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The R language, a freely available environment for statistical computing and graphics is widely used in many fields. This 'expert-friendly' system has a powerful command language and programming environment, combined with an active user community. We discuss how R is ideal as a platform to support experimentation in mathematical statistics, both at the undergraduate and graduate levels. Using a series of case studies and activities, we describe how R can be used in a mathematical statistics course as a toolbox for experimentation. Examples include the calculation of a running average, maximization of a nonlinear function, resampling of a statistic, simple Bayesian modeling, sampling from multivariate normal, and estimation of power. These activities, often requiring only a few dozen lines of code, offer students the opportunity to explore statistical concepts and experiment. In addition, they provide an introduction to the framework and idioms available in this rich environment. KEY WORDS: Mathematical statistics education; Statistical computing., 1. INTRODUCTION The R language (Ihaka and Gentleman 1996; Hornik 2004) is a freely available environment for statistical computing and graphics. It allows the handling and storage of data, supports [...]