Howe's Method
This post elucidates the mathematical foundations of Howe's method.
David Templin's Blog
A blog about mathematics, computer science, and related topics.
Latest posts
Applicative Bisimilarity
This post examines a notion of equivalence for terms of the lambda calculus known as applicative bisimilarity.
Coinduction and Bisimulation
This post introduces the concepts of coinduction and bisimulation via the theory of fixed points of monotone maps.
The Shoelace Formula
This post discusses the Shoelace Formula for computing the area of arbitrary simple polygons.
Structural Induction
This post explores structural induction and recursion based on the theory of monotone maps on powersets.
A Note on Surface Integrals
This post describes a method for computing surface area solely based on the dominant component of the normal vector at each point along the surface.
The Hyperreal Numbers
This post discusses the basics of non-standard analysis.
Solid Angle via Differential Geometry
This post analyzes solid angle using concepts from differential geometry.
Definability of Recursive Functions
This post discusses recursive functions and their definability in arithmetic.
The Real Numbers
This post examines the real numbers.
The Darboux Integral
This post describes the classical notion of an integral from calculus in terms of the Darboux integral, which is equivalent to the Riemann integral, but often more computationally tractable.
Darboux's Theorem
This post gives a detailed overview of Darboux's theorem, discussing the significance of the theorem and providing two different proofs.
Hamiltonian Mechanics
This post introduces Hamiltonian mechanics using the formalism of differential geometry, culminating in Noether's theorem, which describes the correspondence between certain symmetries and conservation laws.
Harmonic Oscillators
This post offers a brief overview of simple and damped harmonic oscillators.
Distributions
This post gives a cursory overview of the concept of distributions from functional analysis.