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Basic Language of Mathematics

Author: Juan Jorge Schäffer

Publisher: World Scientific

Published: 2014-05-16

Total Pages: 320

ISBN-13: 9814596116

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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

Book Synopsis Basic Language of Mathematics by : Juan Jorge Schäffer

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

The Language of Mathematics

Author: Bill Barton

Publisher: Springer Science & Business Media

Published: 2007-12-24

Total Pages: 186

ISBN-13: 0387728597

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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.

Book Synopsis The Language of Mathematics by : Bill Barton

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.

The Language of Mathematics

Author: Robert L. Baber

Publisher: John Wiley & Sons

Published: 2011-09-09

Total Pages: 350

ISBN-13: 1118061764

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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.

Book Synopsis The Language of Mathematics by : Robert L. Baber

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.

An Introduction to the Language of Mathematics

Author: Frédéric Mynard

Publisher: Springer

Published: 2018-11-24

Total Pages: 185

ISBN-13: 3030006417

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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.

Book Synopsis An Introduction to the Language of Mathematics by : Frédéric Mynard

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.

Basic Concepts in Modern Mathematics

Author: John Edward Hafstrom

Publisher: Courier Corporation

Published: 2013-01-01

Total Pages: 209

ISBN-13: 0486497291

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An in-depth overview of some of the most readily applicable essentials of modern mathematics, this concise volume is geared toward undergraduates of all backgrounds as well as future math majors. Topics include the natural numbers; sets, variables, and statement forms; mappings and operations; groups; relations and partitions; integers; and rational and real numbers. 1961 edition.

Book Synopsis Basic Concepts in Modern Mathematics by : John Edward Hafstrom

Download or read book Basic Concepts in Modern Mathematics written by John Edward Hafstrom and published by Courier Corporation. This book was released on 2013-01-01 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth overview of some of the most readily applicable essentials of modern mathematics, this concise volume is geared toward undergraduates of all backgrounds as well as future math majors. Topics include the natural numbers; sets, variables, and statement forms; mappings and operations; groups; relations and partitions; integers; and rational and real numbers. 1961 edition.

Basic Concepts of Mathematics and Logic

Author: Michael C. Gemignani

Publisher: Courier Corporation

Published: 2004-01-01

Total Pages: 290

ISBN-13: 0486435067

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This text emphasizes logic and the theory of sets. Students who take no further courses in the field will find it an excellent resource for developing an appreciation for the nature of mathematics. Others will discover the foundations for future studies — set theory, logic, counting, numbers, functions, and more. 1968 edition. 43 figures. 25 tables.

Book Synopsis Basic Concepts of Mathematics and Logic by : Michael C. Gemignani

Download or read book Basic Concepts of Mathematics and Logic written by Michael C. Gemignani and published by Courier Corporation. This book was released on 2004-01-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text emphasizes logic and the theory of sets. Students who take no further courses in the field will find it an excellent resource for developing an appreciation for the nature of mathematics. Others will discover the foundations for future studies — set theory, logic, counting, numbers, functions, and more. 1968 edition. 43 figures. 25 tables.

Basic Mathematics

Author: Lawrence A. Trivieri

Publisher: Harper Collins

Published: 2011-10-18

Total Pages: 506

ISBN-13: 0062115057

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Master Your Coursework with Collins College Outlines From fraions, decimals, and geometric measurement to exponents, scientific notation, and an introduion to algebra, the Collins College Outline in Basic Mathematics explores and explains the topics that students will find in introduory mathematics classes. Completely revised and updated by Dr. Lawrence Trivieri, Basic Mathematics includes a test yourself seion with answers and complete explanations at the end of each chapter. Also included are bibliographies for further reading, as well as numerous graphs, charts, and example problems. The Collins College Outlines are a completely revised, in-depth series of study guides for all areas of study, including the Humanities, Social Sciences, Mathematics, Science, Language, History, and Business. Featuring the most up-to-date information, each book is written by a seasoned professor in the field and focuses on a simplified and general overview of the subje for college students and, where appropriate, Advanced Placement students. Each Collins College Outline is fully integrated with the major curriculum for its subje and is a perfe supplement for any standard textbook.

Book Synopsis Basic Mathematics by : Lawrence A. Trivieri

Download or read book Basic Mathematics written by Lawrence A. Trivieri and published by Harper Collins. This book was released on 2011-10-18 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master Your Coursework with Collins College Outlines From fraions, decimals, and geometric measurement to exponents, scientific notation, and an introduion to algebra, the Collins College Outline in Basic Mathematics explores and explains the topics that students will find in introduory mathematics classes. Completely revised and updated by Dr. Lawrence Trivieri, Basic Mathematics includes a test yourself seion with answers and complete explanations at the end of each chapter. Also included are bibliographies for further reading, as well as numerous graphs, charts, and example problems. The Collins College Outlines are a completely revised, in-depth series of study guides for all areas of study, including the Humanities, Social Sciences, Mathematics, Science, Language, History, and Business. Featuring the most up-to-date information, each book is written by a seasoned professor in the field and focuses on a simplified and general overview of the subje for college students and, where appropriate, Advanced Placement students. Each Collins College Outline is fully integrated with the major curriculum for its subje and is a perfe supplement for any standard textbook.

The Mathematics of Language

Author: Marcus Kracht

Publisher: Walter de Gruyter

Published: 2003

Total Pages: 616

ISBN-13: 9783110176209

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Table of contents

Book Synopsis The Mathematics of Language by : Marcus Kracht

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

Basic Mathematics for Electricity and Electronics

Author: Bertrand B. Singer

Publisher:

Published: 1965

Total Pages: 616

ISBN-13:

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Book Synopsis Basic Mathematics for Electricity and Electronics by : Bertrand B. Singer

Download or read book Basic Mathematics for Electricity and Electronics written by Bertrand B. Singer and published by . This book was released on 1965 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Learning Basic Mathematics

Author: John C. Hunter

Publisher:

Published: 1980

Total Pages:

ISBN-13: 9780791532386

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Book Synopsis Learning Basic Mathematics by : John C. Hunter

Download or read book Learning Basic Mathematics written by John C. Hunter and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: