Writing Guidelines - Math 343

Writing clearly helps promote clear thinking, so we will focus some of our attention on learning to write more clearly. 

An overall guideline is to write solutions in a form that you could understand if you looked back at the assignment a year after completing the course (try this with previous work!) or in a form that is understandable to another student who is not in the course with you.

Guidelines for each assignment include guidelines for all previous assignments. 

These guidelines are adapted from those developed by Dr. Tracy Payne. 

Abbreviations are as follows:
(M)
 Mechanics                                                                                        
(P) Presentation
(O)
 Organization
(L)
 Logic
(E)
 Enhancement

Assignment 1
(M) Use complete, clear, concise English sentences.
(P)
 Include carefully drawn, precise pictures to illustrate your proof.  Clearly label the information you are given or derive in the course of your proof on the picture.
 
Assignment 3
(L) Each object you use in the course of your proof must either be
  • chosen to be arbitrary,
  • assumed to exist,
  • or shown to exist.
You must explicitly and carefully state the origin of any object you refer to.
(L)
 When you apply a theorem or previous result, it should be clear which objects you are applying it to.
 
Assignment 4
(L) When you apply a theorem or previous result, you should fully justify earlier in your proof that the hypothesis of the theorem is satisfied.
(L)
 Do not include extraneous results or consequences that you do not use later in your proof.
 
Assignment 5
(L) There is no ambiguity in math.  Short sentences may carry heavily condensed significance.
  • Read the statement of the problem carefully and repeatedly.  Read and interpret every word carefully.
  • Words have precisely defined meanings.  For instance, "similar" and "corresponding" are different and "thus" suggests that what comes next follows from what was just previous.
  • You, too, should use language precisely to support the logical structure of your proof.
(L)
 Do not make any assumptions not included in the hypothesis of the statement you are proving.

Assignment 6
(M) Use a balance of mathematical symbols and words to make your writing concise but clear and understandable.
(O)
 Signpost your progress and direction.  Use phrases like "first we will show", "next", "the last step is", "we are now able to", and others.

Assignment 7
(O) Break your proof into its main steps.  Label the steps.
(M)
 Cite a theorem or result used either by number or by stating the hypothesis and conclusion.