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This little book is especially concerned with those portions of
?advanced calculus? in which the subtlety of the concepts and
methods makes rigor difficult to attain at an elementary level. The
approach taken here uses elementary versions of modern methods
found in sophisticated mathematics. The formal prerequisites
include only a term of linear algebra, a nodding acquaintance with
the notation of set theory, and a respectable first-year calculus
course (one which at least mentions the least upper bound (sup) and
greatest lower bound (inf) of a set of real numbers). Beyond this a
certain (perhaps latent) rapport with abstract mathematics will be
found almost essential.
This little book is especially concerned with those portions of
?advanced calculus? in which the subtlety of the concepts and
methods makes rigor difficult to attain at an elementary level. The
approach taken here uses elementary versions of modern methods
found in sophisticated mathematics. The formal prerequisites
include only a term of linear algebra, a nodding acquaintance with
the notation of set theory, and a respectable first-year calculus
course (one which at least mentions the least upper bound (sup) and
greatest lower bound (inf) of a set of real numbers). Beyond this a
certain (perhaps latent) rapport with abstract mathematics will be
found almost essential.
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