Adjective Adverb Interfaces in Romance
Adjective Adverb Interfaces in Romance

Author: Martin Hummel

Publisher: John Benjamins Publishing Company

Published: 2017-12-21

Total Pages: 382

ISBN-13: 9027264872

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Within the current discussion on grammatical interfaces, the word-classes of adjective and adverb are of particular interest because they appear to be separated or joined in manifold ways at the level of word-class or syntax, with morphology playing a prominent role, especially in Romance. The volume provides typological and theoretical insights into the common or different usage of adjectives and adverbs in Romance. Diachronic change is discussed alongside with synchronic variation and the representation in grammar. The discussion turns out to be controversial, calling into question traditional assumptions such as the dogma of the invariability and the categorial status of the adverb.

Measure Theory and Integration
Measure Theory and Integration

Author: Michael Eugene Taylor

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 338

ISBN-13: 0821841807

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This self-contained treatment of measure and integration begins with a brief review of the Riemann integral and proceeds to a construction of Lebesgue measure on the real line. From there the reader is led to the general notion of measure, to the construction of the Lebesgue integral on a measure space, and to the major limit theorems, such as the Monotone and Dominated Convergence Theorems. The treatment proceeds to $Lp$ spaces, normed linear spaces that are shown to be complete (i.e., Banach spaces) due to the limit theorems. Particular attention is paid to $L2$ spaces as Hilbert spaces, with a useful geometrical structure. Having gotten quickly to the heart of the matter, the text proceeds to broaden its scope. There are further constructions of measures, including Lebesgue measure on $n$-dimensional Euclidean space. There are also discussions of surface measure, and more generally of Riemannian manifolds and the measures they inherit, and an appendix on the integration ofdifferential forms. Further geometric aspects are explored in a chapter on Hausdorff measure. The text also treats probabilistic concepts, in chapters on ergodic theory, probability spaces and random variables, Wiener measure and Brownian motion, and martingales. This text will prepare graduate students for more advanced studies in functional analysis, harmonic analysis, stochastic analysis, and geometric measure theory.

Hamilton’s Ricci Flow
Hamilton’s Ricci Flow

Author: Bennett Chow

Publisher: American Mathematical Society, Science Press

Published: 2023-07-13

Total Pages: 648

ISBN-13: 1470473690

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Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty. The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible. Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions. A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincaré conjecture and Thurston's geometrization conjecture.

Cross-Lingual Word Embeddings
Cross-Lingual Word Embeddings

Author: Anders Søgaard

Publisher: Springer Nature

Published: 2022-05-31

Total Pages: 120

ISBN-13: 3031021711

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The majority of natural language processing (NLP) is English language processing, and while there is good language technology support for (standard varieties of) English, support for Albanian, Burmese, or Cebuano--and most other languages--remains limited. Being able to bridge this digital divide is important for scientific and democratic reasons but also represents an enormous growth potential. A key challenge for this to happen is learning to align basic meaning-bearing units of different languages. In this book, the authors survey and discuss recent and historical work on supervised and unsupervised learning of such alignments. Specifically, the book focuses on so-called cross-lingual word embeddings. The survey is intended to be systematic, using consistent notation and putting the available methods on comparable form, making it easy to compare wildly different approaches. In so doing, the authors establish previously unreported relations between these methods and are able to present a fast-growing literature in a very compact way. Furthermore, the authors discuss how best to evaluate cross-lingual word embedding methods and survey the resources available for students and researchers interested in this topic.

Modern Geometric Structures and Fields
Modern Geometric Structures and Fields

Author: Сергей Петрович Новиков

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 658

ISBN-13: 0821839292

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Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.

