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Understanding & Creating Proofs CSE 191. William J. Rapaport Department of Computer Science & Engineering, Department of Philosophy, Department of Linguistics, and Center for Cognitive Science [email protected] http://www.cse.buffalo.edu/~rapaport. 3 Writing Tasks.

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understanding creating proofs cse 191

Understanding & Creating ProofsCSE 191

William J. Rapaport

Department of Computer Science & Engineering,

Department of Philosophy, Department of Linguistics,

and Center for Cognitive Science

[email protected]

http://www.cse.buffalo.edu/~rapaport

3 writing tasks
3 Writing Tasks
  • Read the following story & answer the questions:
    • John went to a restaurant for dinner.He ordered a steak.When he was finished, he paid the bill & left.

Q1: Who is the main character?

Q2: Did he eat dinner?

(easy & straightforward)

3 writing tasks cont d
3 Writing Tasks (cont’d)
  • Write a brief e-mail message (4–5 sentences) about what you did on vacation.

(easy; but requires a bit of thinking)

3 writing tasks concluded
3 Writing Tasks (concluded)
  • Write a beautiful, original poem about your favorite thing. It must rhyme. If it is publishable, it will make you famous.

(hard; lots of pressure on you)

3 tasks of language ability
3 Tasks of Language Ability
  • Understanding (listening, reading)
    • Relatively easy (with practice)
  • Generation (speaking, writing)
    • Much more difficult
  • Creative language use (writing creative prose, poetry)
    • Hard!
3 tasks of proof ability mathematical maturity
3 Tasks of Proof Ability(“Mathematical Maturity”)
  • Understanding (& verifying) proofs
    • Easy:
      • Use Rapaport’s “slow reading” technique
  • Generating proofs
    • Harder
      • But there are algorithms & heuristics
  • Creating new proofs
    • Beyond our scope!
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