We report on seven years of experience with teaching an annual, full-term, university course devoted entirely to SETI. SETI is usually featured in only one or a few lectures in traditional astronomy or astrobiology courses. However, SETI's rich interdisciplinary character provides a powerful vehicle for introducing a full term's worth of foundational concepts to Science, Technology, Engineering, and Math (STEM) students. The UCLA SETI course has introduced such concepts to 120+ advanced undergraduate and 10+ graduate students so far. During the course, students use astronomical catalogs to identify preferred targets, design an observing sequence for the 100 m Green Bank Telescope, participate in remote observations, analyze the data to identify prominent sources of radio frequency interference and narrowband technosignature candidates, contribute source code improvements to the UCLA SETI data processing pipeline, and co-author peer-reviewed journal articles that describe the results. In the process, they learn about exoplanets, celestial mechanics, celestial coordinate systems, electromagnetic wave radiation and propagation, radio astronomy, signal processing and Fourier analysis, probability distributions and statistics, database management and structured query language, collaborative software development, accelerated computing, machine learning, and scientific writing. So far, our search has sampled over 40 thousand known stars in 100+ distinct sky directions and detected over 60 million narrowband signals. A syllabus, course evaluations, publications, and student testimonials are available at https://seti.ucla.edu.