Math 545-546 2022, Homework Guidelines
Reading Assignments and Reports
Typically you will be assigned one chapter a week to read. You should read the assignment over once before we discuss it in class and before the Reading Report (see below) is due. For this first reading, you are just getting an overview, and may skip the proofs or other details. If there is too much new material for you even to get all the main ideas, stop early (and tell me where you stopped in your report). 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.
**Important note: Be careful of the distinction in the textbook
between Problems, which appear at the end of each chapter and are labeled by numbers separated by a dash, and Exercises, which appear throughout the text and are labeled by numbers separated by a period. Thus "2-11" refers to a Problem at the end of Chapter 2, while "2.11" indicates an Exercise (appearing between Proposition 2.10 and Proposition 2.12).
Reading Reports. After your first reading of the material, you will email me a brief report on your reading by 6 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 prompts 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 just responses to each prompt. 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.
The prompts for the first report will be listed in the assignment. Prompts for the second and later reports are listed below. They indicate the kind of information I'd like to see in Reading Reports after the first week. If you have other thoughts to share about the reading that don't directly answer these prompts, they may replace your responses to the first or second prompt. A response to the third prompt is required. Write at least three or four sentences, and no more than a few paragraphs.
- What 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?
- State at least one question or request for discussion in class about material in the reading. Questions can be very specific ("I got lost in the middle of p. nn." "Please give some more examples of X.") or more general ("I don't feel comfortable with the idea of Y." "I can follow the computations, but don't understand the big picture here."), or anything in between; or even speculative about generalizations or related ideas.
Problem Sets
Problem sets will be due on Fridays at 6 PM on Gradescope. They will include two kinds of problems and exercises.
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 (see **Important Note above). Sometimes I will say you should "work" a Problem (again see ** above). Ideally you would write down a detailed sketch of the solutions for W Exercises and Problems (for yourself, not to hand in).
In the real world, you should think about the result and the proof at least briefly, and as thoroughly as you have time to. Part of the reason to label some Problems or parts of Problems with a W is so they count at "previously assigned work" which you may use in later assignments without giving a proof.
Homework to be Handed In (HI). Several Problems (and sometimes an Exercise or a problem not in the book) will be assigned almost every week. You should write up careful solutions; more information about format below. This written homework is the heart of the course.
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 Problem Set homework is not all ready to turn in on the due date, turn in as much as you can on time, and email the lecturer with a cc to both TAs saying what you are turning in on time, and when the rest will be turned in.
If you submit late work, no more than 3 days late, only once or twice a quarter, you do not even have to give a reason. For your third late submission, or if your work will be more than 3 days late,
you must give an explanation and get permission from the lecturer.
Grading of Problem Sets and Tests
Each 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. 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 explaining why. Occasionally 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 explaining 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 if handwritten, 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 Problem Solutions
- Making use of available resources:
- 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.
- 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 develop the outline of this proof" are
encouraged, and will never be counted against you.
- 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.
- If you look up something in another book besides our text or
on a website, cite the source.
- With two TAs splitting the grading, it is essential that you
make it easy to find each problem, and to know where it start and ends.
Submit the problems in the order they appear in the assignment (or write a note at
the spot where a problem should be saying where it is in your paper).
Start each problem with either the statement of the problem as given, or
a clear statement of what you have proved for the solution of the problem.
Either start each problem on a new page, or leave several blank lines between problems.
Handwritten work should be neat, well organized, and
have one-inch margins on all four edges of the page.
(Remember this dictum if you take prelims in person!!
Work written near the edge of the page, especially in the upper left corner,
may disappear when papers are stapled, photocopied, or scanned.)
- 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.
- 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. (But be very clear how to locate
your lemma when you reference it;
remember that the same TA may not be grading both problems.)
- 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).
- Avoid abuse of symbols. In particular beware of run-on sentences
from overuse of the symbols for "if and only if" and "implies".
- 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.
(Do include one of these, so if someone, possibly you, looks at the paper later,
they don't need to check in the text to figure out what question
is being answered.)
- 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.
- 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.
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Most recently updated on January 3, 2022.