In our first talk by a faculty member this year, Prof Amit Kuber of the Department of Mathematics and Statistics, IIT Kanpur, introduced non-standard analysis, more specifically the concept of hyperreals. This allows us to formalize notions like infinity and infinitesimal numbers in analysis which often simplifies several proofs. It has been shown that these methods are equivalent to standard methods in analysis.
The only pre-requisites? Some knowledge of real numbers as taught in an introductory undergraduate level real analysis course (MTH101 here at IITK) and an open mind to learn more mathematics.