Writing Guidelines - Math 499/599
Spring, 2008

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, grammatically correct English sentences.
(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".

Assignment 3
(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.
(P)
Split your proof into cases when necessary and strive to give a unified, concise proof when cases are not necessary.

Assignment 4
(L) Be careful to justify each conclusion you draw as following by hypothesis, construction, or from a previous theorem or result.
(P/O)
Include sufficient detail and organize it effectively so the reader can easily follow the train of thought (imagine the reader is a colleague in the same course, not someone who already knows how to prove the result).

Assignment 5
(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. 
(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