8.1 Stevin, Polynomials, and GCD8.2 Göttingen and German Mathematics8.3 Noether and the Birth of Abstract Algebra8.4 Rings8.5 Matrix Multiplication and Semirings8.6 Application: Social Networks and Shortest Paths8.7 Euclidean Domains8.8 Fields and Other Algebraic Structures8.9 Thoughts on the Chapter