Applied Mathematics for Database Professionals

by Lex DeHaan, Toon Koppelaars

This book touches on an area seldom the mathematical underpinnings of the relational database. The topic is important, but far too often ignored. This is the first book to explain the underlying math in a way that’s accessible to database professionals. Just as importantly, if not more so, this book goes beyond the abstract by showing readers how to apply that math in ways that will make them more productive in their jobs. What’s in this book will "open the eyes" of most readers to the great power, elegance, and simplicity inherent in relational database technology.

Genres: Technical, Programming, Computer Science

407 pages, Hardcover

First published January 1, 2007

Reviews

[Ronny · Rating 5 out of 5]

This book ties together predicate calculus, set theory, set theoretic functions and databases. It shows how databases can be developed using the mathematical tools outlined above, and teaches those tools for those unfamiliar. Even if you don't do any database work, this is an excellent book as the subjects are useful for all sorts of development tasks as it drives home the power of set theoretic thinking with regards to software development.

[Peter Aronson · Rating 3 out of 5]

Three-and-a-half stars. The first four chapters are a nice, relatively straightforward review of set theory, Boolean algebra and basic mathematical logic – pretty much what you might expect from the title. There is a certain unfortunately tendency for the authors to define some of their own terminology and symbols, and unfortunately, like most mathematicians, they tend not to make particularly readable choices.

However, once having introduced those concepts, the book spends the remaining seven chapters using them as a means for modeling a database via table definitions and constraints (including state change constraints), following a relatively obscure methodology created by a couple of Dutch academics.

The approach taken is not bad, but the authors big thing is converting constraints and queries into a dense mixture of logic and set theory. This, in itself is not necessary a bad thing, as the resulting descriptions can be then manipulated by rewrite rules. However, it is unlikely to be readable by either the database's users or its administrators. So it might do as a form of technical documentation, but it rather fails as means of communicating. Also, they make a big point about the inherent ambiguity of natural language business rules and requirements, but they spend very little time on how you are supposed to make sure that your translations from this ambiguous form into mathematical logic are actually what the user wanted (this seems to be a problem in general with logicians).

Also, their dense mathematical notation has very little redundancy, as opposed to, say, SQL. Now a lack of redundancy might sound good, but it makes it entirely possible that a single mistyped or misread character could change the entire meaning of an constraint or query. A less dense notation would be more resistant to this.

The book also suffers from the fact that the authors had worked extensively with, and for, Oracle, and tended to use its non-standard SQL (for example, for outer joins) and rather poor level of default transaction isolation. A broader view of the field would have served them better.

I did find the book a useful review of logic and set theory, and their constraint-centric approach is rather interesting. I am slightly bothered that I couldn't find a errata for it though, as I did find a number of typos and incorrect references to diagrams, and who knows what I missed?

[Topilno]

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