Designed for the high-school level. Popular, easily followed yet accurate, profound. Topics include curved space time as a higher dimension, special relativity and shape of space-time. Accessible to layman but also of interest to specialist. Major topics include non-metric affine geometry, inner products of vector spaces and metric affine geometry.
Linear algebra is a prerequisite.
Numerous exercises from routine to highly challenging. This superb study, generously illustrated, systematically investigates geometric forms in nature at the molecular and atomic levels. Underlying equations are provided, as well as rules for generating various forms. Topics include algebraic and combinatoric preliminaries, isometries and similarities, crystallography, fields and vector spaces, a fine spaces, projective space, much more Advanced undergraduate level.