The Language Of Mathematics

Author : Bill Barton
Publisher : Springer Science & Business Media
Page : 186 pages
File Size : 45,9 Mb
Release : 2007-12-24
Category : Education
ISBN : 9780387728599

Get Book

The Language of Mathematics by Bill Barton Pdf

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.

Author : Keith Devlin
Publisher : Macmillan
Page : 372 pages
File Size : 43,7 Mb
Release : 2000-03-13
Category : Mathematics
ISBN : 0805072543

Get Book

The Language of Mathematics by Keith Devlin Pdf

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.

Author : Mohan Ganesalingam
Publisher : Springer
Page : 260 pages
File Size : 43,6 Mb
Release : 2013-03-14
Category : Computers
ISBN : 9783642370120

Get Book

The Language of Mathematics by Mohan Ganesalingam Pdf

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

Author : Robert L. Baber
Publisher : John Wiley & Sons
Page : 350 pages
File Size : 51,5 Mb
Release : 2011-09-09
Category : Mathematics
ISBN : 9781118061763

Get Book

The Language of Mathematics by Robert L. Baber Pdf

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.

Author : Frank William Land
Publisher : Unknown
Page : 280 pages
File Size : 49,9 Mb
Release : 1963
Category : Mathematics
ISBN : UIUC:30112125290269

Get Book

The Language of Mathematics by Frank William Land Pdf

Author : Alexis Manaster-Ramer
Publisher : John Benjamins Publishing
Page : 401 pages
File Size : 55,5 Mb
Release : 1987-01-01
Category : Language Arts & Disciplines
ISBN : 9789027274427

Get Book

Mathematics of Language by Alexis Manaster-Ramer Pdf

By mathematics of language is meant the mathematical properties that may, under certain assumptions about modeling, be attributed to human languages and related symbolic systems, as well as the increasingly active and autonomous scholarly discipline that studies such things. More specifically, the use of techniques developed in a variety of pure and applied mathematics, including logic and the theory of computation, in the discovery and articulation of insights into the structure of language. Some of the contributions to this volume deal primarily with foundational issues, others with specific models and theoretical issues. A few are concerned with semantics, but most focus on syntax. The papers in this volume reveal applications of the several fields of the theory of computation (formal languages, automata, complexity), formal logic, topology, set theory, graph theory, and statistics. The book also shows a keen interest in developing mathematical models that are especially suited to natural languages.

Author : Juan Jorge Schäffer
Publisher : World Scientific
Page : 320 pages
File Size : 50,9 Mb
Release : 2014-05-16
Category : Mathematics
ISBN : 9789814596114

Get Book

Basic Language of Mathematics by Juan Jorge Schäffer Pdf

This book originates as an essential underlying component of a modern, imaginative three-semester honors program (six undergraduate courses) in Mathematical Studies. In its entirety, it covers Algebra, Geometry and Analysis in One Variable. The book is intended to provide a comprehensive and rigorous account of the concepts of set, mapping, family, order, number (both natural and real), as well as such distinct procedures as proof by induction and recursive definition, and the interaction between these ideas; with attempts at including insightful notes on historic and cultural settings and information on alternative presentations. The work ends with an excursion on infinite sets, principally a discussion of the mathematics of Axiom of Choice and often very useful equivalent statements. Contents:SetsMappingsProperties of MappingsFamiliesRelationsOrdered SetsCompletely Ordered SetsInduction and RecursionThe Natural NumbersFinite SetsFinite SumsCountable SetsSome Algebraic StructuresThe Real Numbers: Complete Ordered FieldsThe Real Number SystemThe Real Numbers: ExistenceInfinite Sets Readership: Undergraduate and graduate students in mathematics; Mathematicians. Key Features:Comprehensive and rigorous in its coverageProvides alternative insights on concepts and definitionsProvides a list of sections with some unusual but insightful approachesKeywords:Sets;Mappings;Families;Order;Natural Numbers;Inductive Proofs;Recursive Definitions;Real Numbers

Author : Marcus Kracht
Publisher : Walter de Gruyter
Page : 616 pages
File Size : 40,7 Mb
Release : 2003
Category : Language Arts & Disciplines
ISBN : 3110176203

Get Book

The Mathematics of Language by Marcus Kracht Pdf

Table of contents

Author : Frédéric Mynard
Publisher : Springer
Page : 185 pages
File Size : 47,5 Mb
Release : 2018-11-24
Category : Mathematics
ISBN : 9783030006419

