Geometries, Groups and Algebras in the Nineteenth Century - A History

Yaglom's treatise is a history primarily of geometries, groups and algebras in the nineteenth century, spilling over into the early part of the twentieth century. The less advanced mathematics is clearly explained, while the more advanced material is described, examples are given, and the reader is provided references in the notes for further study. Yaglom includes biographical information that makes his presentation colorful. A theme that occurs throughout the book is the rather rough classification of certain mathematicians as left-brained "logicians" vs. right-brained "physicists," who have approached their subjects differently and were sometimes antagonistic to one another. The book is based on the author's lectures to graduate-level students majoring in "pure" mathematics, most of whom subsequently go on to teach in secondary schools. This probably influenced the choice of material and the nature of the narrative.