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.

Writing for each assignment should follow guidelines for that assignment and 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 on the picture the information you are given or derive in the course of your proof.
 
Assignment 2
(M) Start each proof with "Proof :" and end each proof with a box or "qed".
(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.

Assignment 3
(L) Do not include extraneous results or consequences that you do not use later in your proof.
(L)
 Be careful to justify each conclusion you draw as following by hypothesis or from a previous theorem or result.

Assignment 4
(M) If using a theorem or result to draw a conclusion, cite the theorem or result by name or number or by stating the hypothesis and conclusion.
(P)
 Use Geometer's Sketchpad to produce pictures to illustrate your proofs and/or color coding of text and pieces of your figure to make the argument easier to follow.

Assignment 5
(L) When you apply a theorem or previous result, it should be clear which objects you are applying it to.
(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 to tell the reader where you are headed.

Assignment 6
(M) Use a balance of mathematical symbols and words to make your writing concise but clear and understandable.
(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.

Assignment 7
(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.
(E)
 Strive for clear and concise arguments over longer more complicated arguments  One thing that will help with this is citing a previous result or proof of a result rather than repeating the steps in its proof.

Assignment 8
(O) Break long proofs into main steps and label the steps.
(L)
 Do not make any assumptions not included in the hypothesis of the statement you are proving.

Assignment 9
(P) Include sufficient detail so the reader can easily follow the train of thought.
(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.