or expert, could afford to ignore it. Some results are really difficult to be found in other monographs, while others are for the first time included in a book." -- Mathematica "Each chapter begins with an excellent summary of the content and ends with an exercise section... This is really an outstanding book, well written and beautifully produced. It is both a graduate text and a monograph, so it can be recommended to graduate students as well as to specialists." -- Publicationes Mathematicae Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to expert: initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups. Topics include a description of all simply connected Lie groups in terms of semisimple Lie groups and semidirect products, the Cartan theory of complex semisimple Lie algebras, the Cartan-Weyl theory of the structure and representations of compact Lie groups and representations of complex semisimple Lie algebras, the classification of real semisimple Lie algebras, the structure theory of noncompact reductive Lie groups as it is now used in research, and integration on reductive groups. Many problems, tables, and bibliographical notes complete this comprehensive work, making the text suitable either for self-study or for courses in the second year of graduate study and beyond..
Price: $50.04 [Notify me when price goes down.]

This book investigates the nature of generalization in language and examines how language is known by adults and acquired by children. It looks at how and why constructions are learned, the relation between their forms and functions, and how cross-linguistic and language-internal generalizations about them can be explained.
Constructions at Work is divided into three parts: in the first Professor Goldberg provides an overview of constructionist approaches, including the constructionist approach to argument structure, and argues for a usage-based model of grammar. In Part II she addresses issues concerning how generalizations are constrained and constructional generalizations are learned. In Part III the author shows that a combination of function and processing accounts for a wide range of language-internal and cross-linguistic generalizations. She then considers the degree to which the function of constructions explains their distribution and examines cross-linguistic tendencies in argument realization. She demonstrates that pragmatic and cognitive processes account for the data without appeal to stipulations that are language-specific.
This book is an important contribution to the study of how language operates in the mind and in the world and how these operations relate. It is of central interest for scholars and graduate-level students in all branches of theoretical linguistics and psycholinguistics. It will also appeal to cognitive scientists and philosophers concerned with language and its acquisition..
Price: $27.46 [Notify me when price goes down.]

(01/01/2007).
Price: $34.97 [Notify me when price goes down.]

Comprehensive coverage of the foundations, applications, recent developments, and future of conformal differential geometry

Conformal Differential Geometry and Its Generalizations is the first and only text that systematically presents the foundations and manifestations of conformal differential geometry. It offers the first unified presentation of the subject, which was established more than a century ago. The text is divided into seven chapters, each containing figures, formulas, and historical and bibliographical notes, while numerous examples elucidate the necessary theory.

Clear, focused, and expertly synthesized, Conformal Differential Geometry and Its Generalizations
* Develops the theory of hypersurfaces and submanifolds of any dimension of conformal and pseudoconformal spaces.
* Investigates conformal and pseudoconformal structures on a manifold of arbitrary dimension, derives their structure equations, and explores their tensor of conformal curvature.
* Analyzes the real theory of four-dimensional conformal structures of all possible signatures.
* Considers the analytic and differential geometry of Grassmann and almost Grassmann structures.
* Draws connections between almost Grassmann structures and web theory.

Conformal differential geometry, a part of classical differential geometry, was founded at the turn of the century and gave rise to the study of conformal and almost Grassmann structures in later years. Until now, no book has offered a systematic presentation of the multidimensional conformal differential geometry and the conformal and almost Grassmann structures.

After years of intense research at their respective universities and at the Soviet School of Differential Geometry, Maks A. Akivis and Vladislav V. Goldberg have written this well-conceived, expertly executed volume to fill a void in the literature. Dr. Akivis and Dr. Goldberg supply a deep foundation, applications, numerous examples, and recent developments in the field. Many of the findings that fill these pages are published here for the first time, and previously published results are reexamined in a unified context.

The geometry and theory of conformal and pseudoconformal spaces of arbitrary dimension, as well as the theory of Grassmann and almost Grassmann structures, are discussed and analyzed in detail. The topics covered not only advance the subject itself, but pose important questions for future investigations. This exhaustive, groundbreaking text combines the classical results and recent developments and findings.

This volume is intended for graduate students and researchers of differential geometry. It can be especially useful to those students and researchers who are interested in conformal and Grassmann differential geometry and their applications to theoretical physics..
Price: $82.78 [Notify me when price goes down.]

Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and conceptual power they confer on geometry. The aim of the present book is to fill the gap in the literature on differential geometry by the missing notion of Cartan connections. Although the author had in mind a book accessible to graduate students, potential readers would also include working differential geometers who would like to know more about what Cartan did, which was to give a notion of "espaces généralisés" (= Cartan geometries) generalizing homogeneous spaces (= Klein geometries) in the same way that Riemannian geometry generalizes Euclidean geometry. In addition, physicists will be interested to see the fully satisfying way in which their gauge theory can be truly regarded as geometry..
Price: $47.97 [Notify me when price goes down.]

Combining concepts of mathematics and computer science, this book is about the sequences of symbols that can be generated by simple models of computation called "finite automata". Suitable for graduate students or advanced undergraduates, it starts from elementary principles and develops the basic theory. The study then progresses to show how these ideas can be applied to solve problems in number theory and physics..
Price: $12.43 [Notify me when price goes down.]

This book presents very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods from spectral theory and qualitative properties of solutions of PDEs to comparison theorems in Riemannian geometry and potential theory.

All needed tools are described in detail, often with an original approach. Some of the applications presented concern the topology at infinity of submanifolds, L^p cohomology, metric rigidity of manifolds with positive spectrum, and structure theorems for Kähler manifolds.

The book is essentially self-contained and supplies in an original presentation the necessary background material not easily available in book form.

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Price: $56.17 [Notify me when price goes down.]