The unifying approach of functional analysis is to view functions
as points in some abstract vector space and the differential and
integral operators relating these points as linear transformations
on these spaces. The author presents the basics of functional
analysis with attention paid to both expository style and technical
detail, while getting to interesting results as quickly as
possible. The book is accessible to students who have completed
first courses in linear algebra and real analysis. Topics are
developed in their historical context, with accounts of the past
including biographies appearing throughout the text. The book
offers suggestions and references for further study, and many
exercises. Karen Saxe is Associate Professor of Mathematics at
Macalester College in St. Paul, Minnesota. She received her Ph.D.
from the University of Oregon. Before joining the faculty at
Macalester, she held a two-year FIPSE post-doctoral position at St.
Olaf College in Northfield, Minnesota. She currently serves on the
editorial board of the MAA's College Mathematics Journal. This is
her first book.
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