Last modified: November 26, 2021
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One primary goal of the course is to give you practice writing mathematics with feedback. By the end of the course you will have accumulated a proof portfolio, described below and worth half the course grade.
Each Monday I'll post a selection of recommended problems on material covered up to that point. The following Monday you'll turn in written solutions. I'll comment these (but not grade for credit) and normally return by the next class meeting. I'll also post “model” solutions to selected problems.
Some of the problems, the portfolio candidates, will be marked with a topic from the ten listed below. I plan to assign at least three candidates for each topic, so you have choice about which to submit for grading. By the end of the semester, you'll submit a final draft write-up of one problem for each topic.
Each final draft will be graded excellent (100%), good (85%), satisfactory (70%), or unsatisfactory (0%). An excellent write-up is one I could photocopy and distribute to the class. A good write-up substantially answers the question and shows effort of exposition (clarity, completeness, neatness, legibility). A satisfactory write-up answers the question, but requires effort to read, for reasons including logical disorganization or illegibility. Anything less is unsatisfactory.
You may resubmit a write-up multiple times in order to raise your score on that topic. To resubmit, you must re-write the entire problem, not make corrections to an existing draft. Please consider this an incentive to turn in excellent work with minimal revisions. You may submit up to four proof portfolio write-ups in any given seven-day period.
To emphasize, you only need to submit a written solution for one question for each of the ten topics, and (aside from the four-per-week limit) may turn in these write-ups any time on or before Friday, December 10. On the assumption you'll need an average of one revision per question, expect to turn in about two proof portfolio write-ups per week.
The topics are:
Academic Integrity: Accuracy and honesty, including specific, easy-to-locate citations and proper attribution, are essential skills for producing useful written work. The guidelines below are intended to help you develop habits of good scholarship, including honest collaboration, detailed citation, clarity and completeness of written expression.
Because the final drafts are a primary indicator of your individual work, they are subject to special rules: Once you decide to submit a particular question as a final draft, you must not discuss that problem with anyone but me. Your wording, calculations, and structure of the overall argument must be yours alone. Any instances that appear to violate this policy will result in a score of zero for that problem, and (as mandated by College policy) in my bringing a formal charge of academic dishonesty.
Except for problems on which you submit a final draft write-up, you may discuss solutions freely with classmates. When you turn in your weekly write-up, you must acknowledge by name any classmates or others you worked with by writing “I worked with...” at the top of your assignment.
If you use an external resource, give an appropriate formal bibliographic citation, such as the author of the resource, the complete URL, and the date on which you retrieved the content; or a book title, author, publisher, date of publication, and page number(s). My goals are to help you develop good habits of documenting your work. This allows others to verify your work more easily.
Please consult the College policy for definitions of plagiarism, cheating, and collusion. In this course, for example, using wording from a classmate (or anyone else, such as a user on a math question and answer web site) on a proof portfolio question is cheating. The same act is, in addition, plagiarism if you do not mention the other person's name. Sharing your own proof portfolio work with a classmate is collusion.
To summarize, these policies are spelled out in order to clarify their scope and purpose. I want each of you to learn mathematical writing. You can only do this by actually writing, in your own words. In “real” writing, you have multiple drafts. Similarly, I expect you'll sometimes turn in excellent write-ups on a first try, but other times will turn in work that could use improvement in some respect. For each topic, you can resubmit write-ups until your work is as good as you like. It is in your interest and mine to turn in as few drafts as possible. Normally I expect three is plenty. If necessary I may make this a requirement.
December 6 The questions from the Activity sheets 31–37 corresponding to each day's class are recommended as usual, but the only "assignment" is portfolio problems.
November 22 The questions from Activity sheets 28–30 are highly recommended as preparation, but the only "assignment" this week is portfolio problems.
November 15
| Activity sheet 26 | 1, 2, 3 |
| Activity sheet 27 | 1, 2 |
November 8
| Activity sheet 23 | 1, 2 |
| Activity sheet 24 | 1, 3 |
| Activity sheet 25 | 1, 2 |
November 1
| Activity sheet 20 | 3, 4 |
| Activity sheet 21 | 3, 4, 5 |
| Activity sheet 22 | 2, 3 |
October 25
| Activity sheet 17 | 1, 2, 3 |
| Activity sheet 18 | 1 |
| Activity sheet 19 | 2 |
October 18
| Activity sheet 14 | 1, 3 |
| Activity sheet 15 | 3 |
| Activity sheet 16 | 2 |
October 4
| Activity sheet 12 | 1, 3(c), 4(b) |
| Activity sheet 13 | 1 |
September 27
| Activity sheet 9 | 1, 2 |
| Activity sheet 10 | 1, 2, 3 |
| Activity sheet 11 | 1 |
September 20
| Activity sheet 5 | 2, 5(e) and (f), 4 |
| Activity sheet 7 | 2, 3, 4 |
| Activity sheet 8 | 1, 2 |
September 13 Turn in the ten questions listed. For the proof portfolio questions whose topic number is given, you only need to submit a written solution for one question for each of the ten topics, and may turn in these write-ups any time on or before Friday, December 10. Write up and turn in each proof portfolio question separately, as a stand-alone document.
| Activity sheet 1 | 2, 3, 4, 5 |
| Activity sheet 2 | 4, 6, 7 |
| Activity sheet 3 | |
| Activity sheet 4 | 1, 2, 3 |