The language of mathematics : utilizing math in practice

著者

    • Baber, Robert Laurence

書誌事項

The language of mathematics : utilizing math in practice

Robert L. Baber

Wiley, c2011

  • : hardback

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注記

Includes bibliographical references and index

Summary: "The subject of this book is how to formulate a mathematical model from an English description of a problem. This book views mathematical notation as a language and develops the implications of this view for translating English text into mathematical expressions and mathematical models, i.e. for applying mathematics to problems described in English. In order to apply mathematics to a practical problem, one must first transform an English statement of the problem and the requirements for its solution into mathematical expressions. This book examines this process in detail, presents new insight into it, and develops explicit guidelines for this important step. This book identifies the basic elements (values, variables, and functions) of the language of mathematics and presents the grammatical rules for combining them into expressions and other structures. Different notational forms for expressions are described and defined. Correspondences between parts of speech and other grammatical elements in

Summary: "This book views mathematical notation as a language and develops the implications of this view for translating English text into mathematical expressions and mathematical models, i.e. for applying mathematics to problems described in English. In order to apply mathematics to a practical problem, one must first transform an English statement of the problem and the requirements for its solution into mathematical expressions. This book examines this process in detail, presents new insight into it, and develops explicit guidelines for this important step"--Provided by publisher

内容説明・目次

内容説明

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.

目次

Preface. Acknowledgements. Part A. Introductory overview. 1. Introduction. 2. Preview: Some Statements in English and the Language of Mathematics. Part B. Mathematics and its language. 3. Elements of the Language of Mathematics. 4. Important Structures and Concepts in the Language of Mathematics. 5. Solving Problems Mathematically. Part C. English, the Language of Mathematics and translating between them. 6. Linguistic Characteristics of English and the Language of Mathematics. 7. Translating English to Mathematics. 8. Examples of Translating English to Mathematics. Part D. Conclusion. 9. Summary. Appendices. Appendix A. Representing numbers. Appendix B. Symbols on the Language of Mathematics. Appendix C. Sets of numbers. Appendix D. Special structures in mathematics. Appendix E. Mathematical logic. Appendix F. Waves and the wave equation. Appendix G. Glossary: English to the Language of Mathematics. Appendix H. Programming languages and the Language of Mathematics. Appendix I. Other literature. Index.

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