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Applied Mathematics for Database Professionals (Expert's Voice) [Hardcover]

Lex de Haan , Toon Koppelaars
4.7 out of 5 stars  See all reviews (6 customer reviews)

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Book Description

June 18, 2007 1590597451 978-1590597453 1

Relational databases hold data, right? They do indeed, 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.

The math that you'll learn in this book will put you above the level of understanding of most database professionals today. You'll better understand the technology and be able to apply it more effectively. You'll 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.

Table of Contents

  1. Logic: Introduction
  2. Set Theory: Introduction
  3. Some More Logic
  4. Relations and Functions
  5. Tables and Database States
  6. Tuple, Table, and Database Predicates
  7. Specifying Database Designs
  8. Specifying State Transition Constraints
  9. Data Retrieval
  10. Data Manipulation
  11. Implementing Database Designs in Oracle
  12. Summary and Conclusions

Frequently Bought Together

Applied Mathematics for Database Professionals (Expert's Voice) + Beginning Relational Data Modeling, Second Edition + Beginning Database Design: From Novice to Professional
Price for all three: $105.54

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Editorial Reviews


From the reviews:

"It starts with the mathematical foundation of relational databases: concepts and their notation are introduced step-by-step, defined, and clearly explained. … this book is a very good introduction to the foundations of database design for an intermediate or advanced audience … ." (K. Balogh, ACM Computing Reviews, Vol. 49 (12), December, 2008)

About the Author

Lex de Haan studied applied mathematics at the University of Technology in Delft, the Netherlands. His experience with Oracle goes back to the mid-1980s, version 4. He worked for Oracle Corporation from 1990 to 2004 in various education-related roles, ending up in Server Technologies (product development) as senior curriculum manager for the advanced�database administration�curriculum. In that role, he was involved in the development of Oracle9i and Oracle Database 10g. In March 2004, he decided to go independent and founded Natural Join B.V. ( From 1999 until his passing in 2006, he was involved in the ISO SQL language standardization process, as a member of the Dutch national body. He was also one of the founding members of the OakTable network (

Toon Koppelaars studied computer science at the University of Technology in Eindhoven, The Netherlands. He is a veteran Oracle technology user, having used the Oracle DBMS and tools since 1987. During his career he has been involved in both application development and database administration. �His experience encompasses solutions involving terminals and hosts, two-tier client-server applications, and modern-day Java Enterprise Edition and web development. His interest areas include performance tuning (ensuring scalability, SQL-tuning), architecting applications in a DBMS-centric way, and logical/physical database design. Within the database design area, the formal specification and robust implementation of data integrity constraints (often referred to as business rules) is one of his special interest areas. Toon is a frequent presenter at Oracle-related conferences, a member of the Oaktable Network (, and a coauthor of the books Applied Mathematics for Database Professionals (Apress 2007) and Leerboek Oracle SQL (in Dutch, Academic Service 2013).

Product Details

  • Series: Expert's Voice
  • Hardcover: 376 pages
  • Publisher: Apress; 1 edition (June 18, 2007)
  • Language: English
  • ISBN-10: 1590597451
  • ISBN-13: 978-1590597453
  • Product Dimensions: 1.1 x 7.1 x 9.4 inches
  • Shipping Weight: 2.1 pounds (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #471,179 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
49 of 52 people found the following review helpful
3.0 out of 5 stars Formal Database Specification September 2, 2007
Writing a book is no easy task. Completing a book when your co-author and friend passes away early in the process, must be a monumental task, this is what Toon Koppelaars achieved with this work.

I ordered this book expecting it to contain examples of using statistics, probability and data mining algorithms as applied to databases. In retrospect, I am not sure why I made that assumption. It is actually about formally specifying database designs using logic and set theory. This book is reviewed and endorsed by C. J. Date and features a foreword by him, which would be high praise for any book on the subject of databases.

It is split into 3 parts and 12 chapters as follows:
1. Logic: Introduction
2. Set Theory: Introduction
3. Some More Logic
4. Relations and Functions
5. Tables and Database States
6. Tuple, Table, and Database Predicates
7. Specifying Database Designs
8. Specifying State Transition Constraints
9. Data Retrieval
10. Data Manipulation
11. Implementing Database Designs in Oracle
12. Summary and Conclusions

If you've studied mathematics (or a tertiary subject with a mathematics element to it) you will most probably be familiar with the sections on set theory and logic. If you have not then they provide an as excellent introduction to these topics that you are likely to find anywhere.

This book makes the following claims and I have made my comments against each one:

"This book will help you":
* "Become a better database designer. You'll make fewer mistakes, and your designs will be more flexible in response to changing data needs." I agree 100% that having a good, if not intuitive, grasp of logic and basic set theory will help you to create better DB schemas.
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28 of 29 people found the following review helpful
5.0 out of 5 stars Only for those who want to master the database September 3, 2007
Finally, a book has come along that is not a simple restating of the manual. This is not a book that will tell you how to install a database or how to write RMAN scripts.

This book deconstructs all of what it is to be a database. This book is like a vivsection on the "brain" of an RDBMS (specifically, but not exclusively, Oracle).

Why this book succeeds is because it walks you, step-by-step, through the simple (yes simple) and well defined (yes, you don't really have to guess) logic that the database uses for EVERY request made of it.

It is a must-have for anyone serious about truly understanding why databases work the way they do. Have you sat in any of those meetings where people guessed or even voted on how they thought the database worked? It's so silly.

This book will not help you get certified with any database. Certifications are vendor specific and cover a lot more than the narrow focus of this book. So you'll be disappointed if you expect a broad database education.

The narrow focus of this book is laying out the internal rules of the database's "thought process." If you understand the power of that narrow focus, this book is for you. If not, keep it on your wish list and I'll bet you'll come back to it someday.

I have made this book mandatory reading for my Oracle and SQL Server DBA's (the only databases I currently have DBA's for).

While it is in no way a complete database education, I think no database education can be complete without it.
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12 of 12 people found the following review helpful
5.0 out of 5 stars A Very Valuable Volume on the Relational Model December 19, 2007
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.
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