Reading a Mathematics Paper · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reading a paper out of order, on purpose

Mathematics · Mathematical Thinking · ages 22-23
Name ______________________   Date ____________

  1. What should you extract from a mathematics paper before reading any proof?

    • The statement of the main theorem and its hypotheses
    • Every line of the first proof
    • The reference list
    • The author affiliations

  2. What should you extract from a mathematics paper before reading any proof?

    • Every line of the first proof
    • The reference list
    • The statement of the main theorem and its hypotheses

  3. Why run the theorem on an example before touching the proof?

    • It shows what the theorem does
    • It replaces the proof
    • It lists the references

  4. A paper uses compact without defining it but carefully defines tame cover. Compact is assumed background and tame cover is introduced.

    Circle one:   True   False

  5. How do you separate definitions a paper assumes from ones it introduces?

    • Introduced ones are defined in the text (we call, define); assumed ones are used without definition
    • Assumed ones appear in the title
    • Introduced ones are never used again
    • They cannot be told apart

  6. A lemma is cited exactly once in the main proof, to bound an error term. What is the lemma doing for the main argument?

    • Restating the main theorem
    • Supplying the error bound the main argument needs
    • Listing the paper hypotheses

  7. A theorem reads: let f be continuous on the closed interval from 0 to 1. Then f attains a maximum. What are its hypotheses?

    • f attains a maximum
    • f is differentiable on the interval
    • f is continuous and the domain is the closed interval

  8. A theorem reads: Let f be continuous on [0, 1]. Then f attains a maximum. What are its hypotheses?

    • f is continuous and the domain is the closed interval [0, 1]
    • f attains a maximum
    • f is differentiable on [0, 1]
    • The maximum value is unique

  9. The workable route opens the technical machinery before the statement, example, and proof sketch make sense.

    Circle one:   True   False

  10. You open a short paper with one theorem, one example, and two lemmas. What is the correct first pass?

    • Verify every line of the second lemma first
    • State the theorem and list its hypotheses without following proofs line by line
    • Memorize the reference list
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Reading a paper out of order, on purpose W1-mt_pTF-HzLWE6-s1

  1. The statement of the main theorem and its hypotheses · Knowing what is claimed and under which assumptions lets you read the proof with purpose.
  2. The statement of the main theorem and its hypotheses · Knowing what is claimed and under which assumptions lets you read with purpose.
  3. It shows what the theorem does · An example exhibits the claim in action, giving the proof a target to aim at.
  4. True · The undefined term is background, while the defined one is new.
  5. Introduced ones are defined in the text (we call, define); assumed ones are used without definition · Signal phrases mark new definitions, while background terms arrive with no explanation.
  6. Supplying the error bound the main argument needs · Its role is the single job it performs at the citing step.
  7. f is continuous and the domain is the closed interval · Everything before Then is assumed; the maximum is the conclusion.
  8. f is continuous and the domain is the closed interval [0, 1] · The hypotheses are the assumptions (continuity, closed interval); attaining a maximum is the conclusion.
  9. False · Machinery comes last, only when the rest already makes sense.
  10. State the theorem and list its hypotheses without following proofs line by line · The first pass extracts the target; line-by-line checking comes later.
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