Junior Number Theory Seminar | Mathematical Institute

Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

Past events in this series

Mon, 05 May 2025
16:00

Modular arithmetic in the lambda-calculus

Maximilien Mackie

(University of Oxford)

Abstract

The lambda-calculus was invented to formalise arithmetic by encoding numbers and operations as abstract functions. We will introduce the lambda-calculus and present two encodings of modular arithmetic: the first is a recipe to quotient your favourite numeral system, and the second is purpose-built for modular arithmetic. A highlight of the second approach is that it does not require recursion i.e., it is defined without fixed-point operators. If time allows, we will also give an implementation of the Chinese remainder theorem which improves computational efficiency.