Download or read book The Language of Mathematics written by Bill Barton and published by Springer Science & Business Media. This book was released on 2007-12-24 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Language of Mathematics written by Keith Devlin and published by Macmillan. This book was released on 2000-03-13 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Language of Mathematics written by Robert L. Baber and published by John Wiley & Sons. This book was released on 2011-09-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Language of Mathematics written by Mohan Ganesalingam and published by Springer. This book was released on 2013-03-14 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book An Introduction to the Language of Mathematics written by Frédéric Mynard and published by Springer. This book was released on 2018-11-24 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Mathematics of Language written by Marcus Kracht and published by Walter de Gruyter. This book was released on 2003 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Download or read book Mathematics of Language written by Alexis Manaster-Ramer and published by John Benjamins Publishing. This book was released on 1987-01-01 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Basic Language of Mathematics written by Juan Jorge Schäffer and published by World Scientific. This book was released on 2014-05-16 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book How We Understand Mathematics written by Jacek Woźny and published by Springer. This book was released on 2018-05-07 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Introduction to Formal Languages written by György E. Révész and published by Courier Corporation. This book was released on 2015-03-17 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Language and Communication in Mathematics Education written by Judit N. Moschkovich and published by Springer. This book was released on 2018-03-27 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book English Language Learners in the Mathematics Classroom written by Debra Coggins and published by Corwin Press. This book was released on 2007-01-30 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Strengthen mathematical understandings and academic vocabulary with standards-based strategies! With straightforward language and examples, the authors help teachers develop specialized understanding and knowledge of strategies for supporting a high level of mathematics learning along with language acquisition for ELLs. Providing specific suggestions for teaching standards-based mathematics, this resource: Demonstrates how to incorporate ELL supports and strategies through sample lessons Uses concrete materials and visuals to connect mathematical concepts with language development Focuses on essential mathematical vocabulary Includes brief research summaries with rationales for recommended practices
Download or read book The Problem with Math Is English written by Concepcion Molina and published by John Wiley & Sons. This book was released on 2012-09-06 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching K-12 math becomes an easier task when everyoneunderstands the language, symbolism, and representation of mathconcepts Published in partnership with SEDL, The Problem with Math IsEnglish illustrates how students often understand fundamentalmathematical concepts at a superficial level. Written to inspire?aha? moments, this book enables teachers to help students identifyand comprehend the nuances and true meaning of math concepts byexploring them through the lenses of language and symbolism,delving into such essential topics as multiplication, division,fractions, place value, proportional reasoning, graphs, slope,order of operations, and the distributive property. Offers a new way to approach teaching math content in a waythat will improve how all students, and especially English languagelearners, understand math Emphasizes major attributes of conceptual understanding inmathematics, including simple yet deep definitions of key terms,connections among key topics, and insightful interpretation This important new book fills a gap in math education byillustrating how a deeper knowledge of math concepts can bedeveloped in all students through a focus on language andsymbolism.
Download or read book Einstein s Heroes written by Robyn Arianrhod and published by Oxford University Press. This book was released on 2006 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Blending science, history, and biography, this book reveals the mysteries of mathematics, focusing on the life and work of three of Albert Einstein's heroes: Isaac Newton, Michael Faraday, and James Clerk Maxwell.
Download or read book Math is Language Too written by Phyllis Whitin and published by National Council of Teachers of English (Ncte). This book was released on 2000 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes strategies for helping children learn about math in which students write, draw, and talk to each other about the individual ways they work through math concepts.
Download or read book Language and Mathematics Education written by Judit N. Moschkovich and published by Information Age Pub Incorporated. This book was released on 2010 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometry written by John Tabak and published by Infobase Publishing. This book was released on 2014-05-14 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Greek ideas about geometry, straight-edge and compass constructions, and the nature of mathematical proof dominated mathematical thought for about 2,000 years.
