Geometry and Topology

by Miles Reid

Geometry is central to many branches of mathematics and physics, and offers a complete range of views on the universe. This introduction includes many simple explanations and examples. With minimal prerequisites, the book provides a first glimpse of many research topics in modern algebra, geometry and theoretical physics. The book is based on many years' teaching experience, and is thoroughly class-tested. There are copious illustrations, and each chapter ends with exercises. Further teaching material is available via the web, including assignable problem sheets with solutions.

Genres: Mathematics, Geometry, Textbooks

196 pages, Paperback

First published January 1, 2005

Reviews

[Simon Mcleish]

Readable textbook on the topics of geometry and topology, aimed at the early years of an undergraduate degree. Perhaps it is a little on the swift side for readers without any familiarity with some of the concepts - it covers Euclidean geometry, vector spaces, transformation groups, and basic topological concepts which are related to geometric ideas. The final chapter is a less didactic sprint through some of the wider concepts related to these fields, from spherical and hyperbolic geometry to the mathematical foundations of the standard model of physics. I would expect it to be a good secondary textbook to ones which cover some of the ground in more detail, aiding mathematical comprehension - inspiring, but perhaps a little confusing to less advanced students.

[Niels van Winden]

Though not very accessible for early undergraduates unfamiliar with group theory and linear algebra, this is a very good first exposure to the ideas of modern geometry and topology.

It includes a solid introduction to classical geometries such as euclidean, spherical, hyperbolic, affine, and projective geometry, while steering away from more advanced concepts like Lie theory and manifold theory. At the same time, it does not shy away from introducing topological ideas and combining them with group theory, for example by defining topologies on groups themselves and studying their topology and geometric interpretation.

The cover color looks like diarrhoea though.

In short, if you have had group theory and linear algebra, this is an excellent first exposure to modern geometry.

[Hollis Williams]

Generally a good book and useful especially if you need to recall basic facts about metric spaces and point-set topology. My only issue with the book is that the section on hyperbolic geometry was rather unhelpful. It didn't feel like any geometric intuition was developed and the authors actually derive some incorrect conclusions regarding hyperbolic motions. Since hyperbolic geometry is almost the highlight of a first course on geometry, that seems a bit disappointing.

There are however other good books you can read on hyperbolic geometry so I would say this is still a recommended read even with its flaws.

[Wendelle]

great refresher for topology, and group transformations using matrices