Adaptive learning systems personalize education based on individual learner knowledge and progress. Knowledge tracing: Bayesian Knowledge Tracing (BKT) models probability of each skill mastery from practice sequence. Deep Knowledge Tracing (DKT) uses LSTM to model more complex knowledge relationships. Features: response correctness, time taken, hint usage, prerequisite mastery. Spaced repetition optimization: SuperMemo SM-2 or FSRS (Free Spaced Repetition Scheduler) algorithms compute optimal review intervals based on performance. AI enhancement: ML models personalize interval calculation per student based on their retention patterns. Learning path optimization: given current knowledge state and learning goal, compute optimal sequence of topics. Constraint: prerequisite dependencies between topics. Reinforcement learning for dynamic path adjustment based on engagement and performance. LLM tutoring: Socratic method prompting - instead of giving answers, ask guiding questions: "What do you already know about X? What happens if we change Y?" Detect misconceptions from student explanations, provide targeted correction. Adaptive difficulty: performance model adjusts problem difficulty to keep student in "zone of proximal development" (70-80% success rate). Too easy = boredom, too hard = frustration. Assessment generation: LLM generates novel problems at appropriate difficulty level with verified correct solutions. Implementation: PostgreSQL + pgvector for student models, Redis for session state, FastAPI backend, Next.js frontend.