Assess students' ability to design and construct an explicit infinite family of Cayley-graph expanders arising from SL(2, F_p) (p prime): require explicit generating sets for each p, a rigorous proof of a uniform spectral gap independent of p (via representation-theoretic, arithmetic, or combinatorial methods), and detailed analysis of combinatorial and spectral properties including girth lower bounds, diameter estimates, and eigenvalue bounds/asymptotics.