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

Exam II will be in the usual classroom on Monday, October 17, 2005. It will cover the material from sets up through (but not including) greatest common divisors.

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.

The exam will have some problems similar to those on the homework, including homework problems not from the book, and some questions related to the lectures. It has a lot of definitions and a lot of short proofs--- but each of the proofs can be written in just a few lines. As with any exam, give answers that are brief and to the point, and to answer all the questions that you are sure of before going on to those about which you are less confident.

The main topics are the basic concepts about sets, proving and disproving properties of sets, the basic concepts about functions, proving and disproving that functions have properties, the divides relation on the set of integers and its properties, and prime integers and the Fundamental Theorem of Arithmetic. The following will definitely be covered, although the exam not necessarily limited to these topics:
  1. Subset, union, intersection, complement, Cartesian product.
  2. Domain, codomain, range, preimage, image, and graph of a function.
  3. The surjective and injective properties of functions, proving that specific functions are or are not surjective or injective.
  4. The divides relation on integers and its basic properties.
  5. Prime and composite integers, the Fundamental Theorem of Arithmetic.

One should be familiar with interval notation for connected subsets of the real numbers. It is very important to know the important definitions from memory and to be able to apply them in different notations. It is not possible to write proofs if one does not even know the definitions of the concepts involved. Proving that functions are (or are not) surjective or injective will be emphasized more than proving properties of set union and intersection.

The following do not appear on this exam: intersections or unions of infinitely many sets, cardinality, power sets, derivatives of inverse functions, the Prime Number Theorem.