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This course offers an introduction to real analysis
at the senior undergraduate level. Real analysis is
a continuation of calculus, and many of the concepts
we introduce in this class should be familiar from
calculus, e.g., functions, continuity, convergence,
etc. But we will introduce these concepts in new,
more abstract, contexts. The biggest change from
calculus to real analysis is a shift in emphasis
from calculations to formal arguments or proofs.
We will cover Chapters 1--4 from the
book Lindstrøm:
Spaces An Introduction to Real Analysis. Topics
covered include preliminaries (proofs, sets,
functions, etc.), completeness, basics of metric
spaces, convergence, compactness, and spaces of
continuous functions. Emphasis will squarely be on
constructing sound mathematical arguments, i.e.,
proofs.
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