This general, introductory tutorial on mathematical modeling (in pdf format) is intended to provide an introduction to the correct analysis of data. It addresses, in an elementary way, those ideas that are important to the effort of distinguishing information from error. This distinction constitutes the central theme of the material described herein. Both deterministic modeling (univariate regression) as well as the (stochastic) modeling of random variables are considered, with emphasis on the latter. No attempt is made to cover every topic of relevance. Instead, attention is focussed on elucidating and illustrating core concepts as they apply to empirical data.
Here one finds a collection of applets and famous problems in probability (as well as other areas of mathematics such as calculus and geometry). Some of the topics/problems include: Bertrand's Paradox, Birthday Coincidence, Buffon's Needle (Noodle), Lewis Carroll's Problem, Monty Hall Dilemma, Parrondo Paradox, and Three pancakes problem.