Teaching Growth of Functions Using Equivalence Classes An Alternative to Big O Notation

摘要

Understanding growth of functions using the standard big O definition and notation is a challenge for many undergraduate students. This paper 1. presents an approach to teaching growth of functions that utilizes equivalence classes and partial ordering, 2. identifies those mathematical concepts students should comprehend in order to understand the principles underlying growth of functions, 3. demonstrates pedagogical inadequacies in existing order of complexity notation and definitions and 4. gives a rationale for restricting functions under consideration to positive-valued, monotonic increasing.