David Templin's Blog

The lambda calculus represents a minimalistic, prototypical programming language.

A previous post indicated how lambda terms comprise the states of a particular labeled transition system and that the natural notion of equivalence of states within this system is applicative bisimilarity.

In these notes, I discuss Cantor's famous "zigzag" argument.

This post discusses the denotational semantics of the lambda calculus.

In this post, I will discuss Howe's method (due to computer scientist Douglas J.

In this post we will explore a notion of equivalence between terms in the lambda calculus known as applicative bisimilarity.

A previous post explored the concept of structural induction.

How is the area of an arbitrary simple polygon computed?

The principle of mathematical induction on the natural numbers is well known: it states that the set of natural numbers \(\mathbb{N}\) is the smallest set containing \(0\) and closed under the successor operation \(n \mapsto n + 1\).

In this post, we will prove a useful theorem about surface integrals.

The notion of infinitesimals, i.e., infinitely small quantities, was applied historically by figures such as Newton and Leibniz to problems of analysis.

In a previous post, I described solid angle using tools from calculus.

The recursive functions are one model of computation.

What are the real numbers?

An integral is a continuous analog of a sum.

This post will examine Darboux's theorem, an important theorem in symplectic geometry.

There are three standard approaches to classical mechanics, each named after their respective originator: Newtonian mechanics - after Sir Isaac Newton, Lagrangian mechanics - after Joseph-Louis Lagrange, Hamiltonian mechanics - after Sir William Rowan Ham…

Imagine a spring suspended vertically downward from a horizontal surface with an object attached to the bottom of the spring, as in the following figure.

There are many situations in which various classical mathematical theories fail to apply yet we would like them to apply nonetheless.