Dynamical Numerics for Numerical Dynamics
An expository presentation on the assessment of the validity of numerical simulations of continuous-time dynamical systems by treating numerical methods as discrete-time dynamical systems. The basics of the assessment of the convergence and stability of numerical methods are introduced and discussed.
Gauge Theories and the Gauge Argument
An expository presentation on the gauge argument, which is a classic argument in gauge field theory that claims that gauge fields arise naturally by imposing locally (at each spacetime point) a global internal symmetry of a Lagrangian field. A criticism of this argument given by Healy in his book Gauging What's Real: The Conceptual Foundations of Gauge Theories (2007) is then considered.