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
abelian abelian group affine plane axioms called Cantor's cardinal number cardinally equivalent cards Chapter commutative ring congruence countable sets cyclic group defined definition discussion distinct divisible divisor equal equivalence class equivalence relation example Exercise fact factor Fermat finite set form 4n function G onto G geometry given greatest common divisor Hence infinite number infinite set instance intersection inverse Josephus permutation Lagrange's theorem Lemma Let G lines mathematical induction mathematician mathematics mod q modulo Moulton plane multiplication notation Note number of elements number of points number of primes number theory odd number one-to-one correspondence one-to-one mapping parallel parallelogram plane of order polynomial positive integers possible prime number proof properties prove rational numbers real numbers relatively prime result set of integers set of positive Show squares subgroup of G subsets Suppose theorem tion unique verify Wilson's theorem write