The Mathematics Of Language
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The Mathematics Of Language
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Author : Marcus Kracht
language : en
Publisher: Walter de Gruyter
Release Date : 2003
The Mathematics Of Language written by Marcus Kracht and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Language Arts & Disciplines categories.
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The Language Of Mathematics
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Author : Mohan Ganesalingam
language : en
Publisher: Springer
Release Date : 2013-03-14
The Language Of Mathematics written by Mohan Ganesalingam and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Computers categories.
The Language of Mathematics was awarded the E.W. Beth Dissertation Prize for outstanding dissertations in the fields of logic, language, and information. It innovatively combines techniques from linguistics, philosophy of mathematics, and computation to give the first wide-ranging analysis of mathematical language. It focuses particularly on a method for determining the complete meaning of mathematical texts and on resolving technical deficiencies in all standard accounts of the foundations of mathematics. "The thesis does far more than is required for a PhD: it is more like a lifetime's work packed into three years, and is a truly exceptional achievement." Timothy Gowers
The Language Of Mathematics
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Author : Bill Barton
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-24
The Language Of Mathematics written by Bill Barton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-24 with Education categories.
The book emerges from several contemporary concerns in mathematics, language, and mathematics education. However, the book takes a different stance with respect to language by combining discussion of linguistics and mathematics using examples from each to illustrate the other. The picture that emerges is of a subject that is much more contingent, much more relative, much more subject to human experience than is usually accepted. Another way of expressing this, is that the thesis of the book takes the idea of mathematics as a human creation, and, using the evidence from language, comes to more radical conclusions than most writers allow.
The Language Of Mathematics
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Author : Robert L. Baber
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-09
The Language Of Mathematics written by Robert L. Baber and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-09 with Mathematics categories.
A new and unique way of understanding the translation of concepts and natural language into mathematical expressions Transforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process—not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and improve their ability to apply mathematics more efficiently and effectively to practical problems in their own work. Using parts of speech to identify variables and functions in a mathematical model is a new approach, as is the insight that examining aspects of grammar is highly useful when formulating a corresponding mathematical model. This book identifies the basic elements of the language of mathematics, such as values, variables, and functions, while presenting the grammatical rules for combining them into expressions and other structures. The author describes and defines different notational forms for expressions, and also identifies the relationships between parts of speech and other grammatical elements in English and components of expressions in the language of mathematics. Extensive examples are used throughout that cover a wide range of real-world problems and feature diagrams and tables to facilitate understanding. The Language of Mathematics is a thought-provoking book of interest for readers who would like to learn more about the linguistic nature and aspects of mathematical notation. The book also serves as a valuable supplement for engineers, technicians, managers, and consultants who would like to improve their ability to apply mathematics effectively, systematically, and efficiently to practical problems.
The Language Of Mathematics
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Author : Keith Devlin
language : en
Publisher: Macmillan
Release Date : 2000-03-13
The Language Of Mathematics written by Keith Devlin and has been published by Macmillan this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-13 with Mathematics categories.
Taking the reader on a wondrous journey through the invisible universe that surrounds us--a universe made visible by mathematics--Devlin shows us what keeps a jumbo jet in the air, explains how we can see and hear a football game on TV, and allows us to predict the weather, the behavior of the stock market, and the outcome of elections. Microwave ovens, telephone cables, children's toys, pacemakers, automobiles, and computers--all operate on mathematical principles. Far from a dry and esoteric subject, mathematics is a rich and living part of our culture.
Statistical Universals Of Language
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Author : Kumiko Tanaka-Ishii
language : en
Publisher: Springer Nature
Release Date : 2021-04-01
Statistical Universals Of Language written by Kumiko Tanaka-Ishii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-01 with Mathematics categories.
This volume explores the universal mathematical properties underlying big language data and possible reasons why such properties exist, revealing how we may be unconsciously mathematical in our language use. These properties are statistical and thus different from linguistic universals that contribute to describing the variation of human languages, and they can only be identified over a large accumulation of usages. The book provides an overview of state-of-the art findings on these statistical universals and reconsiders the nature of language accordingly, with Zipf's law as a well-known example. The main focus of the book further lies in explaining the property of long memory, which was discovered and studied more recently by borrowing concepts from complex systems theory. The statistical universals not only possibly lie as the precursor of language system formation, but they also highlight the qualities of language that remain weak points in today's machine learning. In summary, this book provides an overview of language's global properties. It will be of interest to anyone engaged in fields related to language and computing or statistical analysis methods, with an emphasis on researchers and students in computational linguistics and natural language processing. While the book does apply mathematical concepts, all possible effort has been made to speak to a non-mathematical audience as well by communicating mathematical content intuitively, with concise examples taken from real texts.
Mathematical Methods In Linguistics
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Author : Barbara B.H. Partee
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Methods In Linguistics written by Barbara B.H. Partee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. Forupper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language.
Introduction To Formal Languages
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Author : György E. Révész
language : en
Publisher: Courier Corporation
Release Date : 2015-03-17
Introduction To Formal Languages written by György E. Révész and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-17 with Mathematics categories.
Covers all areas, including operations on languages, context-sensitive languages, automata, decidability, syntax analysis, derivation languages, and more. Numerous worked examples, problem exercises, and elegant mathematical proofs. 1983 edition.
Language And Mathematics Education
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Author : Judit N. Moschkovich
language : en
Publisher: Information Age Pub Incorporated
Release Date : 2010
Language And Mathematics Education written by Judit N. Moschkovich and has been published by Information Age Pub Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Education categories.
A volume in Research in Mathematics Education Series Editor Barbara J. Dougherty, Iowa State University Marketing description: Issues of language in mathematics learning and teaching are important for both practical and theoretical reasons. Addressing issues of language is crucial for improving mathematics learning and teaching for students who are bilingual, multilingual, or learning English. These issues are also relevant to theory: studies that make language visible provide a complex perspective of the role of language in reasoning and learning mathematics. What is the relevant knowledge base to consider when designing research studies that address issues of language in the learning and teaching of mathematics? What scholarly literature is relevant and can contribute to research? In order to address issues of language in mathematics education, researchers need to use theoretical perspectives that integrate current views of mathematics learning and teaching with current views on language, discourse, bilingualism, and second language acquisition. This volume contributes to the development of such integrated approaches to research on language issues in mathematics education by describing theoretical perspectives for framing the study of language issues and methodological issues to consider when designing research studies. The volume provides interdisciplinary reviews of the research literature from four very different perspectives: mathematics education (Moschkovich), Cultural-Historical-Activity Theory (Gutierrez, Sengupta-Irving, & Dieckmann), systemic functional linguistics (Schleppegrell), and assessment (Solano-Flores). This volume offers graduate students and researchers new to the study of language in mathematics education an introduction to resources for conceptualizing, framing, and designing research studies. For those already involved in examining language issues, the volume provides useful and critical reviews of the literature as well as recommendations for moving forward in designing research. Lastly, the volume provides a basis for dialogue across multiple research communities engaged in collaborative work to address these pressing issues.