Get Book

An Introduction to the Language of Mathematics by Frédéric Mynard Pdf

This is a textbook for an undergraduate mathematics major transition course from technique-based mathematics (such as Algebra and Calculus) to proof-based mathematics. It motivates the introduction of the formal language of logic and set theory and develops the basics with examples, exercises with solutions and exercises without. It then moves to a discussion of proof structure and basic proof techniques, including proofs by induction with extensive examples. An in-depth treatment of relations, particularly equivalence and order relations completes the exposition of the basic language of mathematics. The last chapter treats infinite cardinalities. An appendix gives some complement on induction and order, and another provides full solutions of the in-text exercises. The primary audience is undergraduate mathematics major, but independent readers interested in mathematics can also use the book for self-study.

Author : Judit N. Moschkovich,David Wagner,Arindam Bose,Jackeline Rodrigues Mendes,Marcus Schütte
Publisher : Springer
Page : 279 pages
File Size : 55,6 Mb
Release : 2018-03-27
Category : Education
ISBN : 9783319750552

Get Book

Language and Communication in Mathematics Education by Judit N. Moschkovich,David Wagner,Arindam Bose,Jackeline Rodrigues Mendes,Marcus Schütte Pdf

This book considers some of the outstanding questions regarding language and communication in the teaching and learning of mathematics – an established theme in mathematics education research, which is growing in prominence. Recent research has demonstrated the wide range of theoretical and methodological resources that can contribute to this area of study, including those drawing on cross-disciplinary perspectives influenced by, among others, sociology, psychology, linguistics, and semiotics. Examining language in its broadest sense to include all modes of communication, including visual and gestural as well as spoken and written modes, it features work presented and discussed in the Language and Communication topic study group (TSG 31) at the 13th International Congress on Mathematical Education (ICME-13). A joint session with participants of the Mathematics Education in a Multilingual and Multicultural Environment topic study group (TSG 32) enhanced discussions, which are incorporated in elaborations included in this book. Discussing cross-cutting topics it appeals to readers from a wide range of disciplines, such as mathematics education and research methods in education, multilingualism, applied linguistics and beyond.

Author : Jacek Woźny
Publisher : Springer
Page : 118 pages
File Size : 48,7 Mb
Release : 2018-04-25
Category : Mathematics
ISBN : 9783319776880

Get Book

How We Understand Mathematics by Jacek Woźny Pdf

This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested in the engaging question of how mathematics works and why it works so well.

Author : Judit N. Moschkovich
Publisher : Information Age Pub Incorporated
Page : 180 pages
File Size : 46,8 Mb
Release : 2010
Category : Education
ISBN : 1617351598

Get Book

Language and Mathematics Education by Judit N. Moschkovich Pdf

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.

Author : Frank Land
Publisher : Unknown
Page : 264 pages
File Size : 44,6 Mb
Release : 1966
Category : Mathematics
ISBN : OCLC:716437343

Get Book

The Language of Mathematics by Frank Land Pdf

Author : Clare Lee
Publisher : McGraw-Hill Education (UK)
Page : 136 pages
File Size : 55,5 Mb
Release : 2006-06-16
Category : Education
ISBN : 9780335226146

Get Book

EBOOK: Language for Learning Mathematics: Assessment for Learning in Practice by Clare Lee Pdf

Assessment for learning is a powerful way to raise standards and improve learning. However, as this book shows, effective assessment for learning in the mathematics classroom depends on pupils being able and willing to use mathematical language to express their ideas. When discussion, negotiation and explanation are encouraged, teachers use assessment for learning creatively, the work quickly becomes more challenging and the pupils come to see themselves as successful learners. Many pupils find it difficult to express ideas in mathematics because of problems with the language that is used to convey mathematical concepts. This book shows teachers how to help pupils express what they really know and understand, so that assessment for learning can be used. The book: Discusses what mathematical language is, and what it is not Suggests practical approaches to introducing more discourse into the classroom Explores the ideas of assessment for learning – rich questioning and dialogue, effective feedback, and peer and self assessment – and suggests how these can be used effectively in mathematics classrooms to improve learning Language for Learning Mathematics is key reading for teachers and trainee teachers in mathematics, as well as assessment advisors at LAs.

Author : György E. Révész
Publisher : Courier Corporation
Page : 208 pages
File Size : 48,6 Mb
Release : 2015-03-17
Category : Mathematics
ISBN : 9780486169378

Get Book

Introduction to Formal Languages by György E. Révész Pdf

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.