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This project is being
supported by NSF grant DUE #0837810. The learning materials and notes on implementation will be
published as Learning Materials for a First Course in Real
Analysis, by B. Shipman. A preliminary
edition will be available on a website to appear soon.
The final version is expected to appear by the end of 2010. If you would like to try out the preliminary materials in your
class, you are invited to contact Dr. Shipman for the most current and complete
version.
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The Classroom Version of the learning materials
presents each activity in a form that can be presented to the students in class. The activity may
be presented on a projector, displaying each question one at a time, with the subsequent questions
and solutions covered. The questions are written in large italic type, while the solutions are
included underneath, in smaller regular type, with enough space to conveniently cover them while
presenting the questions.
Concept Check: Interpretations of “unique”
Guided Discovery Exercise: More circles or more
squares?
Guided Discovery Exercise: Cauchy implies
bounded
Guided Discovery Exercise: Comparing definitions of
continuity
Scaffolded Collaborative Task: Derivatives of
two sine functions
Capstone Connection: Levels of structure in (R,+,●)
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These materials are designed for a first course in real
analysis, treating functions, cardinality, algebraic properties of (R,+,●),
boundedness properties of subsets of R, sequences, limits, and continuity, with a brief look
forward to differentiation and integration. They may be used as a supplement to a good textbook as
a means to engage students in discovering and communicating mathematics in a collaborative setting.
Notes on the purpose and implementation of each activity are embedded within the Instructors’
Version; these notes, and the solutions, are written in regular type. Text in italics is part of
the activity itself, as presented in the Classroom Version.
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