Introduction to Real Analysis
Course Portfolio

In this course, 40% of your grade will be based on a portfolio of your work. The portfolio is your opportunity to document the quality and quantity of your work. It should be a finished product in which you can take pride. That means it should be neat, attractive, well organized, and assembled with some care. It should not be thrown together at the last minute.

Your portfolio should be a three ring binder with separate sections as described below. Note that there are different criteria of evaluation for the different sections. In particular, the material in your Polished Work section should be high quality finished products. In contrast, the section of your homework assignments should include all of your problem sets. These should be neat, legible, and mathematically complete and correct, but will not be held to as high a standard as the polished work. These ideas are presented in greater detail below.

Your portfolio is not the same as a course notebook. In particular, the following items should not be in your portfolio: assignment sheets, handouts with information about the course, class notes.

Each of the following sections describes a section that should be in your portfolio. The heading for each section is the title you should use for the corresponding section of the portfolio.

Problem Sets Handed In

This section should include all of the problem sets that have been handed in and returned.  Include a cover sheet showing which problems were turned in from each assignment, and any late problems you have added that were not turned in.  Problem sets will be assigned and collected weekly. All problem sets should be included in your portfolio. Each problem set should have a heading on the first page indicating the section of the text to which it corresponds.  Please follow the format guidelines from the detailed course instructions handout.

Polished Work (+ Problems)

Approximately one problem in each set will be marked with a + on the assignment sheet.  These are plus problems.  The recommended approach to these problems is to treat the solutions handed in with homework as rough drafts. Based on further thought, class discussion, or comments on your returned homework paper, you will the opportunity to prepare a second, polished draft, with the same standards of neatness and format that you would follow for a term paper. Periodically, I will collect all the second drafts of + problems, and give you a second set of comments, and a grade. This graded draft should be placed in the Polished Work section of the portfolio. 

The polished version of each problem should begin on a separate sheet of paper, and should be clearly labeled. A clear statement of what is to be proven should appear first, followed by your solution. You may wish to organize your work by proving lemmas that you can cite in the main proof. In this case, each lemma should have a clear statement and proof separate from the main question.

Your polished versions of these problems should be logically correct(!) and explanations should be clear and in correct English prose: complete sentences, correct punctuation, etc. You are encouraged (but not required) to type these, following the style conventions of the text: variables in italics, centered equations, etc.   Additional details about this format are provided here.   Suggestions about mathematical word processing are provided here.

The polished work is supposed to be your own work. As discussed elsewhere, you may sometimes work with other students on homework problems the first time you do them.  But you should not work with anyone else on polished drafts of + problems.  If you have questions about those, please consult only me.

If you wish, you may include polished versions of additional problems in this section. This may be appropriate to document significant additional work that you wish to highlight, particularly if you have received assistance with many of the assigned problems for the Polished Work Section.

Exams and Corrections

After an exam has been returned, you are expected to find and correct all errors. Make your corrections on separate sheets of paper, not on the exam itself, and indicate briefly why each error occurred. This work is not expected to be polished - apply the same standards as for the homework. Include the corrections and the exams in this section of the portfolio.

Exam corrections will influence my assessment of your portfolio at the end of the course.  Errors on exams show some amount of misunderstanding of the material, and corrections are your chance to learn the ideas you missed.  If your exam corrections do not show that you have learned this material, for example because you still have incorrect answers to some of the exam items, that indicates to me that you do not care very much about whether you understand the missed items.  To make sure you understand your errors and the needed corrections, feel free to talk with classmates, tutors, other students, or me.