Associate Professor and
Distinguished Teaching Professor
Department of Mathematics
The University of Texas at Arlington

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NSF Analysis Project -- Sample Materials
Overview
For an overview of the project and an explanation of the five types of materials, go here.
Publication

         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.

Excerpts from the Classroom Version

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,+,●)

Excerpts from the Instructors’ Version

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.

Concept Check: Consequences of the Intermediate Value Theorem

Concept Check: Recollections on sequences

Concept Check: Which implies the other?

Guided Discovery Exercise: Same size?

Guided Discovery Exercise: Cardinality of a power set

Scaffolded Collaborative Task: Cardinality of the power set of N

Historical Vignette: Early writings on the notion of a limit

Capstone Connection: Levels of structure in (R,+,●)