Resumen de Functional DNA: teaching infinite series through genetic analogy.

R. Travis Kowalsky

• 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.