\(\def\Real{\mathbb{R}}

\def\Comp{\mathbb{C}}

\def\Rat{\mathbb{Q}}

\def\Field{\mathbb{F}}

\def\Fun{\mathbf{Fun}}

\def\e{\mathbf{e}}

\def\f{\mathbf{f}}

\def\bv{\mathbf{v}}

\)

#### Convexity

Convex sets. Convex hulls. Supporting hyperplanes.

Convex functions; properties. Log-convex functions.

#### Sample problems

- Is the set of continuous functions on \(\Real^2\) positive at all points with rational coordinates numbers convex?