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Teaching autonomous systems is challenging because it is a rapidly advancing cross-disciplinary field that requires theory to be continually validated on physical platforms. For an autonomous vehicle (AV) to operate correctly, it needs to satisfy safety and performance properties that depend on the operational context and interaction with environmental agents, which can be difficult to anticipate and capture. This paper describes a senior undergraduate level course on the design, programming and racing of 1/10th-scale autonomous race cars. We explore AV safety and performance concepts at the limits of perception, planning, and control, in a highly interactive and competitive environment. The course includes an ethics-centered design philosophy, which seeks to engage the students in an analysis of ethical and socio-economic implications of autonomous systems. Our hypothesis is that $1/10th-scale autonomous vehicles sufficiently capture the scaled dynamics, sensing modalities, decision making and risks of real autonomous vehicles, but are a safe and accessible platform to teach the foundations of autonomous systems. We describe the design, deployment and feedback from two offerings of this class for college seniors and graduate students, open-source community development across 36 universities, international racing competitions, student skill enhancement and employability, and recommendations for tailoring it to various settings.