Writing Intensive Homework II
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The second writing intensive assignment will be submitted twice, first as
a rough draft and second as the final draft. The rough draft is due
October 31st, the final draft due one week after the rough draft is
returned. The rough draft will probably be returned on November 12th.
When you're handing in the final draft, attach
the rough draft also. Failing to do so will result in loss of
substantial part of the points.
The assignment has four parts:
- part a) Give a careful exposition of the
following four concepts: function, sequence, limit of a function,
limit of a sequence.
- part b) Let f be a function defined on an
interval (a,b) of the real line. Let
,
be a sequence of real numbers in (a,b) such
that
. Suppose that
Give a complete proof that
- part c) Using part b), prove that
does not exist.
- part d) Let g be a function defined on an
interval (u,v) of the real line, and
let K be a real number. Suppose that for every sequence
,
of real numbers in (u,v) such that
, we have
. Give a complete proof that
Good luck!
Reference materials:
The first two of the following books are at the Mathematics Library
reference, you may use them only in the library. The last one is on the
shelf, please try to use it in the library and do not check it out
unless it is absolutely necessary to do so.
- Higham, Nicholas J., Handbook of Writing for the Mathematical
Sciences, Society for Industrial and Applied Mathematics,
1993.
- Gillman, Leonard, Writing Mathematics Well : A Manual for
Authors, Mathematical Association of America,
1987.
- Knuth, Donald E., Larrabee Tracy, and Roberts, Paul M., Mathematical
Writing, Mathematical Association of America,
1989.
Please check the checklist page for some
comments on how to type and organize your paper.
Good luck!