Set Theory for The (Smart) Masses

Abstract

Proof Designer is a computer software program designed to help Mathematics students learn to write mathematical proofs. Under the guidance of the user, Proof Designer assists in writing outlines of proofs in elementary set theory. Proof Designer was designed by Daniel Velleman in association with his book "How To Prove It: A Structured Approach" to help students apply the methods discussed in the book, making classes based on the book more interactive. This article is an early report on the progress of our effort to "bring set theory to the masses" by developing Proof Maker, a new Proof Designer-inspired software that ports Proof Designer to hand-held devices such as smart-phones and tablets. Proof Maker, when completed, will allow students to use Proof Designer with the ease of a touch, literally, on their smart devices. Our goal behind developing Proof Maker is to enable any one who is interested enough to develop elementary set theory proofs anywhere he or she might be (think of doing proofs while waiting at a bus stop!) and at any time he or she wishes (think of writing proofs before going to bed, or even in bed!). In this paper we report on the improvements we made to Proof Designer so far, and on the (many) steps remaining for us to have a fully-functioning Proof Maker "in our hands".