The Language of Mathematics

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.

A new and unique way of understanding the translation ofconcepts and natural language into mathematicalexpressionsTransforming a body of text into corresponding mathematicalexpressions and models is traditionally viewed and taught as amathematical problem; it is also a task that most find difficult.The Language of Mathematics: Utilizing Math in Practicereveals a new way to view this process--not as a mathematicalproblem, but as a translation, or language, problem. By presentingthe language of mathematics explicitly and systematically, thisbook helps readers to learn mathematics¿and improve theirability to apply mathematics more efficiently and effectively topractical problems in their own work.Using parts of speech to identify variables and functions in amathematical model is a new approach, as is the insight thatexamining aspects of grammar is highly useful when formulating acorresponding mathematical model. This book identifies the basicelements of the language of mathematics, such as values, variablesand functions, while presenting the grammatical rules for combiningthem into expressions and other structures. The author describesand defines different notational forms for expressions, and alsoidentifies the relationships between parts of speech and othergrammatical elements in English and components of expressions inthe language of mathematics. Extensive examples are used throughoutthat cover a wide range of real-world problems and feature diagramsand tables to facilitate understanding.The Language of Mathematics is a thought-provoking bookof interest for readers who would like to learn more about thelinguistic nature and aspects of mathematical notation. The bookalso serves as a valuable supplement for engineers, techniciansmanagers, and consultants who would like to improve their abilityto apply mathematics effectively, systematically, and efficientlyto practical problems.

Preface.Acknowledgements.Part A. Introductory overview.1. Introduction.2. Preview: Some Statements in English and the Language ofMathematics.Part B. Mathematics and its language.3. Elements of the Language of Mathematics.4. Important Structures and Concepts in the Language ofMathematics.5. Solving Problems Mathematically.Part C. English, the Language of Mathematics and translatingbetween them.6. Linguistic Characteristics of English and the Language ofMathematics.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 ofMathematics.Appendix H. Programming languages and the Language ofMathematics.Appendix I. Other literature.Index.