This online tool has been created through support from the Blended Online Learning and Development Program (BOLD) through the Center for Teaching and CIRTL at Vanderbilt University. If you are using this tool, it most likely because you are enrolled in the BIOS7631 course, Advanced Concepts in Probability and Real Analysis for Biostatisticians. You are being provided with this online supplement before the course begins to expose you to some of the information that will be covered in the first few lectures of the course.
The online supplement is organized into three sections: Proof Toolkit, Random Walks, and lim sup/lim inf. The Proof Toolkit tab provides some examples of different types of proofs that can be used throughout the course, and each landing page in the toolkit provides a general description of how to use the proof (hover over the “Proof Toolkit” tab to navigate the different landing pages, and click on the “Proof Toolkit” tab for a more thorough overview of what to expect from this section). The Random Walks tab includes a short video that discusses random walks in a more theoretical context, an exercise to work on yourself, and some R-code that is used in the video. The lim sup/lim inf tab also includes a short video with multiple in-video questions, and a couple of exercises to work on yourself.
To get the most out of this online supplement, I highly encourage you to go through this material in its entirety before the course starts. In addition, I encourage you to try out the practice problems and in-video questions yourself before viewing the worked out solutions. The use of this module: videos, exercises, and handouts are for your benefit and completion/correct answers will NOT go towards your final grade.