Research paper mathematics

Mathematical writing, like good mathematics thinking, is a skill which must be practiced and developed for optimal performance. The purpose of this paper is to provide assistance for young mathematicians writing their first paper. The aim is not only to aid in the development of a well written paper, but also to help students begin to think about mathematical writing. I will reference many direct quotations, especially from the section written by paul halmos, but i suspect that nearly everything idea in this paper has it origin in my reading of the booklet. Although studying mathematics from bad mathematical writing is not the best way to learn good writing, it can provide excellent examples of procedures to be avoided. Thus, one activity of the active mathematical reader is to note the places at which a sample of written mathematics becomes unclear, and to avoid making the same mistakes his own atical communication, both written and spoken, is the filter through which your mathematical work is viewed.

If the creative aspect of mathematics is compared to the act of composing a piece of music, then the art of writing may be viewed as conducting a performance of that same piece. If you do mathematics purely for your own pleasure, then there is no reason to write about it. If you hope to share the beauty of the mathematics you have done, then it is not sufficient to simply write; you must strive to write essay will begin with general ideas about mathematical writing. The next section will describe the difference between "formal" and "informal" parts of a paper, and give guidelines for each one. When you write about your own mathematical research, you will have another goal, which includes these two; you want your reader to appreciate the beauty of the mathematics you have done, and to understand its importance. If the whole of mathematics, or even the subfield in which you are working, is thought of as a large painting, then your research will necessarily constitute a relatively minuscule portion of the entire work.

Its beauty is seen not only in the examination of the specific region which you have painted (although this is important), but also by observing the way in which your own work 'fits' in the picture as a two goals--to convince your reader of the truth of your deductions, and to allow your audience to see the beauty of your work in relation to the whole of mathematics--will be critical as you develop the outline for your paper. Successful mathematical writer will lay out for her readers two logical maps, one which displays the connections between her own work and the wide world of mathematics, and another which reveals the internal logical structure of her own order to advise your reader, you must first consider for yourself where your work is located on the map of mathematics. If your reader has visited nearby regions, then you would like to recall those experiences to his mind, so that he will be better able to understand what you have to add and to connect it to related mathematics. Is necessary that you explicitly consider this question of placement in the structure of mathematics, because it will linger in your readers' minds until you answer it. Failure to address this very question will leave the reader feeling quite addition to providing a map to help your readers locate your work within the field of mathematics, you must also help them understand the internal organization of your work:Are your results concentrated in one dramatic theorem? 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?

Your reader does not know what you will be proving until after he has read your paper, advising him beforehand about what he will read, just as the travel agent prepares his customer, will allow him to enjoy the trip more, and to understand more of the things you lead him honestly and deliberately explain where your work fits into the big picture of mathematical research may require a great deal of humility. Mathematics has been accumulating for thousands of years, based on the work of thousands (or millions) of practitioners. You have considered the structure and relevance of your research, you are ready to outline your paper. The accepted format for research papers is much less rigidly defined for mathematics than for many other scientific fields. The reader hopes to have certain questions answered in this section: why should he read this paper? If he isn't familiar with the first concepts of probability, then he should be warned in advance if your paper depends on that understanding.

Remember at this point that although you may have spent hundreds of hours working on your problem, your reader wants to have all these questions answered clearly in a matter of the second section of your paper, the introduction, you will begin to lead the reader into your work in particular, zooming in from the big picture towards your specific results. You, as the world expert on the topic of your paper, are in a unique situation to direct future research in your field. S)he will naturally have her/his own questions, but you, having worked on this paper, will know, better than your reader, which questions may be interesting, and which may not. These are the questions which your readers will hope to have answered in the final section of the paper. Formal and informal 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. The next stage in the writing process may be to develop an outline of the logical structure of your paper.

Which ones follow naturally from others, and which ones are the real work horses of the paper? However, few research papers actually have a linear structure, in which lemmas become more and more complicated, one on top of another, until one theorem is proven, followed by a sequence of increasingly complex corollaries. The exact way in which this will proceed depends, of course, on the specific technique to assist you in revealing the complex logical structure of your paper is a proper naming of results. By naming your results appropriately (lemmas as underpinnings, theorems as the real substance, and corollaries as the finishing work), you will create a certain sense of parallelness among your lemmas, and help your reader to appreciate, without having struggled through the research with you, which are the really critical ideas, and which they can skim through more r technique for developing a concise logical outline stems from a warning by paul halmos, in htwm, never to repeat a proof:If several steps in the proof of theorem 2 bear a very close resemblance to parts of the proof of theorem 1, that's a signal that something may be less than completely understood. Issues of structure should be well thought through before you begin to write your paper, although the process of writing itself which surely help you better understand the that we have discussed the formal structure, we turn to the informal structure. The formal structure contains the formal definitions, theorem-proof format, and rigorous logic which is the language of 'pure' mathematics.

In effect, you are inventing a language which your readers must learn in order to understand your paper. Bad notation, on the other hand, is disastrous and may deter the reader from even reading your paper. On the other hand, extraneous assumptions will simply distract from the point of the theorem, and should be eliminated 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. Many of these ideas are from htwm, and are more fully justified on that hasn't been used in several pages (or even paragraphs) should carry a reference or a reminder of the structure should be easily discernible by headings and should be a clear definition of the problem at hand all the way title is the first contact that readers will have with your paper. 1983,Digitalcommons@university of nebraska - tations, theses, research atics, department tations, theses, and student research papers in candidates: you are welcome and encouraged to deposit your dissertation here, but be aware that. Click the "submit your paper or article" link at the bottom of the gray box at left.

Spectra of cables of 2-bridge knots, nicholas john ations of discrete mathematics for understanding dynamics of synapses and networks in neuroscience, caitlyn parmelee. Problems in extremal set theory, joshua brown ability in the ring z[√–5], laura cal integration of linear and nonlinear wave equations, laura context to search:Across all me via email or to cite items from this ght your paper or ibility lcommons@university of nebraska - tations, theses, research atics, department tations, theses, and student research papers in candidates: you are welcome and encouraged to deposit your dissertation here, but be aware that. Problems in extremal set theory, joshua brown ability in the ring z[√–5], laura cal integration of linear and nonlinear wave equations, laura context to search:Across all me via email or to cite items from this ght your paper or ibility l of mathematics -based impact factor (2016): 3.