A temperature control system operates by sensing the difference between the thermostat setting and the actual temperature and then opening a fuel valve an amount proportional to this difference. Draw a functional closedloop block diagram similar to Figure 1.8(d) identifying the input and output transducers, the controller, and the plant. Further, identify the input and output signals of all subsystems previously described. [Section 1.4: Introduction to a Case Study]

CS 70 Discrete Mathematics and Probability Theory Spring 2016 Rao and Walrand Note 2 1 Proofs In science, evidence is accumulated through experiments to assert the validity of a statement. Mathematics, in contrast, aims for a more absolute level of certainty. A mathematical proof provides a means for guar- anteeing that a statement is true. Proofs are very powerful and are in some ways like computer programs. Indeed, there is a deep historic link between these two concepts that we will touch upon in this course — the invention of computers is intimately tied to the exploration of the idea of a mathematical proof about a century ago. So what types of “computer science-related” statements might we want to prov