This book was published
by John Wiley & Sons, Inc.,
September 2011.
You can order The
Language of
Mathematics: Utilizing Math in Practice from any
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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,
- 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.
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:
- 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
More specifically, the intended readership includes:
- 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
The prerequisites for reading this book are:
- 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
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.
