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Undergraduate Topology - A Working Textbook (Paperback)
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Undergraduate Topology - A Working Textbook (Paperback)
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This textbook offers an accessible, modern introduction at
undergraduate level to an area known variously as general topology,
point-set topology or analytic topology with a particular focus on
helping students to build theory for themselves. It is the result
of several years of the authors' combined university teaching
experience stimulated by sustained interest in advanced
mathematical thinking and learning, alongside established research
careers in analytic topology. Point-set topology is a discipline
that needs relatively little background knowledge, but sufficient
determination to grasp ideas precisely and to argue with straight
and careful logic. Research and long experience in undergraduate
mathematics education suggests that an optimal way to learn such a
subject is to teach it to yourself, pro-actively, by guided reading
of brief skeleton notes and by doing your own spadework to fill in
the details and to flesh out the examples. This text will
facilitate such an approach for those learners who opt to do it
this way and for those instructors who would like to encourage this
so-called 'Moore approach', even for a modest segment of the
teaching term or for part of the class. In reality, most students
simply do not have the combination of time, background and
motivation needed to implement such a plan fully. The
accessibility, flexibility and completeness of this text enable it
to be used equally effectively for more conventional instructor-led
courses. Critically, it furnishes a rich variety of exercises and
examples, many of which have specimen solutions, through which to
gain in confidence and competence.
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