The Language of Mathematics: Utilizing Math in Practice
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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.


ROBERT LAURENCE BABER is Professor Emeritus in the Department of Computing and Software at McMaster University, Canada. A Fellow of the BCS, The Chartered Institute for IT, he has published numerous journal articles in his areas of research interest, which include mathematical modeling and the conception, planning, and design of computer-based systems for technical and business applications.




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.


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.



“This text presents a new and original point of view on mathematics that will be useful for simplifying applications of mathematics to practical problems by translating English statements of a problem into the Language of Mathematics. The reviewer shares the author's opinion that \this book will improve and increase the reader's insight into mathematics and how to utilize it in practice.”  (Zentralblatt MATH, 2012)