Math 544, Autumn 2007 - Homework Guidelines and Grades

Reading Assignments and Reports

Reading. Typically you will be assigned one chapter a week to read. You should read the assignment over once quickly before we discuss it in class. For this first reading, you are just getting an overview, and may skip the proofs or other details. After discussion in class and as you work on the problems, you should reread the material, working through all the details. Ideally, you should include all the Problems at the end of each chapter in one of your readings of the material. Occasionally I will point out a Problem which you should be sure to read and ponder.

Reading Reports. Email me a brief report (after your first reading of the material) by noon on Monday. I'm asking for this partly to give you more incentive to do the reading early, but mostly to encourage communication between you and me. By sharing your reaction to the reading, you can help me plan class to be more useful to more people. Reading reports should not be chapter summaries, but instead should answer the following three questions. (Exception: The first reading report has a special set of questions, see the homework assignments page.) Additional comments are also welcome.

• What do you think was the most important idea (or one of the most important ideas) in the reading, and why?
• What is another idea in the reading that you thought was important or interesting, and why?
• What questions do you have about the reading, or what parts of it would you most like to see addressed in class?

Exercises. You should work work out for yourself all the Exercises that appear interspersed in the text (as contrasted with the Problems which appear at the end of the chapter). These won't be collected or graded; most are routine. But understanding them is important for following the book and the course. Sometimes I will say you should "Work Problem x for yourself." This means you should work that Problem out for yourself, but don't have to write it up to hand in.

Written Assignments

Written homework. Several Problems (and sometimes an Exercise or a problem not in the book) will be assigned each week for you to write up solutions to turn in on Fridays. This written homework is the heart of the course. On the due date, turn your paper in to the lecturer in class, or to the TA's mailbox by 4 PM.

Late homework policy.

Reading reports will be accepted late, but if they are habitually late or exceptionally late without good reason, a credit deduction may be made. If your written homework is not all ready to turn in on the due date, turn in as much as you can on time, and email the TA with a cc to the lecturer saying when the rest will be turned in (and why, if it will be more than one day late). Credit deductions on late work are at the discretion of the TA. No credit for work that is more than five days late except under exceptional circumstances.

Grading of written homework.

Each homework problem will be graded for some number of points (usually 10). In addition to these problem points, each assignment will have five "writing points" for the whole assignment. The goal of this part of the grading is to direct a bit of your attention to your writing skills, and to provide the TA with a mechanism for giving you some feedback on these skills. Your total score for the assignment will be in the form (m + n)/(p + 5), where m is the sum of your points on the problems, p is the number of points possible on the problems, and n is the number of writing points you earned. Note that these 5 points per assignment are a small portion of the score. You should give some thought to good writing, but I'm not expecting you to spend several extra hours polishing your exposition!

Most or all of you probably already are pretty good mathematical writers, or you wouldn't be here. So usually most of you will get the full five writing points. If any points are deducted, there will be a note explaning why. Occcasionally you may get an extra writing point or two, if your writing was particularly good, and in this case also there will be a note explaning why. Here are some aspects of writing for which points may be deducted or awarded.

• Notation: Proper use of standard notation, defining your own notation clearly.
• Organization, both the overall structure of proofs and whether the logic of individual arguments is clear.
• Proper English, e.g., spelling, grammar, use of complete sentences and paragraphs.
• Readability: neatness, a good balance between conciseness and completeness, and "flow" -- does your writing make it easy for your reader to follow your line of thought.

Guidelines for writing up homework.

1. Making use of available resources:
   1. You are encouraged to work with other students. Discussing problems and ideas with your classmates is one of the best ways to learn the material. However, we recommend that you do not look at anyone's complete written solution before turning in your homework. (This includes proofs in other written resources: texts or websites.) We should not see evidence in the homework that you are going beyond discussing the problems to studying someone else's written solutions.
   2. If you use an idea suggested by someone else, or a significant step in your argument was developed in collaboration with another person, it is common courtesy, as well as good practice in professional ethics, to acknowledge that person's contribution. Comments such as "I got the idea for this proof from A", or "I worked with B to develope the outline of this proof" are encouraged, and will never be counted against you.
   3. You may freely cite results of Exercises from the appendix or earlier in the book. You may not use another Problem without giving its solution unless otherwise stated, or if the Problem was part of previous homework.
   4. If you look up and use something proved in another book, cite it.
2. If unsure of the level of detail expected for full credit on a problem, the rule of thumb is that we expect roughly the same detail as in the text. See also Jack Lee's "Conventions," discussed in point 7 below. Please ask us for additional guidance if needed.
3. Start each problem on a new page, staple them in order, write neatly, and leave margins on all four edges of the page.
4. Think about organization of your proofs. For example, if it makes things cleaner, prove a lemma or two and then the main result. You might use the lemma again on another problem. Divide your work into appropriate paragraphs. Note that each paragraph should have a "topic sentence" which summarizes the paragraph or at least states its main topic. This topic sentence may be first, last, or even implicit, but by the end of the paragraph, it should be obvious to the reader what the topic is!
5. Use English, and use it correctly. Pay attention to grammar, spelling, punctuation, and using complete sentences as much as possible.
6. Avoid abuse of symbols. In particular beware of run-on sentences from overuse of the symbols for "if and only if" and "implies".
7. For Math 544 last year, Jack Lee posted some "Conventions for Writing Mathematical Proofs." This four-page guide describes a writing standard suitable for publication. It will be wonderful if your homework papers can achieve this level of writing. I believe that in homework papers, abbreviations and symbols may be used a bit more freely than Jack's "Conventions" recommend, but that he describes very well the goal to aim for. Please read his discussion.
8. For additional guidance on writing mathematics (either now, or later when you are writing more formally, e.g. for your general exam paper or thesis) I recommend Mathematical Writing by Knuth, Larrabee, and Roberts, MAA Notes Number 14. The first chapter is a six page minicourse on technical writing.

Course grades will be based on weekly homework and a take-home final exam, approximately 2/3 on homework and 1/3 on the final. The final will be comprehensive and a bit longer than a homework assignment. You will have at least a week to work on it.

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