This is the second meeting of the Probability/Analysis Circle, a new event for juniors, seniors, and master’s students interested in probability and analysis. Eigenvalues of a symmetric matrix are complicated functions of the matrix’s entries. If we view the mapping from the entries of a symmetric matrix to its eigenvalues and eigenvectors as a change of variables, what is the Jacobian? We will compute it for the 2x2 case and discuss the general nxn case. Then, we’ll use this formula to explore the distribution of random eigenvalues for certain random symmetric matrices. Students are expected to know multivariable calculus.