Applied Mathematics for Database
Professionals (Experts Voice) by
Toon Koppelaars
A Very Valuable Volume On The Relational Model
Relational databases hold data, right? They indeed do, but to think of a
database as nothing more than a container for data is to miss out on the
profound power that underlies relational technology. A far more powerful
way of thinking lies in relational technologys foundation in the
mathematical disciplines of logic and set theory.
Databases contain truths or propositions describing some area of
interest such as a business. Those truths are organized into sets.
Operations from logic and set theory can be applied to existing sets of
truths to derive new sets of truths. Applied Mathematics for Database
Professionals introduces you to this way of thinking, to the logic and set
theory that underlies relational database technology. All this may sound

abstract now, but there are profound benefits from the deeper
understanding youll gain from this book. Youll learn to
Become a better database designer. Youll make fewer mistakes,
and your designs will be more flexible in response to changing data needs.
Use the expressive power of mathematics to precisely specify designs and
business rules. Communicate effectively about design using the
universal language of mathematics. Develop and write complex SQL
statements with confidence. Avoid pitfalls and problems from common
relational bugaboos such as null values and duplicate rows. The
math that you learn in this book will put you above the level of
understanding of most database professionals today. Youll better
understand the technology and be able to apply it more effectively. Youll
avoid data anomalies like redundancy and inconsistency. Understanding
whats in this book will take your mastery of relational technology to heights
you may not have thought possible.
This book is reviewed and endorsed by C. J. Date and features a
foreword by the same.
Personal Review: Applied Mathematics for Database
Professionals (Experts Voice) by Toon Koppelaars
This book from Lex de Haan (RIP) and Toon Koppelaars is a very
welcome addition to those relatively few technical volumes to date that
attempt to apply the rigours of a sound theoretical mathematical framework
to the Relational Model, and the varied and various manifestations thereof.
This well written and well structured book takes the reader gently through
rudimentary relations and sets in Part I, to the more complex database-
related aspects in Part II, and finally culminating in Part III where the
theoretical is applied to the practical - in this case through Oracle, but will
equally apply to any of the major Database Management System (DBMS)
vendors.
Although the reader is taken `gently' through the learning process, I believe
that any experience in Formal System Specification would be a great help
to the reader, similarly with any degree of knowledge of relations and sets.
With no knowledge of either of these then the curve may not be so `gentle',
but what can be assured, however, is that the exercises are well enough
designed to bring the knowledge levels up appropriately as the book
progresses.
Conversely, what probably isn't of great assistance is a high degree of
proficiency with SQL, with its manifold attendant shortcomings and
deficiencies. The difficulty here arises where the reader will tend to
approach it logically from an SQL perspective (with the perhaps now

instinctive mental workarounds), where this book approaches from a much
more logically complete, theoretically sound, and neutral angle.
That said, however, there is much of value in this book for the seasoned
SQL practitioner, if only to alert as to how incomplete the current DBMS
offerings are, how this (potentially) compromises data integrity on several
levels (tuple, table, database), how to avoid those same shortcomings, and
on how to exploit the maximum declarative constraining from those same
DBMSes in their current incarnations. For the not so seasoned, it will lay a
solid, sound theoretical basis that will serve very well throughout a career
with databases.
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