Book Review: Combinatorial problems and exercises
Béla Bollobás · Bulletin of the American Mathematical Society · 1981
REVIEWS and computations are presented on a generous scale.Quadratic fields, cyclotomic fields, units, class numbers, discriminants and différents are among the topics treated with meticulous care.The fundamental theorem-every ideal is uniquely a product of prime ideals-arrives on p. 387 (but in fairness it should be noted that the delay in getting there is due partly to strict adherence to the local-global plan).At the end of every major episode there is a parallel treatment of the function field case.Where there is a big difference there is appropriate added material, e.g. the Riemann-Roch theorem.It is trite but true: Every number-theorist should have this book on his or her shelf.In closing I shall maintain the tradition of the reviewing craft by recording the typos I noticed: pages 99, 309, 388, 575, 616; lines -3, -6, 16, 7, 21; quadratic, been, is, fields, Rogers.