Overview: client chooses ordered sets for the set-theoretic topic and trees for application. Describe the Set-Theoretic topic in general. Give a brief overview of the mathematics involved. If you are writing about (for example) finite versus infinite axiomatizations, then your topic is comparisons of different axiomatizations of Set Theory and you would write an overview of it, much as you would find in a textbook. Describe the full range of applications for your chosen topic. Although the rest of your paper will be devoted to the single application of your chosen topic, for this section the idea is to paint a picture of the full range of applications that are possible. For example, logic and set theory can be used anywhere that you have inductive and recursive reasoning, and this occurs not only in abstract mathematics but also in linguistics, theory of computation, automata, and the like. Be sure to list each of the different application areas and briefly (a sentence or two for each different application) indicate how your chosen topic is used for each type of application. For example, in linguistics is used to model how human beings acquire speech and are able to communicate and make conventions or agreements. Now it is time to zero in on the specific “topic + application” combination that you have chosen. In this part of the paper, you should describe how the specific topic you chose is applied to the area you have chosen. Essentially this is the same idea as item 2 above, but because you are focusing here on only your one single chosen application, you can go into it in much more depth and detail than you did for the brief overviews you wrote in item 2. Continuing with our example, you might describe in detail how Set Theory is used within linguistics. What kinds of fundamental issues regarding the human mind and intelligence is it used for? Could the linguistic problems be addressed any other way, and if so what is the advantage of using set-theoretic concepts? To what extent, if any, is the process computerized, and what changes, if any, are made to it in order to accommodate computerization? These particular questions might not apply to your own particular topic+application, but I am sure you can think of many similar aspects to discuss once you have done the research. The last part of the paper centers on doing some illustrative conclusions. The total paper should be approximately 4 pages in length (not counting the cover page, references page, or any exhibits), and include a full set of references (including the textbook if you use it, as I assume you will). APA format requires that the font used should be Arial or Times New Roman, 10 or 12 point only; the pages be double spaced, and the margins should be no more than one inch all around.
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