A Beginner's Guide to Mathematical Logic (Anglais) Broché – 25 juillet 2014
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There are lots of good exercises in each chapter, but I find myself constantly flipping back and forth to and from the answers section to keep moving on. A good amount of the information required to solve the problems, terminology, ideas etc is not revealed until you skip ahead to read the answer. I love being mentally challenged but it's demoralizing to try at a riddle and then realize that the answer required a concept or a set of terms that was withheld. Of course, the author is not only famous as a mathematician but as a writer of puzzles and riddle books, so I guess "trick" questions are in his nature. I don't get the feeling at all that he's trying to prove how clever he is, just that he may be a little out of touch with the process of coming across certain types of problems for the very first time.
Still, once you do understand the answers they are generally clear and well written. I think this book is about as friendly as a book on set theory and logic can get to someone who is interested in mathematical concepts but not enrolled in an undergrad program like myself.
The book itself has some typos ( okay, a lot of typos ) but they don't distract from the really good information that's presented. Overall, four stars. A good book for self study.
As a result, when I saw that Smullyan had written a more formal guide to mathematical logic, I quickly availed myself of the opportunity of buying it and digging in. Unfortunately, I became somewhat frustrated for two separate but related reasons, one of which was due simply to having purchased the Kindle edition.
The first difficulty is due to a quirk of mine, but one I believe may be shared by others. Often in academic texts about math or the hard sciences problems or exercises are given at the end of chapters which allow one to practice the topics covered in that particular chapter. Most teachers of math generally agree that having the students do a number of such problems is very useful, maybe even essential, to allowing students to gain mastery of the topic in question. I agree with this general attitude or belief. I also believe, however, that doing the exercises should not be essential before moving on to the next chapter. In particular, a number of texts make it necessary to complete some of the final exercises because the answers provide essential information required to be able to understand the following chapters. This is a tendency that I dislike and find both unnecessary and manipulative, even if not intended to be so by the author. Well, Smullyan's text interposes every few paragraphs or pages within each chapter puzzles, similar to those in his more puzzle-oriented books, that one must complete before one can understand or appreciate the paragraphs that follow. This tendency, even if one is not bothered by such (as I am, at least in more formal, not puzzle, books) slows down the reading of the text, and breaks the flow of study a bit too much for my liking.
The other difficulty I had with the text is due to having the Kindle version. In a normal book version, as one dealt with each of the puzzles mentioned above, one could flip to the end of each chapter to check one's solution with that given by Smullyan, or, by reading the first part of the answer, get a useful hint to how best to solve the puzzle. It would also be easy to flip back and forth readily, should there be the desire or need to do so. With the Kindle, paging forward a large number of screens and then paging back, particularly if one had to do that a number of times for each puzzle/teaching point, becomes definitely burdensome and frustrating. If the desire to keep the puzzles in the text rather than simply explain the points being made by them is strong enough, one could put the answers immediately following each respective puzzle question, thus eliminating the constant flipping back and forth. This work-around, however, would require presumably a good deal of time and money changing the format from the printed version to the e-book version, so I understand why this will probably not happen.
Anyway, I remain a fan of Smullyan, and will continue to purchase his books (the solid ones, not any future e-books), but it was frustrating that this one, which I really wanted to learn from, was so difficult and tiring to deal with.
It's like cheating, but with more work.