Mathematics: Functions and Series

This lecture covers various topics related to functions and series, including the concepts of maximum, minimum, supremum, and infimum. The instructor discusses how to identify global maximum and minimum points, as well as majorants and minorants of functions. Examples are provided to illustrate these concepts, such as functions that are bounded, unbounded, even or odd. The lecture also touches on the notion of periodicity and the properties of functions with symmetry. Additionally, the instructor explains the importance of understanding the behavior of functions near critical points and how to determine if a function is majorized or minorized. The session concludes with a discussion on Gaussian functions and the relationship between maximum, minimum, supremum, and infimum.