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.
How to Check Proofs.
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:
During a global analysis you consider your proof as a whole:
Acknowledgements and References.
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., ... jointly obtained by J. Doe and myself, we thank J. Doe for her helpful advice.
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., see J. Doe: Analysis Problem Solver, Sunshine Press, N.Y. 1874, Theorem 2.1.3 ..... It is also necessary to ``adjust" the proof so that it can be understood with the knowledge of notations, definitions and theorems used in class. Using a result from a source without giving the proper reference constitutes an act of plagiarism.