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The Language Of Mathematics by Mohan Ganesalingam

Title The Language of Mathematics
Author Mohan Ganesalingam
Publisher Springer
Release Date 2013-03-14
Category Computers
Total Pages 260
ISBN 9783642370120
Language English, Spanish, and French
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Book Summary:

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

Title The Language of Mathematics
Author Keith Devlin
Publisher Macmillan
Release Date 2000-03-13
Category Mathematics
Total Pages 344
ISBN 0805072543
Language English, Spanish, and French
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Book Summary:

Award-winning author Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden patterns of life.

The Language Of Mathematics by Robert L. Baber

Title The Language of Mathematics
Author Robert L. Baber
Publisher John Wiley & Sons
Release Date 2011-09-09
Category Mathematics
Total Pages 440
ISBN 9781118061763
Language English, Spanish, and French
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Book Summary:

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.

Title The Language of Mathematics
Author Bill Barton
Publisher Springer Science & Business Media
Release Date 2007-12-24
Category Education
Total Pages 186
ISBN 9780387728599
Language English, Spanish, and French
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Book Summary:

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.

Basic Language Of Mathematics by Juan Jorge Schäffer

Title Basic Language of Mathematics
Author Juan Jorge Schäffer
Publisher World Scientific
Release Date 2014-05-16
Category Mathematics
Total Pages 320
ISBN 9789814596114
Language English, Spanish, and French
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Book Summary:

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

Language And Mathematics by Marcel Danesi

Title Language and Mathematics
Author Marcel Danesi
Publisher Walter de Gruyter GmbH & Co KG
Release Date 2016-06-06
Category Language Arts & Disciplines
Total Pages 344
ISBN 9781614513186
Language English, Spanish, and French
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Book Summary:

This book explores the many disciplinary and theoretical links between language, linguistics, and mathematics. It examines trends in linguistics, such as structuralism, conceptual metaphor theory, and other relevant theories,to show that language and mathematics have a similar structure, but differential functions, even though one without the other would not exist.

Title Literacy Strategies for Improving Mathematics Instruction
Author Joan M. Kenney
Publisher ASCD
Release Date 2005
Category Education
Total Pages 113
ISBN 9781416602309
Language English, Spanish, and French
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Book Summary:

Provides teachers with classroom-proven ways to prepare students to be successful math learners by teaching the vocabulary and comprehension skills needed to understand mathematics.

Title The Language of Mathematics Education
Author Shannon W. Dingman
Publisher Brill - Sense
Release Date 2019
Category Education
Total Pages 126
ISBN 9004409394
Language English, Spanish, and French
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Book Summary:

The Language of Mathematics Education provides definitions, summaries, and bibliographic references for over 100 key terms and concepts commonly used in mathematics teaching and learning.

Language And Mathematics Education by Judit N. Moschkovich

Title Language and Mathematics Education
Author Judit N. Moschkovich
Publisher IAP
Release Date 2010-11-01
Category Education
Total Pages 199
ISBN 9781617351617
Language English, Spanish, and French
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Book Summary:

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), CulturalHistoricalActivity Theory (Gutiérrez, SenguptaIrving, & Dieckmann), systemic functional linguistics (Schleppegrell), and assessment (SolanoFlores). 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.

Title An Introduction to the Language of Mathematics
Author Frédéric Mynard
Publisher Springer
Release Date 2018-11-24
Category Mathematics
Total Pages 185
ISBN 9783030006419
Language English, Spanish, and French
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Book Summary:

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.

Title The Mathematics of Language
Author Marcus Kracht
Publisher Walter de Gruyter
Release Date 2011-05-12
Category Language Arts & Disciplines
Total Pages 605
ISBN 9783110895667
Language English, Spanish, and French
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Book Summary:

This book studies language(s) and linguistic theories from a mathematical point of view. Starting with ideas already contained in Montague's work, it develops the mathematical foundations of present day linguistics. It equips the reader with all the background necessary to understand and evaluate theories as diverse as Montague Grammar, Categorial Grammar, HPSG and GB. The mathematical tools are mainly from universal algebra and logic, but no particular knowledge is presupposed beyond a certain mathematical sophistication that is in any case needed in order to fruitfully work within these theories. The presentation focuses on abstract mathematical structures and their computational properties, but plenty of examples from different natural languages are provided to illustrate the main concepts and results. In contrast to books devoted to so-called formal language theory, languages are seen here as semiotic systems, that is, as systems of signs. A language sign correlates form with meaning. Using the principle of compositionality it is possible to gain substantial insight into the interaction between form and meaning in natural languages.

