Math 412/612 Modern Algebra Fall 2016
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.  The sections should be separated using tabbed dividers, so I can easily turn to any section I wish.  All material should be placed on the rings of the binder.  Do not put papers into the pockets of the binder, or into covers or pockets that are then placed on the rings.  I should be able to review all the material by turning pages, without having to take pages out of covers or enclosures.

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. I do not expect every one of these problem sets to have the finished quality of a term paper. 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 section that should be in your portfolio is described separately below. Use the headings below (except for the last one, Evaluation) as the titles for the sections of your portfolio.

Reading Log

An important aspect of this course will be the development of active reading strategies designed to decode written mathematics. When you set out to read a section of the text, keep paper and pen or pencil at hand and plan to use them frequently. As you read, you should be formulating and answering questions, making up examples, drawing figures, etc. All of this should be recorded on paper. This work should be included in the portfolio, at least at the start of the course. This is work in progress and is not expected to be in polished form. However, when you sit down to read a section of the text, you should begin a new page of the reading log, with a heading indicating the section of the text and the page number.

The reading log is not an outline of what you have read. I am not asking that you produce a list with the section headings, definitions, and theorems. Instead, you should record ideas that expand on what is in the text. For example, one of the topics we will read about is a kind of number system called a ring. After you read that definition, you might ask, in the log, what familiar algebraic systems satisfy the definition of a ring. Are the integers a ring? Are the real numbers? Are the 2 by 2 matrices? I would like to see such questions in your reading log, as well as any answers you find, of course.

Regular Homework

Problem sets will be assigned from each section of the text and collected daily. All problem sets should be included in your portfolio. Please include the problem sets in chronological order, and staple each set's pages together.

Polished Work

Several problems in each problem set will be marked with an asterisk (*). These problems are to be polished into a final form that meets the same standards for form and neatness that you would expect for a term paper. Generally these will be proofs, and will require written out explanations of your reasoning.

For more information about how polished work should be formulated and presented, including some options for word processing software, see Mathematical Writing.

Class Worksheets

Include any worksheets handed out and completed (or at least started) in class.


This section should include your graded exams, as well as a copy of the graded exam solutions group projects handed in by your group.  .


During the semester individual assignments will be collected and graded, taking into consideration mathematical correctness, readability, clarity, and proper mathematical formatting.  At the end of the semester, complete portfolios will be reviewed.  Based on both the record of graded items and the overall review, a numerical score will be assigned.