Dr. Sarah's Proof-Writing Checklist for MATH 4710

Proof Introduction

  • Are the hypotheses clearly stated?
  • Is the goal of the proof clearly stated?
  • Is the goal of the proof clearly reworded using definitions?
     

    Understanding the Problem and Planning a Solution

    Turn in projects or prepare to present problems even if it they are not complete, even if only to say, "I do not understand such and such" or "I am stuck here." Be as specific as possible. Conjecture.
  • Is there evidence of partial understanding of the problem?
  • Is there evidence of complete and deep understanding of the problem?
  • Is there evidence of a partially correct plan based on correct interpretation of the problem?
  • Is there evidence that the plan could lead to a correct solution if implemented properly?

    Body of the Proof

  • Are all of the hypotheses clearly reworded using definitions?
  • Does the proof use the hypotheses correctly?
  • Does the proof give evidence of deep mathematical understanding of the problem and its solution?
  • Is the proof as brief and elegant as possible?
  • Does the proof make logical sense?
  • Is the proof correct?
  • Is the proof complete?
  • Does this proof prove the general case?
  • In a "Proof by Contradiction", is the contradiction hypothesis correct?
  • In a "Proof by Contradiction", is the contradiction clearly explained?
  • In a "Proof by Examining all Cases", have you explained why the list of cases you have is complete and correct?
  • In a "Proof by Examining all Cases", have all the necessary cases been checked?

    From One Step to the Next

  • Does each step follow logically from the previous step?
  • Is the connection between steps clearly explained?

    • Terminology

  • Are all variables, terminology, and notation that are used in the proof clearly defined?
  • Do all variables, terminology, and notation represent the general case (avoid hidden assumptions)?

    When Using Ideas from Elsewhere...

  • Are any theorems mentioned clearly stated and given acknowledgement?
  • Are all of the hypotheses of theorems used satisfied?
  • Is proper reference to books, classmates or other sources given? It is fine to talk to other people, but you must give proper reference and write it up in your own words. Examples of proper references: "p. 271 from...", "this website...", "this was Henry's idea", or "Jill and I worked on this together",...

    Conclusion

  • Does the proof have the correct conclusion?
  • Is the conclusion clearly restated at the end?