Meaning In Mathematics

Author : John Polkinghorne
Publisher : OUP Oxford
Page : 176 pages
File Size : 42,8 Mb
Release : 2011-05-19
Category : Mathematics
ISBN : 9780191621895

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Meaning in Mathematics by John Polkinghorne Pdf

Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics. The chapters are written by some of the world's finest mathematicians, mathematical physicists and philosophers of mathematics, each giving their perspective on this fascinating debate. Every chapter is followed by a short response from another member of the author team, reinforcing the main theme and raising further questions. Accessible to anyone interested in what mathematics really means, and useful for mathematicians and philosophers of science at all levels, Meaning in Mathematics offers deep new insights into a subject many people take for granted.

Author : Jeremy Kilpatrick,Celia Hoyles,Ole Skovsmose
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 46,7 Mb
Release : 2006-03-30
Category : Education
ISBN : 9780387240404

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Meaning in Mathematics Education by Jeremy Kilpatrick,Celia Hoyles,Ole Skovsmose Pdf

What does it mean to know mathematics? How does meaning in mathematics education connect to common sense or to the meaning of mathematics itself? How are meanings constructed and communicated and what are the dilemmas related to these processes? There are many answers to these questions, some of which might appear to be contradictory. Thus understanding the complexity of meaning in mathematics education is a matter of huge importance. There are twin directions in which discussions have developed—theoretical and practical—and this book seeks to move the debate forward along both dimensions while seeking to relate them where appropriate. A discussion of meaning can start from a theoretical examination of mathematics and how mathematicians over time have made sense of their work. However, from a more practical perspective, anybody involved in teaching mathematics is faced with the need to orchestrate the myriad of meanings derived from multiple sources that students develop of mathematical knowledge. This book presents a wide variety of theoretical reflections and research results about meaning in mathematics and mathematics education based on long-term and collective reflection by the group of authors as a whole. It is the outcome of the work of the BACOMET (BAsic COmponents of Mathematics Education for Teachers) group who spent several years deliberating on this topic. The ten chapters in this book, both separately and together, provide a substantial contribution to clarifying the complex issue of meaning in mathematics education. This book is of interest to researchers in mathematics education, graduate students of mathematics education, under graduate students in mathematics, secondary mathematics teachers and primary teachers with an interest in mathematics.

Author : David Pimm
Publisher : Routledge
Page : 235 pages
File Size : 54,5 Mb
Release : 2002-11
Category : Education
ISBN : 9781134823666

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Symbols and Meanings in School Mathematics by David Pimm Pdf

This timely book explores the various uses and aspects of symbols in school mathematics and the notion of mathematical meaning. In addition, the author addresses a number of key issues for the 1990's eg. changes within mathematical functioning.

Author : Gabriele Lolli
Publisher : MIT Press
Page : 177 pages
File Size : 51,6 Mb
Release : 2022-09-27
Category : Mathematics
ISBN : 9780262371049

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The Meaning of Proofs by Gabriele Lolli Pdf

Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story. In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. The minute mathematicians open their mouths to explain something—the meaning of x, how to find y—they are framing a narrative. Every proof is the story of an adventure, writes Lolli, a journey into an unknown land to open a new, connected route; once the road is open, we correct it, expand it. Just as fairy tales offer a narrative structure in which new characters can be inserted into recurring forms of the genre in original ways, in mathematics, each new abstract concept is the protagonist of a different theory supported by the general techniques of mathematical reasoning. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Euclid’s proofs have roots in poetry and rhetoric. Mathematics, Lolli asserts, is not the mere manipulation of formulas.

Author : John Polkinghorne
Publisher : Oxford University Press
Page : 172 pages
File Size : 49,5 Mb
Release : 2011-05-19
Category : Mathematics
ISBN : 9780199605057

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Meaning in Mathematics by John Polkinghorne Pdf

Is mathematics invented or discovered? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? Famous mathematicians, mathematical physicists and philosophers of mathematics try to answer these questions in a series of accessible chapters that shed light on what mathematics really means.

Author : Graham Flegg
Publisher : Courier Corporation
Page : 304 pages
File Size : 45,9 Mb
Release : 2013-05-13
Category : Mathematics
ISBN : 9780486166513

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Numbers by Graham Flegg Pdf

Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." — Choice.

Author : John Polkinghorne
Publisher : OUP Oxford
Page : 176 pages
File Size : 48,7 Mb
Release : 2011-05-19
Category : Mathematics
ISBN : 9780191621291

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Meaning in Mathematics by John Polkinghorne Pdf

Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics. The chapters are written by some of the world's finest mathematicians, mathematical physicists and philosophers of mathematics, each giving their perspective on this fascinating debate. Every chapter is followed by a short response from another member of the author team, reinforcing the main theme and raising further questions. Accessible to anyone interested in what mathematics really means, and useful for mathematicians and philosophers of science at all levels, Meaning in Mathematics offers deep new insights into a subject many people take for granted.

Author : D. Clarke
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 43,8 Mb
Release : 2006-04-11
Category : Education
ISBN : 9780306472282

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Perspectives on Practice and Meaning in Mathematics and Science Classrooms by D. Clarke Pdf

This is a variegated picture of science and mathematics classrooms that challenges a research tradition that converges on the truth. The reader is surrounded with different images of the classroom and will find his beliefs confirmed or challenged. The book is for educational researchers, research students, and practitioners with an interest in optimizing the effectiveness of classrooms as environments for learning.

