Numbers and Symmetry

This textbook presents modern algebra from the ground up using numbers and symmetry. The idea of a ring and of a field are introduced in the context of concrete number systems. Groups arise from considering transformations of simple geometric objects. The analysis of symmetry provides the student with a visual introduction to the central algebraic notion of isomorphism.Designed for a typical one-semester undergraduate course in modern algebra it provides a gentle introduction to the subject by allowing students to see the ideas at work in accessible examples rather than plunging them immediately into a sea of formalism. The student is involved at once with interesting algebraic structures such as the Gaussian integers and the various rings of integers modulo n and is encouraged to take the time to explore and become familiar with those structures.In terms of classical algebraic structures the text divides roughly into three parts: