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From Polynomials to Sums of Squares describes a journey through the foothills of algebra and number theory based around the central theme of factorization. The book begins by providing basic knowledge of rational polynomials, then gradually introduces other integral domains, and eventually arrives at sums of squares of integers. The text is complemented with illustrations that feature specific examples. Other than familiarity with complex numbers and some elementary number theory, very little mathematical prerequisites are needed. The accompanying disk enables readers to explore the subject further by removing the tedium of doing calculations by hand. Throughout the text there are practical activities involving the computer.
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The main purpose of this book is to show how some general algebraic ideas can be applied to give concrete results. For example, one of the main themes is that of factorization into primes and it is studied in detail in the context of polynomials and quadratic integers before being used to give results about which whole numbers can be expressed as sums or differences of squares.
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