A Pre-Bridge Course: The Natural Role of Sequences and Series

Abstract

The Sequences and Series calculus course (S&S) can be structured to provide students with a unique opportunity to build their proofs skills prior to or concurrently with a bridge course. This article offers a framework for S&S which places logical reasoning on equal footing with content, by employing the theorems and convergence tests as axioms, and lists sufficient supplementary theorems and definitions.

Keywords:

• Sequences
• series
• proof
• bridge course
• logic
• calculus

ACKNOWLEDGMENTS

The students in the first such version of Sequences and Series I taught deserve great thanks, for both their helpful suggestions and for adapting quite well to what was perhaps an alarming turn in their mathematical lives. In no particular order, I extend my appreciation to Dania Morales, Mitch Staehle, Aaron Dull, Emily Trigg, Molly Mack, Ryan Clark, Nick Gard, and Jerry Nance.