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SF State MATH 880 - Outline 40

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2008-05-06 10:51MATH 880 PROSEMINAR JT SMITHOUTLINE 40 (Tentative) SPRING 20081. Assignmenta. We’ll have time in the course for discussion of a couple more topics.Suggestions?b. Research the question proposed by Prof. Ardila, as described below.2. Endgame. This class ends 14 May. There is no scheduled activity after that.3. Writing for PRa. Too few mathematicians have acquired any knack for public-relations writing.As a result, articles about mathematics and mathematicians targeted at abroad audience—for instance, all those who hold degrees in scientific subjects—are often misleading or outright inaccurate. This situation has beenimproving in recent years as a few highly trained mathematicians havebecome professional writers associated with mathematical associations andwith journals that address such audiences.b. But those are the top outlets for such writing. Universities, technical indus-tries, and even schools benefit from good writing about mathematical activityin their communities.c. Each year our College of Science and Engineering publishes an issue of itsIntersci journal containing papers written by the previous year’s science-writing class. Each issue generally contains one article about mathematics.The current issue, due any day now, will contain one about me, by PatriciaWallace. I think Ms. Wallace did a very good job, considering that she hadvirtually no previous experience with mathematics (although, obviously, a lotof experience with the world). She was the best interviewer I’ve ever encoun-tered. One of the problems such writers encounter, incidentally, is theireditors’ own misconceptions about mathematics. We have to persuade morethan one level of writer to say it right!d. Once every two years or so the Mathematics Department publishes a newslet-ter full of this sort of writing. There’s a link to its most recent issue on thiscourse’s home page. Writing and editing these articles was great fun for me,particularly “Shoestrings,” a decorous form of shaggy-dog story. Its story lineand punchline resulted from a rapid-fire elevator conversation one day withProf. Goetz, gleeful after some successful troubleshooting!e. The flashy design of that newsletter was due to the College’s graphics de-signer, Diane Fenster. Mathematicians hold varying opinions about it.f. Cultivating a skill in this kind of writing can lead to interesting sidelines inprofessional work!4. Finding Mathematical Informationa. I introduced my website with that title. There is a link to it on this course’shome page. This effort stemmed from experience when I served on theLibrary Advisory Committee. One year we were concerned with the Library’sOASIS online tutorial. I noted that it didn’t provide much for mathematicsPage 2 MATH 880 SPRING 2008 OUTLINE 402008-05-06 10:51students, observed how it was being designed, then resolved to imitate it forour students in particular.b. You can observe some design features that this kind of writing shares withpresentations: separation into highly-organized high-impact low-contentscreens, terse prose, and unified style.c. This was all done with Microsoft FrontPage, using one of its example style-sheets for the gradiated-fill backgrounds and font choices. Each screen is aseparate *.htm ile. The most difficult aspect of the implementation wasdesigning the links and keeping track of them, and checking them, so that inthe end they’re all connected properly.5. Digging for sources a. In this morning’s Math 490 lecture on Coxeter groups, Prof. Ardila stated andproved a background fact: Sylvester’s theorem about positive-definite realsymmetric matrices. After his elegant recursive proof he wondered howSylvester ever discovered the theorem. (A recursive proof hardly ever revealsthe train of thought that led to the statement of the theorem.)b. I propose his question as an example one for this class.i. Virtue: Sylvester wrote mostly in English.ii. Drawback: some of his work was completed before the beginning of thereview journals.iii. Virtue: I haven’t rehearsed this, so an example search may be realistic.iv. Drawback: That search may not be fruitful!c. The theorem says that a real symmetric matrix is positive-definite if and onlyif all its principal minors are positive. A square matrix A is called positive-definite if vTAv > 0 for all vectors v of compatible dimension. A principalminor of A is the determinant of a square matrix occupying an upper-leftcorner of A.d. Prof. Ardila told me that he had found the proof in a not-too-recent-but-not-old issue of the American Mathematical Monthly.e. Finding Mathematical Information suggested that we search JStor for thatarticle: all but the most recent five years of the Monthly are accessible andsearchable there. We started such a search, but did not succeed in the


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