The overall purpose of this course is to provide the mathematical foundations for the techniques is Biostatistics. A master's-level biostatistician needs to read and understand the statistical/biostatistical literature. This is necessary to not only understand the strength and weaknesses of present statistical methods but to also be able to understand and apply future techniques that will be developed during ones career. Most likely, students would have been exposed to the basics of statistical inference in more applied courses where one is scanning through some SAS code looking for the p-values. Here we will reintroduce these concepts with a view to the mathematical underpinnings. Since this is mathematics, it will be necessary to understand the basic concepts of a mathematical proof. Students should have a good background in applied statistics, and it would be helpful to be somewhat familiar with the basic concepts in univariate calculus.