Lecture Notes 9/1/10

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1. Today, we finished discussing what discrete math is.
   For a summary, see:
   • "What Is Discrete Math?"
   • "Countability"

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2. Then, we discussed why it was worth studying discrete math.
   For a summary, see "Why might this course be useful?"

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3. Finally, we began our study of logic:
   1. Logic is the mathematical theory of "correct" reasoning & representation
      1. George Boole (of "Boolean variables" fame) called it "laws of thought"

      2. Besides the mathematical theory of logic, there is also a psychological theory of how people actually reason (this is a branch of cognitive science).

      3. And there is a computational theory of how to get computers to reason…
         1. either correctly, as in the branch of AI called "knowledge representation & reasoning"&mdashCSE 463

         2. 
            or like humans, as in the branch of AI and computational cognitive science that studies human reasoning; see link above

   2. Logic is at the foundation of math
      …and of CS (as in the Theory of Computation, CSE 396)
      …and of CEN (logic gates are the fundamental building blocks of electronic circuits)