Galois Theory, 5th Edition

Chapter 1Classical Algebra

DOI: 10.1201/9781003213949-1

In the first part of this book, Chapters 1–15, we present a (fairly) modern version of Galois's ideas in the same setting that he used, namely, the complex numbers. Later, from Chapter 16 onwards, we generalise the setting, but the complex numbers are familiar and concrete. By initially restricting ourselves to complex numbers, we can focus on the main ideas that Galois introduced, with the additional advantage that the material is more accessible. Moreover, we appreciate the abstract viewpoint when it finally makes its appearance, and we understand where it comes from. However, the concrete setting is sometimes clumsy compared to the elegance of an axiomatic approach, and we have to ...