Arithmetical Wonderland by Andrew LiuMy rating: 4 of 5 stars
Characters from Lewis Carroll’s Alice's Adventures in Wonderland and Through the Looking-Glass are a common thread in this unorthodox fundamentals textbook in number theory. This mostly takes the form of dialogues between Alice herself and the twins, Tweedledum and Tweedledee. Others, appropriately including the Red Queen, set up motivation for Alice to explain more of the fundamentals of "The Queen of Mathematics". This survey of arithmetic begins with counting numbers, basic operations and such properties as association, commutation, and distribution. The introductory material, character humor, and less than two hundred pages of main text may make this appear to be a breezy review of topics de rigueur in grade school and possibly high school. Actually, the scope here is much more ambitious and the slim size belies an economic and engaging presentation. By the end of the first six pages in Chapter Zero, the reader is proving the uniqueness of the identity element for binary operations...
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