In the field of Education, Educational Technology and Digital Pedagogy, heterogeneous mathematical preparation among incoming university freshmen creates severe learning bottlenecks. This empirical investigation systematically examines AI-Powered Adaptive Tutoring Systems for Personalized Remedial Mathematics Instruction through a multi-stage experimental methodology and rigorous quantitative analytical framework. Utilizing adaptive Bayesian knowledge tracing algorithms integrated into an automated web-based remedial mathematics platform, data were gathered across multiple operational cycles and validated against established international benchmarks. The statistical and computational results reveal that students using the adaptive tutor mastered remedial algebra concepts 35% faster than those in traditional lecture recitations. Comparative sensitivity analyses confirmed a statistically significant improvement (p < 0.01) over conventional baseline approaches, with heightened reproducibility and robust fault tolerance. These comprehensive findings provide actionable theoretical insights and practical implementation guidelines for mathematics departments, developmental education programs, and adaptive e-learning software firms. Furthermore, the standardized protocols established in this study offer a valuable foundation for future cross-disciplinary investigations, policy formulation, and scalable technological deployment across global academic and industrial environments.