A Mathematical Bridge: An Intuitive Journey in Higher Mathematics

Rating:
Summary: Good overall, but too many small errors/typos
Review: I have not yet finished this book, but I am quite pleased with it overall. However, the author makes a number of what seem to be typos, which the editor seems to have failed to catch--mostly in the mathematical equations which show up every now and then. For example, at one point he writes R (the set of real numbers) rather than N (the set of natural numbers)--there is really quite a large difference, and the N and R keys aren't particularly close to each other on the keyboard, either. At other times he mysteriously drops terms from equations with no explanations, which seem more like typos.

If you are a mathematical "layman," so to speak, or things like this bother you a lot, I might suggest you look for another book, to avoid confusion on the layman's part or annoyance on the part of the more knowledgable reader.

Rating:
Summary: An excellent and unusual book
Review: This is a really unusual math book. The author attempts -- and, in my opinion, by and large, succeeds in -- the task of presenting pretty much most of the core elements of an undergrad math course in a descriptive and intuitive way -- he starts from counting and ends up with quantum mechanics!! This book differs from most math books by focusing foremost on the reasons why different mathematical structures exist, with the formalism following afterwards, by which time it is often quite obvious.

This book would not replace standard proof -- theorem style textbooks but supplements them very nicely by providing loads of insight and intuition -- things which usually can only be determined over time by practice. As such I'd recommend it to anyone who requires a substantial math element in their degree, and I wish that I had had a copy before I started analysis etc. at college.

One point to note is that although the text is often almost conversational, the book is really crammed with information and insights -- to read it properly requires a lot of hard work and thought. If you are just after a read about math without needing or wanting to know the details, then I would recommend that you look elsewhere.