This talk presents a multiscale mathematical framework integrating epigenetic inheritance, cellular population dynamics, and multidimensional omics data to investigate the emergence of acquired drug resistance in cancer. By combining stochastic modeling with single-cell transcriptomic analysis, the study quantitatively characterizes the evolutionary dynamics of drug-tolerant persister (DTP) cells and identifies epigenetic instability as a critical driver of resistance progression. The framework further reveals potential biomarkers associated with drug tolerance and provides quantitative predictions for optimal intermittent treatment strategies. This work highlights the power of integrating mathematical modeling with high-dimensional biological data to uncover the mechanisms of cancer adaptation and to guide the development of more effective therapeutic interventions.