CPSC 229, Fall 2000                        Information for the Second Test
--------------------------------------------------------------------------

The second test for this course takes place on Wednesday, October 18.  It 
will cover Sections 2.4, 2.5, 2.6, 3.1, 3.2, and 1.5.  (We skipped
the last parts of section 2.5 and of section 3.1.)  Here is a list of
some terms and ideas that you should be familiar with for this test:

  ordered pair
  cross product
  functional relationships in the real world
  function
  the notation  f: A -> B
  value of a function (for example, "f(a)")
  a function as a set of ordered pairs
  composition of two functions
  domain of a function
  range of a function
  image of a function
  onto function
  one-to-one function
  bijective function
  the set of functions from a set A to a set B
  functions as "first class objects"
  functions in Java/C/C++:
      not all Java "functions" are mathematical functions
      data types as sets
      prototype of a function
      relationship of Java functions to the f: A -> B notation
  counting
  one-to-one correspondence (same as bijection)
  cardinality of a set
  cardinality of:  A union B,
                   A intersection B,
                   the power set of A,
                   the set of functions from A to B
  finite set
  infinite set
  countably infinite set
  countable set (i.e. finite or countably infinite)
  uncountable set
  important sets:  Natural numbers, Integers, Rational numbers, Real numbers
  the set of integers is countable
  the set of rational numbers is countable
  the set of real numbers is uncountable
  there is no one-to-one correspondence 
            between a set X and the set of subsets of X
  Russell's paradox
  Godel's theorem
  methods of proof (how to prove "for all x, P(x)", "p implies q", etc.)
  proof by contradiction
  corrolary
  lemma
  proof that there are infinitely many prime numbers
  valid argument
  invalid argument
  formal proof
  modus ponens
  modus tollens
  translation of arguments between English and logic