Linear Algebra in Action
Linear Algebra in Action

Author: Harry Dym

Publisher: American Mathematical Society

Published: 2023-07-18

Total Pages: 512

ISBN-13: 1470472066

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This book is based largely on courses that the author taught at the Feinberg Graduate School of the Weizmann Institute. It conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that the author has found to be useful in his own research and wishes that he had been exposed to as a graduate student. Roughly the first quarter of the book reviews the contents of a basic course in linear algebra, plus a little. The remaining chapters treat singular value decompositions, convexity, special classes of matrices, projections, assorted algorithms, and a number of applications. The applications are drawn from vector calculus, numerical analysis, control theory, complex analysis, convex optimization, and functional analysis. In particular, fixed point theorems, extremal problems, best approximations, matrix equations, zero location and eigenvalue location problems, matrices with nonnegative entries, and reproducing kernels are discussed. This new edition differs significantly from the second edition in both content and style. It includes a number of topics that did not appear in the earlier edition and excludes some that did. Moreover, most of the material that has been adapted from the earlier edition has been extensively rewritten and reorganized.

The Mathematical Education of Teachers
The Mathematical Education of Teachers

Author: Conference Board of the Mathematical Sciences

Publisher: American Mathematical Soc.

Published: 2001

Total Pages: 164

ISBN-13: 9780821828991

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Now is a time of great interest in mathematics education. Student performance, curriculum, and teacher education are the subjects of much scrutiny and debate. Studies on the mathematical knowledge of prospective and practicing U. S. teachers suggest ways to improve their mathematical educations. It is often assumed that because the topics covered in K-12 mathematics are so basic, they should be easy to teach. However, research in mathematics education has shown that to teach well,substantial mathematical understanding is necessary--even to teach whole-number arithmetic. Prospective teachers need a solid understanding of mathematics so that they can teach it as a coherent, reasoned activity and communicate its elegance and power. This volume gathers and reports current thinkingon curriculum and policy issues affecting the mathematical education of teachers. It considers two general themes: (1) the intellectual substance in school mathematics; and (2) the special nature of the mathematical knowledge needed for teaching. The underlying study was funded by a grant from the U.S. Department of Education. The mathematical knowledge needed for teaching is quite different from that required by students pursuing other mathematics-related professions. Material here is gearedtoward stimulating efforts on individual campuses to improve programs for prospective teachers. This report contains general recommendations for all grades and extensive discussions of the specific mathematical knowledge required for teaching elementary, middle, and high-school grades, respectively.It is also designed to marshal efforts in the mathematical sciences community to back important national initiatives to improve mathematics education and to expand professional development opportunities. The book will be an important resource for mathematics faculty and other parties involved in the mathematical education of teachers. Information for our distributors: This series is published in cooperation with the Mathematical Association of America.

Mathematics for Multimedia
Mathematics for Multimedia

Author: Mladen Victor Wickerhauser

Publisher: Springer Science & Business Media

Published: 2009-10-30

Total Pages: 317

ISBN-13: 0817648801

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This textbook presents the mathematics that is foundational to multimedia applications. Featuring a rigorous survey of selected results from algebra and analysis, the work examines tools used to create application software for multimedia signal processing and communication. Replete with exercises, sample programs in Standard C, and numerous illustrations, Mathematics for Multimedia is an ideal textbook for upper undergraduate and beginning graduate students in computer science and mathematics who seek an innovative approach to contemporary mathematics with practical applications. The work may also serve as an invaluable reference for multimedia applications developers and all those interested in the mathematics underlying multimedia design and implementation.

Dependency Parsing
Dependency Parsing

Author: Sandra Kübler

Publisher: Morgan & Claypool Publishers

Published: 2009

Total Pages: 128

ISBN-13: 1598295969

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Dependency-based methods for syntactic parsing have become increasingly popular in natural language processing in recent years. This book gives a thorough introduction to the methods that are most widely used today. After an introduction to dependency grammar and dependency parsing, followed by a formal characterization of the dependency parsing problem, the book surveys the three major classes of parsing models that are in current use: transition-based, graph-based, and grammar-based models. It continues with a chapter on evaluation and one on the comparison of different methods, and it closes with a few words on current trends and future prospects of dependency parsing. The book presupposes a knowledge of basic concepts in linguistics and computer science, as well as some knowledge of parsing methods for constituency-based representations. Table of Contents: Introduction / Dependency Parsing / Transition-Based Parsing / Graph-Based Parsing / Grammar-Based Parsing / Evaluation / Comparison / Final Thoughts