In "Introduction to Optimization Models" (UVA-QA-0682), we explored the basics of using optimization models, or mathematical programming. In this technical note, we turn our attention to the mathematics underlying optimization. While not essential, a deeper understanding of the math can help you become a significantly more effective and efficient user of optimization models. It is well worth the investment if you anticipate using optimization on a regular basis. Among other things, a deeper understanding of the math enables you to use the more advanced options that are generally available in most optimization software packages. (These options enable you, for example, to solve large models more quickly than you otherwise might.)