The Fascination of Groups

First edition/First printing, Fine. This is not a textbook. It is intended, however, to help teach the field of group theory to budding mathematicians and was written by an experienced secondary school teacher. To quote the author, F.J. Budden, in his preface, "The Fascination of Groups" it is intended "to interest, to enlighten and to transport the reader, rather than to provide him with the strict discipline of a mathematical education." Somewhat unusually for a book of its kind, "The Fascination of Groups" was quickly reviewed by three venerable publications that focus on mathematics and mathematics education. All had praise for Budden's approach, but what criticism they had centered on that lack of "strict discipline of a mathematical education" Budden referred to. Interestingly, the most severe critics were from the New World, while the British critic in the "Gazette," a UK publication, was practically over the moon about "The Fascination of Groups." That critic praised Budden's gradual pace and the wealth of examples that allow theorems and axioms to emerge gradually. They found the diversity and presentation of those examples particularly exciting, citing patterns found in music and art in particular. (Interestingly, Budden, who wrote several more mathematics books and was nominated for the presidency of the Mathematical Association, was at least as well-known as a musician as a mathematician. A school choir he built and conducted sang for Queen Elizabeth's official coronation festivities, for instance, performing a Benjamen Britten composition with the assistance of Britten himself.) The reviewer also praised "a most valuable collection of over 1000 questions that teachers may find useful in building their own lessons." ("Answers are provided!" they added with some excitement.) That didn't mean the book was perfect, but errors were termed "occasional lapses" and "tiny slips." Altogether, they thought the book, "Could become a classic." The American critic, writing a few months later in "Mathematics Magazine," seemed less sure about that. They called the book "leisurely paced," not meaning it as a complement, and the examples "inexhaustible." Working from examples did have its advantages, they conceded, but ".it is our concern that the actual proof will become superfluous in the mind of the student, in which case this book could influence the student to accept arguments which are less than logical. Hence, it could function in a manner contrary to the traditional role of mathematics." The Australian professor reviewing "The Fascination of Groups" for "The American Mathematical Monthly" had similar concerns. They started their review by saying Budden takes 500 pages to cover the same amount of theory that is covered in 30 pages of a standard textbook. Perhaps worse: ".unfortunately the strict mathematical discipline is lacking.to the extent that certain vital hypotheses are missing from the statement of theorems." Yet the review ended with a recommendation to both beginners and those interested in a deeper understanding of group theory! In the end, it may be that how one regards the usefulness of "The Fascination of Groups" depends on what one regards the usefulness of mathematics itself to be. Fine. Missing dust jacket. Slight rubbing along the bottom edge of the front cover and the edges of the spine; otherwise pristine. Gold stamped lettering on the spine is unworn and bright. The pages are tight, square, and intact. Light penciled price in top right corner of the front first free endpaper. Light age toning along edges.…