Paruchuri K. Krishnaiah (Editor), Multivariate Analysis (Academic Press, 1966), xix + 592 pp., 156s

S. D. Silvey
1968 Proceedings of the Edinburgh Mathematical Society  
182 BOOK REVIEWS unduly contracted. In group theory the topics covered include the Sylow theorems, transitive permutation groups, the simplicity of A n for n ^ 5, automorphisms of finite symmetric groups, and the basis theorem for finitely generated abelian groups. An introductory chapter on ring theory then prepares the ground for a detailed study of modules over a commutative ring, which in turn leads naturally into a concise and (for a student's book) unusually sophisticated account of
more » ... -dimensional linear algebra; this last part would certainly be found hard by a student approaching the subject for the first time. Chapters VII and VIII cover the theory of fields up to the proof of the insolubility of the quintic equation, while the final chapter is devoted to the already mentioned proof of the fundamental theorem of algebra. Throughout the book the viewpoint is fairly sophisticated, or " modern ". Maturer mathematicians will enjoy the new look it gives to familiar topics. J. M. HOWTE
doi:10.1017/s001309150001261x fatcat:uvf7en2fubfsvmk3ru2rsqxb44