Writing Guidelines - Math 343
Fall, 2007
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 2
(M) Use complete, clear, concise, grammatically correct 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 3
(M) Write the result you are proving in the form of a statement.  Start each proof with "Proof :" and end each proof with a box or "qed".
(O)
 Introduce names for all objects that arise in the course of the proof, especially if they were not given in the statement of the result to be proven.
 
Assignment 4
(L) Each object you use or construct in the course of your proof must either be
  • chosen to be arbitrary,
  • assumed to exist in the hypothesis,
  • or shown to exist.
You must explicitly and carefully state the origin of any object you refer to. 
(L)
 Be careful to justify each conclusion you draw as following by hypothesis, construction, or from a previous theorem or result.
 
Assignment 6
(L) Do not include extraneous results or consequences that you do not use later in your proof.
(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.

Assignment 7
(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 8
(L) Do not make any assumptions not included in the hypothesis of the statement you are proving.
(P/O)
 Include sufficient detail and organize it effectively so the reader can easily follow the train of thought.