Discrete Structures

Understanding & Creating Proofs

Last Update: 6 October 2010

Note: NEW or UPDATED material is highlighted

  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

  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!

  3. 3 Tasks of Proof Ability ("Mathematical Maturity")

    1. Understanding (& verifying) proofs

    2. Generating proofs

      • Harder

        • But there are algorithms & heuristics

    3. Creating new proofs

      • Beyond our scope!

Copyright © 2008–2010 by William J. Rapaport (rapaport@buffalo.edu)