Title Topology and the Language of Mathematics
Author Chris Cunliffe
Publisher Bobo Strategy
Release Date 2008-07
Category Mathematics
Total Pages 160
ISBN 9780615221021
Language English, Spanish, and French
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Book Summary:

An introduction to topology and the language of mathematics that works. Ideal for the undergraduate student with little to no background in the subject. Excellent for the advanced high school mathematics student, interested in a taste of next steps. Also useful to graduate students looking for a refresher or fresh take on their foundation in the topics.

Mathematics Of Language by Alexis Manaster-Ramer

Title Mathematics of Language
Author Alexis Manaster-Ramer
Publisher John Benjamins Publishing
Release Date 1987-01-01
Category Language Arts & Disciplines
Total Pages 401
ISBN 9789027220493
Language English, Spanish, and French
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Book Summary:

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.

Title The Language of Mathematics
Author Lauris Weber
Publisher Unknown
Release Date 2003
Category Algebra
Total Pages 114
ISBN 187622309X
Language English, Spanish, and French
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Book Summary:

A resource for students unfamiliar with the terminology and language applied in mathematics. The book provides vocabulary lists and definitions, mathematical questions concentrating on vocabulary, crosswords, word searches and more for vocabulary reinforcement. 10 units cover the major aspects of high school mathematics.

Title Language and Communication in the Mathematics Classroom
Author Heinz Steinbring
Publisher National Council of Teachers of
Release Date 1998
Category Mathematics
Total Pages 351
ISBN STANFORD:36105028620982
Language English, Spanish, and French
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Book Summary:

The way in which teachers communicate with their students partly determines what they communicate. This book addresses the communication issue by building on a series of papers whose first versions were presented in 1992 at the Sixth International Congress of Mathematics Education in Quebec. Papers include: (1) "Crossing the Gulf between Thought and Symbol: Language as (Slippery) Stepping-Stones" (Susan E.B. Pirie); (2) "Three Epistemologies, Three Views of Classroom Communication: Constructivism, Sociocultural Approaches, Interactionism" (Anna Sierpinska); (3) "Verbal Interaction in the Mathematics Classroom: A Vygotskian Analysis" (Maria G. Bartolini Bussi); (4) "Discourse and Beyond: On the Ethnography of Classroom Discourse" (Falk Seeger); (5) "From 'Stoffdidaktik' to Social Interactionism: An Evolution of Approaches to the Study of Language and Communication in German Mathematics Education Research" (Heinz Steinbring); (6) "Examining the Linguistic Mediation of Pedagogic Interactions in Mathematics" (Clive Kanes); (7) "Pupil Language-Teacher Language: Two Case Studies and the Consequences for Teacher Training" (Albrecht Abele); (8) "Teacher-Student Communication in Traditional and Constructivist Approaches to Teaching" (Maria Luiza Cestari); (9) "Alternative Patterns of Communication in Mathematics Classes: Funneling or Focusing?" (Terry Wood); (10) "Students Communicating in Small Groups: Making Sense of Data in Graphical Form" (Frances R. Curcio and Alice F. Artzt); (11) "Communication and Learning in Small-Group Discussions" (Kaye Stacey and Anne Gooding); (12) "Mathematical Communication through Small-Group Discussions" (Marta Civil); (13) "Formats of Argumentation in the Mathematics Classroom" (Gotz Krummheuer); (14) "Teaching without Instruction: The Neo-Socratic Method" (Rainer Loska); (15) "The Role of Natural Language in Prealgebraic and Algebraic Thinking" (Ferdinando Arzarello); (16) "How Students Interpret Equations: Intuition versus Taught Procedures" (Mollie MacGregor); (17) "Epistemological and Metacognitive Factors Involved in the Learning of Mathematics: The Case of Graphic Representations of Functions" (Maria Kaldrimidou and Andreas Ikonomou); (18) "Making Mathematics Accessible" (Megan Clark); (19) "Itineraries through Logic To Enhance Linguistic and Argumentative Skills" (Giancarlo Navarra); and (20)"Communication in a Secondary Mathematics Classroom: Some Images" (Judith Fonzi and Constance Smith). (ASK)

