Understanding & Creating Proofs

1. 3 Writing Tasks
   1. 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

   2. Write a brief e-mail message (4–5 sentences) about what you did on vacation.
      • easy; but requires a bit of thinking

   3. 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

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2. 3 Tasks of Language Ability
   1. Understanding (listening, reading)
      • Relatively easy (with practice)

   2. Generation (speaking, writing)
      • Much more difficult

   3. Creative language use (writing creative prose, poetry)
      • Hard!

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3. 3 Tasks of Proof Ability ("Mathematical Maturity")
   1. Understanding (& verifying) proofs
      • Easy:
        • Use Rapaport's "slow reading" technique

   2. Generating proofs
      • Harder
        • But there are algorithms & heuristics

   3. Creating new proofs
      • Beyond our scope!