803355 VO Algebra 1 (2004S)

A large part of modern Algebra has emerged on the one hand from the efforts to draw exact geometric figures with ruler and compass alone and on the other hand from the need to solve equations. The twentieth century has designed algebra with great success by the axiomatic treatment thereby introducing an unusual thinking in mathematics. It is the aim of this lecture to explain why algebra has now this special form. We present the algebraic basic concepts of semigroups, monoids, groups, rings, fields, modules and algebras, intoduce quotient structures, prove the homomorphism theorems, investigate cuyclic groups, discuss the symmetric group, present the theorems of Gauss on factorial rings and the difference between algebraic and transcendent field extensions. I am also going to present the basic properties of the theory of finite fields.