A Course in Galois Theory

Rating:
Summary: Galois Theory in the British Didactic Style: a gem.
Review: Anyone who has at least perused the works of Hardy, Dirac, Swinnerton-Dyer, or any of their suit will know what I mean. There is something unmistakable about this style: pithy, perhaps to a fault, but without any loss of charisma, these authors sacrifice conversational ease for surveyability and structural integrity. With this book, Garling takes a place in the rich British tradition of mathematical artistry.
This is a pretty short book, and while it covers somewhat more than bare-minimum (the ch. on transcendental extensions is unusually deep, for example) it does not aspire to as complete a coverage as something like Dummit and Foote would give. But while theirs is an excellent "standard reference" type text, Garling conveys as much about craftsmanship and mathematical aesthetic as he does about fields and galois groups. This matching of topic and style of course works incredibly well, and here again we find a rich tradition of beautiful exposition (*cough* Artin).
Of course, I shouldn't neglect to mention my favorite part of any text (endeavor?): the problems. Here again Garling displays excellent taste ("Remember that mathematics is not a spectator sport!"). His rule of thumb is to can the (sometimes) dozens of trivial problems commonly presented, opting rather for a choice few interesting and challenging ones. I certainly learn better from this approach - perhaps more importantly, I have a lot more fun. Mathematics is for those with unrealistic daring, tempered
by a dedication so extreme as to make the former at worst asymptotically realistic.

Joshua James Wiley