Math 544, Autumn 2015 - Homework Guidelines and Grades

Reading Assignments and Reports

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 (including all the exercises). Occasionally I may list a *Problem number with the reading. This means you should read the statement of the problem, as an example of a further result that can be proved. You are not required to work a problem listed as part of the reading.

*Note the difference between Problems which are listed at the end of a chapter, and Exercises, which are interspersed in the text.

Reading Reports. After your first reading of the material, you will email me a brief report on your reading by 3 PM on Sunday. The purpose of the report is to jumpstart the dialogue between you and me about the material. 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; instead you should think of them as part of an ongoing conversation with me. There are some questions below to help get you started on your reading reports, but ideally your report should be a couple of paragraphs telling me your reactions to the reading rather than direct answers to each question. Please just write the report as the email; do not attach a separate file. Sometimes I may respond to your report individually by email.

The reading reports for the entire quarter will count towards your course grade as one written assignment. You may miss one report and still get full credit for this assignment.

Prompts for the first Reading Report. For this first report, please do include answers to these specific questions.

• What was most interesting to you in Chapter 1? Or, why are you taking this course, and what are you looking forward to learning in it?
• Was there anything in the Appendix reading that wasn't review for you, or about which you have questions? If yes, give details.
• What material in Chapter 2 to p. 38 (that is, up to the section on "Manifolds") was new to you? Is there any of it you would like to see discussed in class?
• (Optional) Tell me a bit about your mathematical background.

Prompts for the second and all later Reading Reports. These questions indicate the kind of information I'd like to see in Reading Reports after the first week. If you have other ideas about the reading that you want to share and don't directly answer these questions, write about them in place of responding to one of the questions. Write at least three or four sentences, and no more than a few paragraphs.

• 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? Questions can be very specific ("I get lost in the middle of p. nn." "Please give some more examples of X.") or very general ("I don't feel comfortable with the idea of Y."), or anything in between; or even speculative about generalizations or related ideas.

Exercises and Problems

Homework to be Worked (W) but not handed in. As you work through the details of each chapter, you should work out for yourself all the Exercises that appear interspersed in the text. Sometimes I will say you should "work" a Problem. (Note that Problems appear at the end of the chapter. Also problem numbers have the form 2-13, while 2.13 is an exercise number.)

Homework to be Handed In (HI). Several Problems (and sometimes an Exercise or a problem not in the book) will be assigned each week, usually due on Friday. (The day of the week may differ in the later part of November, when the holidays - Veteran's Day 11/11 and Thanksgiving - mess with our schedule.) You should write up careful solutions; more information about format below. 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. 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 as you write, but you should not spend 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 or all 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 earlier in the book. (For this purpose, consider the appendices to be "earlier" than Chapter 1.) Unless otherwise stated, you may not use another Problem without giving its solution, or if the Problem was part of previous (W or HI) homework.
   4. If you look up something in another book besides our text or on a website, cite it.
2. Start each problem on a new page, staple them in order, write neatly, and leave one-inch margins on all four edges of the page. Be sure your name, the assignment number or due date, and the course name or number is on the first page.
3. 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 "Remarks," discussed in point 7 below. Please ask us for additional guidance if you have questions.
4. Think about organization of your proofs. Divide your work into appropriate paragraphs, with a blank line between 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! If it makes things cleaner, prove a lemma or two and then the main result. You might use the lemma again on another problem.
5. Use English, and use it correctly. Pay attention to grammar, spelling, punctuation, and using complete sentences as much as possible. Put a period at the end of of a sentence (even if it ends with a displayed equation).
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. Jack Lee has posted "Some Remarks on Writing Mathematical Proofs" which I encourage you to read. This six-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 "Remarks" recommend, but that he describes very well the goal to aim for. I also do not have a preference about whether you include a verbatim statement of the problem in your homework, or state the result you will be proving as a theorem or sequence of propositions.
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.
9. If you are considering typing some or all of your homework - and please note, this is NOT required - you may find Jack Lee's recommendations for Mathematical Typesetting Resources useful.

Course grades

... will be based on weekly homework and one or two a take-home tests (a midterm and a final, or just a final). If there's only one test, the homework will count about 2/3 and the final about 1/3. If there are two tests, homework will count for about half your grade, and the final will count a little more than the midterm.

Homework assignments.

Gradebook. Please check your scores periodically. If you spot an error, please bring me the graded paper.

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