Sparsity has, of late, become an important concept in Applied Mathematics/Signal Processing. The key idea is that many types of data arising naturally in applications can be described by a small number of significant degrees of freedom (which allows for sensing of data compressively). The question of finding the significant degrees of freedom is answered by compressive sensing theory.  

Syllabus:

Sampling Theorem, Under-determined linear systems, Classical solution techniques, l0 and l1 minimization problems, and their equivalence, Theoretical guarantees and solvers for sparse signal recovery,  Greedy and Convex optimization techniques, Dictionary learning, Applications in signal/image processing.

Pre-requisite:  Linear algebra/Matrix theory