Solid Analytic Geometry

by Abraham Adrian Albert

The first seven chapters of this concise text provide an exposition of the basic topics of solid analytic geometry and comprise the material for a one-semester course on the subject for undergraduate mathematics majors. The remaining two chapters offer additional material for longer courses or supplementary study.
Chapters 1 and 2 contain a treatment of the equations of lines and planes. Subsequent chapters offer an exposition of classical elementary surface and curve theory, a treatment of spheres, and an examination of the classical descriptions of quadric surfaces in standard position. An exploration of the theory of matrices follows, with applications to the three-dimensional case of quadric surfaces. The text concludes with a survey of spherical coordinates and elements of projective geometry.

176 pages, Paperback

Published September 21, 2016

Reviews

[Tom Schulte · Rating 4 out of 5]

This slim volume is a concise introduction to the basic topics of solid analytic geometry. The content is sufficient in quantity and velocity for a one-semester course for undergraduates. There is here a more rigorous consideration of general theory, as opposed to application cases and contrived exercises, than I see in modern texts aimed at the same level. Basically, the author starts from the general into the specific, a trend uncommon in comparable, modern texts. For instance, cylinders are introduced: “A cylinder is a surface consisting all of the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line.” There is something a tad awkward about these introductions. Yet, I appreciate the approach of beginning verbal before the mathematical and defining generally instead of building up from simpler examples, such as a right cylinder. This more easily admits of, say, an elliptic or even hyperbolic cylinder. The latter of which would strike many students as contrary to initial definitions and examples and even unsettling...

[Look for my entire review up at MAA Reviews.]