Title Language in the Mathematics Classroom
Author Rachel Griffiths
Publisher Heinemann
Release Date 1994
Category Mathematics
Total Pages 157
ISBN UVA:X002601673
Language English, Spanish, and French
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Book Summary:

What do children's responses tell us about their understanding of mathematics? How do children's interpretations of mathematical language affect their performance? What are the implications for teaching and learning? Language in the Mathematics Classroom provides imaginative and varied suggestions for extending children's responses in all modes of communication - spoken, written, graphic and activeallowing them to broaden and deepen their mathematical understanding. Language in the Mathematics Classroom explores the connections between mathematics and language, looking at the many ways that children talk about, represent and record mathematics.

Title Language in Mathematical Education
Author Kevin Durkin
Publisher Unknown
Release Date 1991
Category Mathematics
Total Pages 279
ISBN UOM:39015024814892
Language English, Spanish, and French
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Book Summary:

Concerned with various aspects of language in mathematics education, this book aims to reveal some of the ambiguities and complexities in the way language is used in the mathematics curriculum. It aims to present current perspectives and review key issues in mathematics education.

Mathematics by Keith Devlin

Title Mathematics
Author Keith Devlin
Publisher W. H. Freeman
Release Date 1996-12-15
Category Mathematics
Total Pages 216
ISBN 0716760223
Language English, Spanish, and French
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Book Summary:

"The great book of nature," said Galileo, "can be read only by those who know the language in which it is written. And this language is mathematics." A richly illustrated celebration of the beauty and elegance of this ever-evolving language, Mathematics: The Science of Patterns explores the many ways mathematics helps us understand our perceptions of reality--both the physical, biological, and social worlds without, and the realm of ideas and thoughts within.

Title Teaching Mathematics to English Language Learners
Author Gladis Kersaint
Publisher Routledge
Release Date 2014-06-05
Category Education
Total Pages 178
ISBN 9781136227592
Language English, Spanish, and French
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Book Summary:

Today's mathematics classrooms increasingly include students for whom English is a second language. Teaching Mathematics to English Language Learners provides readers a comprehensive understanding of both the challenges that face English language learners (ELLs) and ways in which educators might address them in the secondary mathematics classroom. Framed by a research perspective, Teaching Mathematics to English Language Learners presents practical instructional strategies for engaging learners that can be incorporated as a regular part of instruction. The authors offer context-specific strategies for everything from facilitating classroom discussions with all students, to reading and interpreting math textbooks, to tackling word problems. A fully annotated list of math web and print resources completes the volume, making this a valuable reference to help mathematics teachers meet the challenges of including all learners in effective instruction. Features and updates to this new edition include: An updated and streamlined Part 1 provides an essential overview of ELL theory in a mathematics specific context. Additional practical examples of mathematics problems and exercises make turning theory into practice easy when teaching ELLs New pedagogical elements in Part 3 include tips on harnessing new technologies, discussion questions and reflection points. New coverage of the Common Core State Standards, as well as updates to the web and print resources in Part 4.

Title How Language Informs Mathematics
Author Dirk Damsma
Publisher BRILL
Release Date 2019-11-11
Category Political Science
Total Pages 226
ISBN 9789004395497
Language English, Spanish, and French
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Book Summary:

In How Language Informs Mathematics Dirk Damsma shows how Hegel’s and Marx’s dialectics allow us to understand the structure and nature of mathematical and capitalist systems. Knowledge of such systems allows for an innovative approach to economic modelling.