Math 412/612 Modern Algebra Fall 2016

**Homework Information
**

- Assigned
Reading and Reading Log. The course will follow the
textbook
closely, and you are expected to read each section before it is
discussed in class. To see what will be discussed at each meeting,
consult the class
schedule.

An important goal for the course will be the development of active reading strategies 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 in the Reading Log section, 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 (part of 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.

Your goal is to gain a deep understanding of each section of the text before it is discussed in class. Often, class time will be devoted to discussing homework problems and student reactions (as documented in your reading logs) to the text. Do not expect each class to include a lecture that repeats what is already presented in the text. - Regular homework. This
is traditional homework from problems in the text, to be written up and
handed in. Most of these will be statements you are
asked to prove, though there may also be problems that ask you to work
out properties of a specific example, or to construct an example of
your own. But even for such exercises, you are expected to
"prove" your conclusions. As a prerequisite for this course,
students are assumed to know how to write proofs. For students
who would like a brief review, see this webpage.

The assignments are posted in this**Assignment Sheet**. The required format for regular homework is illustrated here. Please staple the pages of each problem set together.

- Polished Work. One
or more 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.
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 the homework paper, you should then prepare a second, polished draft. Periodically, I will collect all the second drafts of starred problems, and give you a second set of comments, and a grade. Format and writing style requirements for polished work are detailed here.

- Optional & Masters
Problems. Some problems on the assignment sheet are
designated with two
asterisks, like so: 37**. Undergraduates may consider these to be
optional; masters students should consider them to be required.
Typically these problems will either be more difficult than the normal
problems, or will emphasize extensions of the material covered in a
section.

- Exam Solutions. After
each exam, students will work in groups to correct the errors of all
group members. The objective will be to compile, as a group, a
completely correct set of solutions to the exam questions. Each
group will submit one set of solutions for grading, and each member of
the group will receive the same grade for this assignment.

- Class worksheets. Class
time may sometimes involve working alone or in groups to complete
worksheets. If you do not finish a worksheet before the end of
class, you should plan on completing all or most of it before the next
class meeting. These worksheets will not be collected or graded,
but should be kept in the appropriate section of your portfolio.