The
Language of Mathematics: Utilizing Math in Practice

by Robert L. Baber

last modified 2015 September 13

All rights to the material on this web page

are reserved by the author, Robert L. Baber.

by Robert L. Baber

last modified 2015 September 13

All rights to the material on this web page

are reserved by the author, Robert L. Baber.

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

You can order The Language of Mathematics: Utilizing Math in Practice from any bookseller.

You can order The Language of Mathematics: Utilizing Math in Practice from any bookseller.

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* From the publisher's
web page one may read excerpts (the Introduction, the Index, and the
Table of Contents).

** The comments, additional notes, errata and bookmark/flyer are in pdf files.

** The comments, additional notes, errata and bookmark/flyer are in pdf files.

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,

- pupils would be able to associate mathematics with their prior knowledge more clearly and consciously,
- we would make it easier for pupils to learn mathematics,
- more pupils would identify with mathematics and
- fewer pupils would close their minds to mathematics.

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:

- Those who would like to improve their ability to apply mathematics effectively, systematically, and efficiently to practical problems
- Teachers of mathematics who would like to improve their ability to convey to their students a better understanding and appreciation of mathematics and how to apply it in practice
- Those who are curious about the linguistic nature and aspects of mathematical notation

- Engineers, consultants, managers, scientists, technicians, and others who could benefit vocationally and professionally by a greater ability to use and apply mathematics in their work
- Students in tertiary educational institutions
- Students in secondary schools especially interested in mathematics, science, or languages
- Educators designing mathematics curricula, course content, and teaching materials for students at all levels
- Teachers of mathematics, science, or languages in tertiary educational institutions (universities, polytechnics, and vocational and technical schools)
- Teachers of mathematics, science, or languages in secondary schools
- Teachers in primary schools who introduce pupils to mathematics and especially to word problems
- Persons with a general or an intellectual interest in mathematics, science, or language

- Recognition and conscious awareness that mathematics might be useful in your work or other activities
- A desire to realize its potential benefits
- Basic knowledge of the grammar of a natural language such as English

Text on the back cover of the book

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.