From the Preface: ``This book is based on notes prepared for a course at the University of Chicago. The course was intended for nonmajors whose mathematical training was somewhat limited ... Mastery of the material requires nothing beyond algebra and geometry normally covered in high school ... [I]t could be used in courses designed for students who intend to teach mathematics ... We want the reader to see mathematics as a living subject in which new results are constantly being obtained.''
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Sets and Functions
addition affine plane algebraic answer assumption axioms called cardinal cards Chapter common commutative consider correspondence countable counting course cycles defined definition described discussion distinct divides divisible elements equal exactly example Exercise exists fact factor field Figure finite formal four function geometry give given Hence hold infinite instance intersection introduced inverse least leave Lemma Let G lines look mathematics means modulo multiplication namely Note objects one-to-one mapping operation parallel permutation play positive integers possible powers present prime prime number probability problem proof properties prove question rational reader real numbers remaining remark result ring rules satisfy Show squares subgroup subsets Suppose theorem theory thing tion transpositions true unique verify write