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Volume 3, Number 43A  -  October 1998 Discussions

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28 October 1998                                 Vol. 3, No. 43A


This special issue of the Math Forum's weekly newsletter  
highlights interesting conversations taking place during
October of 1998 on Internet math discussion groups. 

For a full list of these groups, with links to topics covered
and information on how to subscribe, see:


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                     OCTOBER SUGGESTIONS   
AP-CALC - the Advanced Placement Calculus mailing list, hosted 
by the Educational Testing Service (ETS) and archived at
- "Function Composition Question (4 Oct. 1998)

  "I am curious as to the response list members might have to 
   these questions: TRUE or FALSE and EXPLAIN your answer:
     1. If f(x) = sqrt(x) and g(x) = x^2
        then f(g(x)) = x.
     2. If f(x) = sqrt(x) and g(x) = x^2
        then g(f(x)) = x.
   [these were questions on my recent AP Calc test...]
           - Sheila King
                           --- + ---

- "Points of inflection/extrema" (8 Oct. 1998)
  "Today in class a kid asked if there is a point of inflection 
   at x = c, then can there be a relative extrema at x = c ?
   I did some hand waving and picture drawing showing points
   of inflection and the behavior of the function near c,
   arguing that the point cannot be a relative extrema also.
   What is bothering me is -- how could one prove that?"
           - Tom Hussey
                           --- + ---

- "piecewise" (22 Oct. 1998)
  "Is the greatest integer function considered a piecewise 
   function? This was the topic of conversation the other 
   day...." - Mary Harrison

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APSTAT-L - the Advanced Placement Statistics mailing list,
archived by the Math Forum at

- "n-1 on standard deviation" (7 Oct. 1998)
  "Can someone explain to me why we divide by n-1 in sample 
   standard deviations and n in populations?" - Liz Joseph
  (Also see "n-1" from 22 Sept. 1998 at

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MATHEDU, a mailing list set up to discuss issues in Mathematics/
Education at the post-calculus level, and archived at
- "geometric means" (2 Oct. 1998)
  "Students are used to the arithmetic mean as an average.
   Does anyone know any easy application where it is natural 
   to use the geometric mean?... this material comes up 
   alongside regular analysis material and is intended for the 
   strongest and most enthusiastic students in a class which 
   is already very able." - David Epstein
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SCI.MATH.NUM-ANALYSIS, a discussion group focused on numerical
analysis that can be read as a Usenet newsgroup or on the Web:

- "MATH and PAIN" (16 Oct. 1998)
  "I ask all of you engineers, scientists, and hobbyists...  
   All the Taylor series, trigonometric formulas, integration 
   methods, etc. Do you truly understand them at a concrete 
   'visual' level? Could you reproduce their derivation in ten 
   minutes or so or less? If you see a completely brand new 
   equation without any easily recognized sub-expressions (e.g. 
   Euler's identity for the natural logarithm in relation to 
   the sin and cosine functions, or the natural logarithm being 
   used as a radial basis function) can you read it like words 
   on a page and immediately know what it does? Or do you look 
   it up when needed to solve a particular problem and that 
   is that?" - Peter Immarco
  "Another interesting question is, why does math become 
   difficult at different stages for different people? For some 
   it is plain arithmetic, for others algebra, for some 
   differentiation,... what is the factor - abstraction?"
             - Jon Campbell
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  We hope you will find these selections useful, and that you
  will browse and participate in the discussion group(s) of
  your choice. 

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