write a note mathematics
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Answer:
Here are some observations about the writing of mathematics that I hope will be useful as
you work on the writing assignment for this course.
Goals and audience: As with any written piece, mathematical exposition must be written
with a particular audience and specific goals in mind. Be sure you have a clear sense of
what these are before you start writing.
The process: It is important to bear in mind that writing is a process, just like proving
a theorem. No one pours forth a well-organized, clear, and error-free exposition the first
time they sit down to write, just as no one produces a complete, well-structured proof the
first time they think about a problem. Most good expository prose has been thoroughly
rewritten at least once or twice before it reaches the reader, with key sections undergoing
perhaps three to five major revisions. To some people, this thought makes the prospect of
writing seem daunting or even overwhelming, but it needn’t: The idea that much of what
you write will eventually be replaced or discarded can be liberating. Just sit down and
write, knowing that anything that doesn’t measure up can later be fixed. You might well
find yourself throwing away the first several pages you write—this is not wasted time, since
the trial and error process helps you immensely in clarifying what you really want to say.
When you begin writing a draft, the introduction may not be the best place to start, since
the structure of the paper may not become completely clear until later in the process. Try
starting somewhere in the middle, with whichever part of the paper is clearest in your mind.
As soon as you have a section or more in relatively coherent form, sit back and read it. Put
yourself in the mind of your audience, and see if it makes complete sense. Then rewrite.
When you have something you think is close to acceptable, give it to someone else to read
and comment on. Then rewrite again.
After you think the paper is finished, go through it with a fine-toothed comb and a sharp
razor. Sharpen your definitions, statements of theorems, and proofs. Clarify your logic
and your intuitive descriptions. Make sure your spelling, punctuation, and grammar are
absolutely correct. Omit needless words, terminology, and symbols.
Note that “rewriting” usually means much more than simply correcting errors. It means
looking critically at what you’ve written both locally and globally, figuring out what works
well and what doesn’t, and doing whatever is necessary to make the whole thing work
perfectly.
Conventions: Although you might not believe it after reading some of the mathematical
writing that has made it into print, mathematical writing should follow the same conven-
tions of grammar, usage, punctuation, and spelling as any other writing. This means, in
particular, that you must write complete sentences organized into paragraphs. While many
mathematical terms have technical meanings that are different from their usage in ordinary
English, you should still be careful to observe the usual rules regarding parts of speech and
subject-verb agreement. Although you will run across (all too many) mathematicians who
write ungrammatical sentences like “Suppose f is an onto map,” don’t you do it!
If you are not a native English speaker, it would be a good idea to cultivate the habit of
asking a native speaker to look over your writing before you submit it.
Explanation:
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