Essays In The Philosophy of Mathematics Book

The book appears to be extremely readable, and judging by the speed with which I'm getting through it, ought to be eminently suitable as a text book. Moreover, the book appears to explain from scratch all of the discrete mathematics that is used, and provides a large number of worked exercises. Of course, this potentially reduces its suitability for advanced computer science undergraduates, who would hopefully already be familiar with the formal underpinnings.

There are a couple of negative points, however. Most significant is the way the publisher (presumably) has decided to include extremely wide margins on the pages - in many places, less than half the available white space is actually used for print. This is a gross waste of paper, and presumably ramps up the book's price completely unnecessarily.

There is also at least one technical error in the footnotes. We are told on page 4 that "it is always possible to represent any element of a discrete set with a finite string (in some alphabet)", where an "alphabet" has previously been defined to mean "any finite set of symbols". This is obviously only true for countable discrete sets; uncountable discrete sets cannot be represented in this way, because there are only countably many finite strings over a finite alphabet.

Nonetheless, this book gives a good account of the field, with due emphasis on key mathematical concepts underpinning it.