Analysis

Differentiation

1. The Frechet derivative

Measure and probability

1. ★★★★★ Sigma fields are Venn diagrams
2. ★★☆☆☆ Introduction to measure
3. ★★☆☆☆ Outer and inner measure, complete measure

Functional analysis

1. Why does uniform convergence really matter? The properties of functions
2. Differential equations
3. Picard iteration

Calculus of variations -- in your study of calculus, you may have often wondered about problems like: given a curve in R^3, how do you find the surface with it as a boundary that minimises its area? Or, what function between two defined points minimises the surface area of its surface of revolution