Problems and proofs in written work are to written up formally and turned in on the dates announced. There are two parts to be turned in, the solution or proof itself and an accompanying narrative.
For these problems, proofs or exercises you should focus not only on
solving them but on noticing how you solve them. Keep notes, while you are working on one of these,
of anything that presents a block, any false starts, what makes you think of trying a
certain approach, and whether and why (if possible) that strategy works or does not work.
When you are finished working the problem, proof or exercise(or alternatively, if you are convinced you will
not be able to solve the problem) write a narrative telling the story, in detail, of the process
you went through to reach that point. Your audience for this narrative is another student in the
class, not a particular student but assume this student is confused by the problem and how you
solved it, or that the student has not yet tried to solve this particular problem. For proofs, pay close attention to
word-usage. In your narrative indicate how confident you are that your proof is correct and discuss any uncertainties you have.
You may have difficulty with many of the assignments in this class. It is expected that you will make use of my office hours
on a regular basis. This is a 300-level class so use of the tutoring program is no longer appropriate. Your problem solutions, exercises and proofs should be
written in such a way that they could be understood by someone who has not just read the book. It is ok to reference theorems, etc. but don't neglect to indicate
what you are proving or what the problem is, etc.
In all cases, if homework is completed collaboratively or after consultation with others,
this must be acknowledged in the accompanying narrative.
The purposes of the narratives are:
1. To enable you to recognize, and remember, strategies that are successful and those that are
not.
2. To help you to develop your own approach to problem solving, one that works for you.
3. To help me to understand the problems you are having and to develop ways to assist you in
learning the material and acquiring the skills this course is designed to teach you.
4. To provide a mechanism for you to share your insights with the rest of the class. You can learn from each other as well as from me. It may be that the approach another student takes may be more instructive, for you, than the one I take.
5. To deepen your understanding of the material.
and,
6. Most importantly, to give me an opportunity to help you to develop your skills not only in using mathematics
to solve
problems but in communicating mathematical ideas and writing mathematical arguments (proofs).
Math is not a spectator sport! You must practice in order to learn. Homework will be assigned after every class. You are encouraged to work together, make use of the tutors and see me outside of class if you are having any trouble. We can schedule additional study sessions if you request them. My office hours are excellent times to schedule group working sessions with your peers in the seminar room. I caution you, however, to remember that on the tests you will be required to work alone. The ability to watch and understand while someone else solves a problem is not the same as the ability to do it yourself. Make sure you work enough problems yourself. Boardwork problems will not be collected but the presenter should not be the only person who has done them. ASK QUESTIONS IF THERE IS A PROBLEM YOU COULD NOT DO!!! Enough problems should be worked in class so that students will be able to check their understanding of concepts. If this is not the case for you, please make use of office hours!!