Numbers and Symmetry: An Introduction to Algebra

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 subjec...