The Text
From the Preface
Teaching a real analysis course in a graduate program for teachers presents special challenges to the instructor. Students' backgrounds are extremely varied: many undergraduate programs no longer require advanced calculus, many students are in-service teachers who may be several years past their undergraduate studies, other students may be on alternative pathways to teaching licensure and have minimal undergraduate mathematics training. Often the class is offered in an abbreviated summer semester. These factors combine to become significant issues for the professor of introductory analysis. We attempt to address these aspects in several ways. Beginning with an overview of typical calculus material helps to refresh students' memory and helps them to refocus in a conceptual, theoretical framework, preparing students to study analysis. Then following a path through introductory analysis that recapitulates the earlier calculus presentation helps students to see development and depth relative to their needs as mathematics instructors. The history of calculus and analysis is woven throughout this text. Historical context helps a student to place the mathematics and to better understand the imperative of developments.
Appalachian's four credit ``Analysis for Teachers'' graduate course can be offered in either a standard fourteen week semester plus final exams or an accelerated four week summer session. Our prerequisites are admission to the mathematics graduate program and the equivalent of an undergraduate mathematics major, including at least three credits of advanced calculus.
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