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Rising star finished paper. Tell us about your essay: Instructions, requirements and deadline. The first step in writing a good proof comes with the statement of the theorem. A well-worded theorem will make writing the proof much easier. The statement of the theorem should, first of all, contain exactly the right hypotheses. Of course, all the necessary hypotheses must be included.
On the other hand, extraneous assumptions will simply distract from the point of the theorem, and should be eliminated when possible. When writing a proof, as when writing an entire paper, you must put down, in a linear order, a set of hypotheses and deductions which are probably not linear in form.
I suggest that, before you write you map out the hypotheses and the deductions, and attempt to order the statements in a way which will cause the least confusion to the reader.
A familiar trick of bad teaching is to begin a proof by saying: This is the traditional backward proof-writing of classical analysis. It has the advantage of being easily verifiable by a machine as opposed to understandable by a human being , and it has the dubious advantage that something at the end comes out to be less than e. The way to make the human reader's task less demanding is obvious: Neither arrangement is elegant, but the forward one is graspable and rememberable.
Such a proof is easy to write. The author starts from the first equation, makes a natural substitution to get the second, collects terms, permutes, inserts and immediately cancels an inspired factor, and by steps such as these proceeds till he gets the last equation. This is, once again, coding, and the reader is forced not only to learn as he goes, but, at the same time, to decode as he goes.
The double effort is needless. By spending another ten minutes writing a carefully worded paragraph, the author can save each of his readers half an hour and a lot of confusion. The paragraph should be a recipe for action, to replace the unhelpful code that merely reports the results of the act and leaves the reader to guess how they were obtained.
The paragraph would say something like this: As in any form of communication, there are certain stylistic practice which will make your writing more or less understandable. These may be best checked and corrected after writing the first draft. Many of these ideas are from HTWM, and are more fully justified there. Structuring the paper The purpose of nearly all writing is to communicate. Does your result strengthen a previous result by giving a more precise characterization of something?
Have you proved a stronger result of an old theorem by weakening the hypotheses or by strengthening the conclusions? Have you proven the equivalence of two definitions? Is it a classification theorem of structures which were previously defined but not understood?
Does is connect two previously unrelated aspects of mathematics? Does it apply a new method to an old problem? Does it provide a new proof for an old theorem? Is it a special case of a larger question? Are your results concentrated in one dramatic theorem? Or do you have several theorems which are related, but equally significant?
Have you found important counterexamples? Is your research purely theoretical mathematics, in the theorem-proof sense, or does your research involve several different types of activity, for example, modeling a problem on the computer, proving a theorem, and then doing physical experiments related to your work?
Is your work a clear although small step toward the solution of a classic problem, or is it a new problem? Formal and Informal Exposition Once you have a basic outline for your paper, you should consider "the formal or logical structure consisting of definitions, theorems, and proofs, and the complementary informal or introductory material consisting of motivations, analogies, examples, and metamathematical explanations.
Writing a Proof The first step in writing a good proof comes with the statement of the theorem. Write the proof forward A familiar trick of bad teaching is to begin a proof by saying: Specific Recommendations As in any form of communication, there are certain stylistic practice which will make your writing more or less understandable. Notation that hasn't been used in several pages or even paragraphs should carry a reference or a reminder of the meaning.
The structure should be easily discernible by headings and punctuation. There should be a clear definition of the problem at hand all the way through. The title is the first contact that readers will have with your paper. It must communicate something of the substances to the experts in your field as well as to the novices who will be interested. Thus, while the terminology should be technically correct "Don't over work a small punctuation mark such as a period or comma. They are easy for the reader to overlook, and the oversight causes backtracking, confusion, delay.
X belongs to the class C, The period between the two X's is overworked A good general rule is: If you insist on starting the sentence with a mention of the thing the symbol denotes, put the appropriate word in apposition, thus: The overworked period is no worse than the overworked comma. The presence of "then" can never confuse; its absence can. The golden mean is golden. Break it up, but not too small; use prose, but not too much. Intersperse enough displays to give the eye a chance to help the brain; use symbols, but in the middle of enough prose to keep the mind from drowning in a morass of suffixes.
A showy way to say "use no superfluous letters" is to say "use no letter only once".
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A Guide to Writing Mathematics Dr. Kevin P. Lee Introduction This is a math class! Why are we writing? When you write a paper in a math class, your goal will be to communicate mathematical reasoning and ideas clearly to another person. The writing done in a math. All you need to do is come to us and say ‘please help me write my papers’ and we will assign you a professional writer who will step in and write you that paper. We have tons of experience in writing papers for students, and you could be one of those students who will receive the best quality of work.
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