Fun with Dick and Jane at relativistic velocities
Years ago, I found a copy of this unusual children’s book at the back of a storage closet in the Ann Arbor Hands-On Museum. It is out of print, but the authors have kindly given me permission to distribute it here. The book is available in two formats: one that you can read on your computer, and one that you can print and bind yourself.
A brilliant first introduction to differential geometry. Working from a coordinate-free point of view, Wald encourages the reader to make direct contact with geometric objects, rather than viewing them through a haze of numbers. Deft coordinate-free calculations are carried out using abstract index notation. The style is informal, but lays a solid foundation for more rigorous studies. There is also some material on general relativity.
Information Theory, Relative Entropy and Statistics
“In a nutshell, the relative entropy K(f ||g) has two arguments f and g, which both are probability distributions belonging to the same simplex. Despite formally similar, the arguments are epistemologically contrasted: f represents the observations, the data, what we see, while g represents the expectations, the models, what we believe. K(f ||g) is an asymmetrical measure of dissimilarity between empirical and theoretical distributions, able to capture the various aspects of the confrontation between models and data...”