Explicit Brauer Induction is a new and important technique in algebra, discovered by the author in 1986. It solves an old problem, giving a canonical formula for Brauer's induction theorem. In this book it is derived algebraically, following a method of R. Boltje--thereby making the technique, previously topological, accessible to algebraists. Once developed, the technique is used, by way of illustration, to reprove some important known results in new ways and to settle some outstanding problems. As with Brauer's original result, the canonical formula can be expected to have numerous...

This book is ideally suited for a two-term, undergraduate algebra course culminating in Galois theory. It gives an introduction to group theory and to ring theory en route. In addition, the chapter on groups, including applications to error-correcting codes and to solving the Rubik's cube, is suitable for a one-term course. The book's concise style is intended to foster student-instructor discussion, as is the selection of exercises of various levels of difficulty.

Were I to take an iron gun, And ?re it o? towards the sun; I grant 'twould reach its mark at last, But not till many years had passed. But should that bullet change its force, And to the planets take its course, 'Twould never reach the nearest star, Because it is so very far. from FACTS by Lewis Carroll 55] Let me begin by describing the two purposes which prompted me to write this monograph. This is a book about algebraic topology and more especially about homotopy theory. Since the inception of algebraic topology 217] the study of homotopy classes of continuous maps between spheres has...

Throughout number theory and arithmetic-algebraic geometry one encounters objects endowed with a natural action by a Galois group. In particular this applies to algebraic K-groups and etale cohomology groups. This volume is concerned with the construction of algebraic invariants from such Galois actions.