Academic advising in higher education is under severe strain, with advisor-to-student ratios commonly exceeding 300:1. These structural bottlenecks limit timely access to guidance, increase the risk of delayed graduation, and contribute to inequities in student support. We introduce Aurora, a modular neuro-symbolic advising agent that unifies retrieval-augmented generation (RAG), symbolic reasoning, and normalized curricular databases to deliver policy-compliant, verifiable recommendations at scale. Aurora integrates three components: (i) a Boyce-Codd Normal Form (BCNF) catalog schema for consistent program rules, (ii) a Prolog engine for prerequisite and credit enforcement, and (iii) an instruction-tuned large language model for natural-language explanations of its recommendations. To assess performance, we design a structured evaluation suite spanning common and edge-case advising scenarios, including short-term scheduling, long-term roadmapping, skill-aligned pathways, and out-of-scope requests. Across this diverse set, Aurora improves semantic alignment with expert-crafted answers from 0.68 (Raw LLM baseline) to 0.93 (+36%), achieves perfect precision and recall in nearly half of in-scope cases, and consistently produces correct fallbacks for unanswerable prompts. On commodity hardware, Aurora delivers sub-second mean latency (0.71s across 20 queries), approximately 83X faster than a Raw LLM baseline (59.2s). By combining symbolic rigor with neural fluency, Aurora advances a paradigm for accurate, explainable, and scalable AI-driven advising.