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SF State MATH 880 - Outline 3

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2008-01-31 13:24MATH 880 PROSEMINAR JT SMITHOUTLINE 3 SPRING 20081. Assignment. This should be determined through some class discussion.a. Are you on our Graduate list server? It disseminates important news.b. Make sure you know how to access, when you are off-campus, Internet materi-als for which our library pays an access fee. Check the library’s home page.c. What are the most important things that we could start doing to help you?Think about these and don’t hesitate to bring them up in class.d. If we should overview research papers a little more, here are three possibili-ties. They’re available online.i. Grünbaum 2007. Prof. Ovchinnikov is enthusiastic about this becauseit tackles a question involved in a current project of his: how to definepolyhedron. I faced the same problem some years ago writing a chapterof Smith 2000. This class faced a version of it again last year. Grün-baum, probably the leading expert on such things, points out that untilnow there has been no good definition, and proposes one.ii. Tarski 1955. This packages a theorem fundamental for Math 800, andprepares it for use in other contexts too. Evidently it’s Tarski’s papermost cited in computer-science research.iii. Agrawal, et al. 2004. This is the famous unexpected elementary proofthat the question whether a natural number n be prime is decidable intime proportional to p(n) where p is some polynomial.e. Think about questions concerning the social organization of the mathematicsdiscipline, including the role of mathematics journals. We’ll begin a somewhatorganized discussion of that topic during the next meeting, alongside othertopics as appropriate.f. Prepare for further discussion of Smith 2002, with attention to thesequestions:i. What methods are used?ii. What would you have to study to be able to understand them?iii. Are there extensions of this material?iv. Does this material have interesting connections to other subjects?v. Are there references to supporting documents?2. We discussed the following aspects of Smith 2002, and will conclude that discussionduring the next meeting.a. What is its subject? Reflection geometry.b. What level? Yours.c. Who’s the author? I, who do a lot of things, but am not a major mathematicalresearcher.d. Who are the audience? Us.e. What are the main questions or points? See the bottom of the first page.f. Where did these thoughts stem from? g. Why was it written?Page 2 MATH 880 SPRING 2008 OUTLINE 32008-01-31 13:243. I described the process I followed to find a story line for that paper.a. I was intrigued by Bachmann’s use of Thomsen’s equation as an elementaryexample in his book referred to in my paper. Couldn’t he have found a simplerexample? This was in the late 1960s. Bachmann’s book was, and probablystill is, the bible of reflection geometry.b. I followed Bachmann’s reference to Thomsen’s book. There I found a para-graph in which Thomsen mentioned and cited Kneser’s work on his problem.c. I followed Thomsen’s reference to Kneser’s concise gem, and voilà!d. I felt this result to be so nice it deserved more publicity. I could give abridgedtalks about it, but didn’t see how to write it up intelligibly until I learnedenough Mathematica to show others how to use it to illustrate an algorithmdescribed in the paper.4. The moral is, keep your eyes open for seductive questions and engaging stories. a. Often, the footnotes in an authoritative source are more interesting than thetext itself! b. I pointed out the rather well-written obituary for Margaret Truman in thatday’s San Francisco Chronicle. The writer had dug up a news story famouswhen I was in high school, about President Truman’s threatening dire physi-cal harm to a critic who had panned his daughter’s performance. Thatprovided an engaging way into the broader life story of a musician, mysterywriter, biographer, and public figure of New York society.5. I stressed that my paper paper had evolved over decades, and was crafted to fit theMonthly’s extremely high standards. Dean Axler told me that only about one intwenty papers submitted there is accepted. This one underwent hardly any modifi-cation by the Monthly editor and referee. Most papers, particularly in researchjournals as opposed expository journals, are not organized so


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