Functional DNA: Teaching Infinite Series Through Genetic Analogy

Abstract

This article presents an extended analogy that connects infinite sequences and series to the science of genetics, by identifying power series as “DNA for a function.” This analogy allows standard topics such as convergence tests or Taylor approximations to be recast in a “forensic” light as mathematical analogs of genetic concepts such as DNA testing or genetic profiling. This gives students, nowadays familiar with the ideas of “extracting DNA” or “getting a hit on CODIS” from pop culture, a familiar vantage point to understand and explore this fascinating part of calculus. We present an outline for implementing such material, and discuss some pedagogical advantages of this method of presentation.

Keywords:

• Infinite series
• sequences
• Calculus II
• convergence tests
• radius of convergence
• analogy
• genetics
• forensics
• DNA

Notes

¹I have employed different methods to motivate this as the appropriate choice for the values a_n, such as the integration by parts technique described by Horowitz in [1]. In recent semesters, however, I have simply cited this as a definition to get students working with it more quickly.