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class1 - cs3102 Theory of Computation(aka cs302 Discrete...

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cs3102: Theory of Computation (aka cs302: Discrete Mathematics II) Spring 2010 University of Virginia David Evans Computation is what Computers do, who needs theory? flickr: gastev [cc] Charles Babbage’s Difference Engine (1822, recreation) “Engining” is what Engines do, who needs theory? Hero of Alexandria’s aeolipile steam engine Matthew Boulton and James Watt steam engine, 1817 Nicolas Carnot (1796 – 1832) “Is the potential work available from a heat source potentially unbounded?" “Can heat engines be improved by replacing the steam with some other fluid or gas?” Carnot’s Answer Efficiency of an ideal engine depends only on the temperature difference between the reservoirs. Does Theory Matter? Theory and Construction of a Rational Heat-engine to Replace the Steam Engine and Combustion Engines Known Today, Rudolf Diesel, 1893
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Theory Drives Practice Drives Theory Math Theorem vs. Science Theory Math Theorem Starts with a simple, well- define model Deductive reasoning: Proven using logical deduction Useful it if provides deep insights Scientific Theory Starts with the complex, messy universe Inductive reasoning: “Proven” by lots of confirming observations and no non- conforming observations Useful if it makes reliable predictions and helps us understand the universe Even wrong theories are useful This class: mostly Math Theorems, but some Scientific Theories Key Questions 1. “Is the potential work available from a heat source potentially unbounded?" 2. “Can heat engines be improved by replacing the steam with some other fluid or gas?” Carnot’s questions about heat engines Analogous questions about computers 1. “Can all problems be solved by computers?" 2. “Can computers solve more problems by changing their operation?” Precise Definitions Needed What is a problem ? What is a computer ? What problems can a computer solve?
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This note was uploaded on 04/05/2010 for the course CS 150 taught by Professor Humphreys,g during the Spring '08 term at UVA.

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class1 - cs3102 Theory of Computation(aka cs302 Discrete...

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