From Polynomials to Sums of Squares - Tapa dura

This text and software describes a "journey" through algebra and number theory based on the central theme of factorization. It begins with basic knowledge of rational polynomials, gradually introduces other integral domains, and eventually arrives at sums of squares of integers. The treatment is made very concrete throughout the main text with illustrations using specific examples. More abstract material is confined to appendices. Other than familiarity with complex numbers and some elementary number theory, very little mathematical prerequisites are required. The accompanying software allows the reader to explore the subject further by removing the tedium of doing calculations by hand. Throughout the text there are practical activities, mostly involving the computer.