Basic Language Of Mathematics
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Basic Language Of Mathematics
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Author : Juan Jorge Schäffer
language : en
Publisher: World Scientific
Release Date : 2014-05-16
Basic Language Of Mathematics written by Juan Jorge Schäffer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-16 with Mathematics categories.
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
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Author : Bill Barton
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-24
The Language Of Mathematics written by Bill Barton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-24 with Education categories.
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.
An Introduction To The Language Of Mathematics
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Author : Frédéric Mynard
language : en
Publisher: Springer
Release Date : 2018-11-24
An Introduction To The Language Of Mathematics written by Frédéric Mynard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-24 with Mathematics categories.
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.
The Language Of Mathematics
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Author : Robert L. Baber
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-09
The Language Of Mathematics written by Robert L. Baber and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-09 with Mathematics categories.
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.
Basic Concepts Of Mathematics And Logic
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Author : Michael C. Gemignani
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
Basic Concepts Of Mathematics And Logic written by Michael C. Gemignani and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
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 Concepts In Modern Mathematics
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Author : John Edward Hafstrom
language : en
Publisher: Courier Corporation
Release Date : 2013-01-01
Basic Concepts In Modern Mathematics written by John Edward Hafstrom and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Mathematics categories.
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.
How We Understand Mathematics
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Author : Jacek Woźny
language : en
Publisher: Springer
Release Date : 2018-04-25
How We Understand Mathematics written by Jacek Woźny and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-25 with Mathematics categories.
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.
The Language Of Mathematics
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Author : Robert L. Baber
language : en
Publisher: Wiley
Release Date : 2011-09-21
The Language Of Mathematics written by Robert L. Baber and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-21 with Mathematics categories.
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.
Sets Functions And Logic
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Author : Keith J. Devlin
language : en
Publisher: Springer
Release Date : 2013-11-11
Sets Functions And Logic written by Keith J. Devlin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
The purpose of this book is to provide the student beginning undergraduate mathematics with a solid foundation in the basic logical concepts necessary for most of the subjects encountered in a university mathematics course. The main distinction between most school mathematics and university mathematics lies in the degree of rigour demanded at university level. In general, the new student has no experience of wholly rigorous definitions and proofs, with the result that, although competent to handle quite difficult problems in, say, the differential calculus, he/she is totally lost when presented with a rigorous definition oflimits and derivatives. In effect, this means that in the first few weeks at university the student needs to master what is virtually an entire new language {'the language of mathematics'} and to adopt an entirely new mode ofthinking. Needless to say, only the very ablest students come through this process without a great deal of difficulty.
Basic Math In Plain English
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Author : Bobby Rabon
language : en
Publisher:
Release Date : 2023-01-31
Basic Math In Plain English written by Bobby Rabon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-31 with categories.
Many, if not most, American high school students have a difficult time with mathematics. The question becomes why. When comparing the math abilities of incoming foreign-born students with native-born students, one apparent distinct difference was that the foreign-born students were becoming bilingual as they were studying math in school. The foreign-born students had to learn the alphabet to form words in English. Does mathematics have an alphabet, and if it does, how is it used to form mathematical sentences? Is there a correlation between the two because mathematics is considered to be the universal language? The germination of that idea is the rationale for this effort.