Naive Lie Theory John Stillwell
It seems to have been decided that undergraduate mathematics today rests
on two foundations: calculus and linear algebra. These may not be the
best foundations for, say, number theory or combinatorics, but they serve
quite well for undergraduate analysis and several varieties of undergraduate algebra and geometry. The really perfect sequel to calculus and linear
algebra, however, would be a blend of the two—a subject in which calculus throws light on linear algebra and vice versa. Look no further! This
perfect blend of calculus and linear algebra is Lie theory (named to honor
the Norwegian mathematician Sophus Lie—pronounced “Lee ”). So why
is Lie theory not a standard undergraduate topic?
