MATH 300 Final Exam (Tuesday December 17, 12-3 PM, in ARC-108)


Sections covered:

1.1-1.7, 2.1-2.5, 3.1-3.4, 4.1-4.4, 4.6.


Advice for studying:

1) Read the book under the assumption that everything is wrong, and let
the author convince you that his claims are in fact true (but look out
for errors!).

2) Examples: check that they are done correctly -- if they don't make
sense then you might have misunderstood the statement of a theorem or
definition.  Go back and read it carefully again.

3) Remember statements of definitions and theorems.  Well, remember
what they mean, not the exact wording.  For definitions, you should be
able to reformulate the definition in your own words and in logical
symbols.  For multi-part theorems like e.g. Theorem 1.2.2, you should
be able to look at any of the points and understand why it is true.

4) When writing solutions / proofs:

* What you write should be an essay with rigorous mathematical
  content.

* Use the skeletons from class.

* Make sure that everything you write about has been introduced.
  For example, say what "x" is before you start making claims and/or
  conclusions about it.  

  For example, if you know that an existence quantifier statement is
  true and you wish to take advantage of this, then CHOOSE and NAME an
  element of the kind that is guaranteed to exist by the statement, so
  that you can continue to work with this element.

  But avoid introducing symbols in ways that don't make sense.
  For example, it does not make sense to say "Let forall x in N".

  Notice also that it is NOT sufficient to simply list all the
  variables you will use at the start of your solution, since the
  order in which the values of variables are chosen is very important.

5) Make sure you know how to do the homework problems and midterms to
perfection.


Note: It is my impression that many of you could have done better on
      Midterm 2 if you had been more on top of the definitions, see
      point 3) above.


Best of luck to all!

Anders