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Mathematics 2513-002 - Discrete Mathematical Structures - Fall 2005
Information about Exam III

Exam III will be in the usual classroom on Monday, November 14, 2005. It will cover the material starting with greatest common divisor, up through and including all material we covered in chapter 3.

Calculators or other mechanical assistance are not needed and are not to be used. Blank paper will be provided, so all you will need is something to write with.

Problems from the homework will be especially important on this exam. As with any exam, give answers that are brief and to the point, and answer all the questions that you are sure of before going on to those about which you are less confident.

Exam III will have two questions that are exact repeats of questions from Exam II. Solutions to Exam II have been posted, so there is no reason not to get those two problems completely correct.

The main topics are the greatest common divisor and least common multiple, congruence modulo m,, relatively prime integers, Cantor's argument showing that the rationals numbers are countable and that the the real numbers are uncountable, and induction. The following will definitely be covered, although the exam not necessarily limited to these topics:
  1. greatest common divisor, least common multiple
  2. relatively prime integers
  3. the Euclidean algorithm
  4. congruence modulo m
  5. Cantor's argument showing that the rational numbers are countable
  6. Cantor's argument showing that the real numbers are uncountable
  7. n!

You do not need to know the statements or proofs of all the various propositions that we proved in class concerning congruence, but you should be familiar with the methods used in the homework problems involving congruence.

The following do not appear on this exam: sequences, summation, strong induction, homework problem #25, differentiation or integration, the Well-ordering Principle and the proof of the Basic Induction Theorem.