Some Remarks on Analysis Homework
Solving the assigned homework problems is an integral part of our course. I assume that you will spend a considerable amount of time on obtaining solutions to the homework assignments.
The objective of writing a proof is to show an informed reader (e.g. a fellow mathematician), why the statement under consideration is correct. Because of its communicative nature, a proof has to satisfy the same standards as other technical writing: It has to be correct (your main concern!), express its thoughts clearly, explain its ideas in the easiest way possible, be coherent, legible and aesthetically pleasing. Alternating between ``proofreading" your proof line-by-line and considering your ``product" as a whole is one way to achieve these goals.
While you are carefully going through each line and each little step of your proof, you should check for the following: - Is this step correct?
- Are there counterexamples?
- Are all symbols defined or explained, the first time they show up in the proof?
- Do I need all the symbols and steps I use?
- Is the spelling correct?
- Can the wording be improved upon?
- Is there a more elegant way of explaining the argument?
During a global analysis you consider your proof as a whole: - Does my proof ``really" show what I am supposed to show?
- Did I forget to prove any of the statements?
- Are all parts of my proof really necessary?
- Do I use all the hypotheses?
- Do I give all necessary references and acknowledgements?
- Does one need all the hypotheses? Does my proof suggest generalizations?
- Does my ``final product" look good?
I encourage cooperation among students in working on the assigned
homework problems. If you work together in obtaining a solution
to a homework problem, proper credit must be given, e.g., There is a fine line between academic cooperation and collusion. To avoid the latter, it is recommended when working in a group, that the participants independently write a final version of their proof. Copying a solution from a classmate or other sources constitutes an act of academic dishonesty.
Occasionally you will be able to find a solution to a homework
problem in another book. In this case you must give the
reference, e.g., |

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