This article presents some ideas about teaching definitions in undergraduate mathematics. All the activities have been used in class or examination with first year undergraduates studying degree programs that lead to careers in applied mathematics, statistics, operations research or quantitative finance. The theoretical framework used for this work comes mainly from applied linguistics, particularly language acquisition for students from non-English speaking backgrounds. The linguistic term for this is functional analysis .
Definitions play an important role in academic writing in all disciplines.
Definitions take on a more critical role as the need for greater precision increases. I don't believe that mathematics is really different from other disciplines in this respect. We need definitions so that we can all talk about the same concept without ambiguity. Language people talk about audience and purpose . Definitions change as we move to more advanced mathematics and so prior knowledge can cause conflict as a student needs to redefine a concept.