Tower of PowerFront cover and spineTower of PowerBack coverThe Language of Mathematics: Utilizing Math in Practice

by Robert L. Baber

last modified 2015 September 13

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This book was published by John Wiley & Sons, Inc., September 2011.
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Brief overview

The subject of this book is how to formulate a mathematical model from an English description of a problem and the requirements its solution must satisfy. This book views mathematical notation as a language and develops the implications of this view for translating English text into mathematical expressions and a mathematical model, which is a prerequisite for applying mathematics to a practical problem. By presenting the Language of Mathematics explicitly and systematically, this book helps its readers – engineers, technicians, managers, students, teachers and many others – to develop and improve their ability to apply mathematics beneficially in their own work.

This book is not so much about mathematics as it is about language. Viewing mathematical notation as a language, it compares and contrasts the grammar and meaning of mathematical expressions with the grammar and meaning of English phrases and sentences.

Implications for teaching and learning mathematics

Mathematical notation is a language. If we would teach it as such,
As a result, today's pupils would be better able to apply mathematics effectively to problems in other areas in their later education and in their later lives.

Goals and Intended Readership

The goal of this book is to help its readers to improve their ability to apply mathematics beneficially in their own work, in particular, by improving their ability to translate English text into the Language of Mathematics. This book is not intended as a textbook on mathematics itself or on any subdiscipline of mathematics.

This book is written for the following general groups of people:
More specifically, the intended readership includes:
The prerequisites for reading this book are:
This book is selfcontained in the sense that no particular mathematical background is assumed or needed. It is assumed that readers will have encountered some mathematics in school.

Text on the back cover of the book

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.