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Glimpses of algebra and geometry. 2nd ed. (English) Zbl 1027.00002

Undergraduate Texts in Mathematics. Readings in Mathematics. New York, NY: Springer. xxii, 450 p. (2002).
Toth’s “Glimpses” offer selected material that connect algebra and geometry (but also number-theoretic and topological topics), at a level that is meant to “fill the gap between undergraduate and graduate mathematics studies”. The concept was to present this in a rather informal style in a discussion that goes far enough to reach interesting results and effects, but to stop before things get “really technical”.
The first edition was reviewed in Zbl 0892.00002. This second edition is a revised and substantially expanded version, so for example it includes a detailed treatment of the solution of the cubic and quartic, as well as a long new chapter on Klein’s famous work on the quintic and the icosahedron.
For the third edition, the reviewer would suggest to add more references and suggestions for further reading, and to name the authors of the many web pages listed, to revise some of the topological material (starting with a usable and consistent definition of “polyhedron” and “surface”), and perhaps to modernize the treatment of regular polytopes (via reflection groups), as well as some of the visualization efforts.

MSC:

00A05 Mathematics in general
05-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics
52-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to convex and discrete geometry
11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry)

Citations:

Zbl 0892.00002
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