Applied Mathematics for Database Professionals
Lex de Haan, Toon Koppelaars
Apress; Springer [distributor]
Logic is the science which treats of the conceptual representation of the real order.  Also, logic is the science of correct reasoning.  These two sentences are examples of categorical propositions.  They are examples of the second fundamental act of the mind, that of making judgments.  And, as such, they are critical components within the discipline of formal logic.

On page six of this text, the authors include the following sentence:

"If Toon is familiar with SQL, then Lex has three daughters."

Now, in form, this would be an example of a conditional proposition.  The first clause would be the antecedent.  And the second clause would be the consequent.  However, any reasonably intelligent child could discern that the antecedent and the consequent in this case are unrelated.  Toon's knowledge, or lack of knowledge, of SQL is related in no meaningful way at all to the size or characterics of the family of Lex.  However, the authors included this corrupt conditional proposition in the attempt to demonstrate their comprehension of logic.  What they have done, therefore, is rather to demonstrate that they are utterly lacking in the knowledge that they pretend to have.  In this, we can see that the authors come from what might be called the "Chris Date School" of relational database science.  Sadly, it seems that a primary tenet of this school is to allow the mathematics to overwhelm the reality of the subject area treated by the quantification available through mathematics.  Another primary tenet of this school seems to be selectively disregarding the sage teachings of Dr. E. F. Codd, the inventor of the Relational Model.

The introduction to this text also includes a description of mathematicians as people who love to create mind games, and who, in the midst of the mind games, often choose to change the rules, as a matter or caprice.  This is not, we would submit, a description of a mathematician, but of a sophist.  If this is the sort of game that the authors enjoy playing, mature adults, on discerning the nature of the game, will tend not to play along. 

Earlier, we had written a scathing review of this book.  Some readers may find our current rendering still to be highly critical.  In the interim between our first review and this amendment to same, we've studied carefully both the mathematics of set theory and symbolic logic.  And this process has revealed a key truth:  One of the major problems with the presentation in this book, in addition to the aforementioned ignorance of formal logic demonstrated by the authors, is their lack of clarity in explaining the fundamentals of set theory and symbolic logic.  Those who have the determination to study these topics independently, from alternative sources, can probably gain value from this text.  However, all readers must bear in mind that the author's outreach here suffers from the tremendous weaknesses outlined above.  Certainly, there is much to be gained from a formal treatment of the mathematics of database science.  But the mathematics must not be allowed to overwhelm the reality of the subject.  And the authors failure to realize this key truth is the major weakness of this otherwise important offering.  

Careful examination of the database design developed by the authors within the corpus of this text also reveals that the authors are really sadly lacking in their knowledge of the discipline of relational database design.  In fact, the design they so meticulously specify with formal expressions in mathematics demonstrates many flaws that any well trained rookie logical data modeler would scrupulously avoid.  Much of the book, far too much, in fact, is nothing more than an attempt to overturn key aspects of Dr. Codd's sound and unimpeachable teachings relative to the Relational Data Model that Codd himself created.  And for this, the authors ought rightly to be rather ashamed.  They stand on the shoulders of a true intellectual giant, only to mock him.  What a shame!