Review of
Lie
Groups: A Problem-Oriented Introduction via Matrix Groups,
by Harriet Pollatsek, the Mathematical Association of America, Washington, D.
C., 2009. 164 pp., $63.95 (hardbound). ISBN 9780883857595.
Five out of five stars
A measure of
how complex Lie groups can be is that it is part of problem number five in the
famous set of twenty-three stated by David Hilbert in 1900.
“Under what conditions is a topological group also a
Lie group?”
In this book, there is a restriction to the matrix Lie
groups, which places them within the skill set of even sophomores, provided
that they have a few courses behind them. Specifically calculus and linear
algebra. This book contains some abstract algebra, but it is presented when
needed, so it can be understood within the flow of the material.
The tactic used
can be summed up by the phrase, “a little bit of explanatory text, a list of
problems, . . . repeat.” The count of problems is stated as 200, which, given
that there are 139 pages of the main content including other material such as suggestions
for further reading, works out to about two problems per page. Hints to the
solutions to some of the problems are given in an appendix.
If you are
interested in developing a special topics or independent study course that is
over material not normally covered in an undergraduate curriculum, this is a
text that will allow you to cover Lie groups. It is very understandable and
readable, the kind of book that a prepared student will be able to read on
their own.
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