Author : Math Vault
Publisher : Math Vault Publishing
Page : 76 pages
File Size : 53,7 Mb
Release : 2020-06-13
Category : Mathematics
ISBN : 8210379456XXX

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Comprehensive List of Mathematical Symbols by Math Vault Pdf

Ever wonder if there's a reference guide out there summarizing most of the symbols used in mathematics, along with contextual examples and LaTeX code so that you can pick up the various topics of mathematics at an unusual speed? Well now there is! In this jam-packed 75-page eBook, the Comprehensive List of Mathematical Symbols will take you through thousands of symbols in 10+ topics and 6 main categories. Each symbol also comes with their own defining examples, LaTeX codes and links to additional resources, making the eBook both a handy reference and a powerful tool for consolidating one's foundation of mathematics. Highlights - Featuring 1000+ of symbols from basic math, algebra, logic, set theory to calculus, analysis, probability and statistics - Comes with LaTeX code, defining contextual examples and links to additional resources - Clear. Concise. Straight-to-the-point with no fluff. - Informative. Engaging. Excellent for shortening the learning/reviewing curve. Table of Contents 1) Constants Key Mathematical Numbers Key Mathematical Sets Key Mathematical Infinities Other Key Mathematical Objects 2) Variables Variables for Numbers Variables in Geometry Variables in Logic Variables in Set Theory Variables in Linear/Abstract Algebra Variables in Probability and Statistics Variables in Calculus 3) Delimiters Common Delimiters Other Delimiters 4) Alphabet Letters Greek Letters Used in Mathematics Other Greek Letters 5) Operators Common Operators Number-related Operators Common Number-based Operators Complex-number-based Operators Function-related Operators Common Function-based Operators Elementary Functions Key Calculus-related Functions and Transforms Other Key Functions Operators in Geometry Operators in Logic Logical Connectives Quantifiers Substitution/Valuation-based Operators Set-related Operators Operators in Algebra Vector-related Operators Matrix-related Operators Vector-space-related Operators Abstract-algebra-related Operators Operators in Probability and Statistics Combinatorial Operators Probability-related Operators Probability-related Functions Discrete Probability Distributions Continuous Probability Distributions and Associated Functions Statistical Operators Operators in Calculus Operators Related to Sequence, Series and Limit Derivative-based Operators Integral-based Operators 6) Relational Symbols Equality-based Relational Symbols Comparison-based Relational Symbols Number-related Relational Symbols Relational Symbols in Geometry Relational Symbols in Logic Set-related Relational Symbols Relational Symbols in Abstract Algebra Relational Symbols in Probability and Statistics Relational Symbols in Calculus 7) Notational Symbols Common Notational Symbols Intervals Notational Symbols in Geometry and Trigonometry Notational Symbols in Probability and Statistics Notational Symbols in Calculus

Author : Ernest Davis,Philip J. Davis
Publisher : Springer
Page : 379 pages
File Size : 49,6 Mb
Release : 2015-11-17
Category : Mathematics
ISBN : 9783319214733

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Mathematics, Substance and Surmise by Ernest Davis,Philip J. Davis Pdf

The seventeen thought-provoking and engaging essays in this collection present readers with a wide range of diverse perspectives on the ontology of mathematics. The essays address such questions as: What kind of things are mathematical objects? What kinds of assertions do mathematical statements make? How do people think and speak about mathematics? How does society use mathematics? How have our answers to these questions changed over the last two millennia, and how might they change again in the future? The authors include mathematicians, philosophers, computer scientists, cognitive psychologists, sociologists, educators and mathematical historians; each brings their own expertise and insights to the discussion. Contributors to this volume: Jeremy Avigad Jody Azzouni David H. Bailey David Berlinski Jonathan M. Borwein Ernest Davis Philip J. Davis Donald Gillies Jeremy Gray Jesper Lützen Ursula Martin Kay O’Halloran Alison Pease Steven Piantadosi Lance Rips Micah T. Ross Nathalie Sinclair John Stillwell Hellen Verran

Author : Matematicheskiĭ institut im. V.A. Steklova
Publisher : Unknown
Page : 384 pages
File Size : 49,8 Mb
Release : 1964
Category : Mathematics
ISBN : UCAL:B3734259

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Mathematics, Its Content, Methods, and Meaning by Matematicheskiĭ institut im. V.A. Steklova Pdf

Author : Richard Courant,Herbert Robbins
Publisher : Oxford University Press, USA
Page : 596 pages
File Size : 40,8 Mb
Release : 1996
Category : Juvenile Nonfiction
ISBN : 0195105192

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What is Mathematics? by Richard Courant,Herbert Robbins Pdf

The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but not real understanding or greater intellectual independence. The new edition of this classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. "Lucid . . . easily understandable".--Albert Einstein. 301 linecuts.

Author : Theresa R. Fitzgerald
Publisher : PRUFROCK PRESS INC.
Page : 146 pages
File Size : 51,9 Mb
Release : 2006
Category : Encyclopedias and dictionaries
ISBN : 9781593631604

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Math Dictionary for Kids by Theresa R. Fitzgerald Pdf

Contains more than four hundred math definitions that will help students solve many of the math challenges they face. Includes instructions for basic operations and tables of commonly-used facts and equivalents.

Author : Oscar Levin
Publisher : Createspace Independent Publishing Platform
Page : 238 pages
File Size : 41,8 Mb
Release : 2018-07-30
Category : Electronic
ISBN : 1724572636

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Discrete Mathematics by Oscar Levin Pdf

Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.

Author : Steven Schwartzman
Publisher : MAA
Page : 276 pages
File Size : 47,8 Mb
Release : 1994
Category : Mathematics
ISBN : 0883855119

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The Words of Mathematics by Steven Schwartzman Pdf

This book explains the origins of over 1500 mathematical terms used in English.