Random matrix theory (RMT) has long served as a cornerstone of modern physics, mathematics, and complex systems analysis. More recently, topological and differential topological methods have emerged as powerful tools to characterize the global structures and stability properties of ecological networks. This article develops an integrated framework bridging RMT with topology and differential topology to study ecological systems, aiming to provide novel insights into their resilience and underlying structural features. We present the relevant mathematical foundations, illustrate computational algorithms (including multiple graphical outputs), and demonstrate these methods on both synthetic and real ecological data. Our findings highlight how topological invariants, combined with the spectral properties of large random matrices, shed light on the stability and transition behaviors of communities under perturbations. Advantages and limitations are discussed, paving the way for future research directions at the intersection of mathematics and ecology.