The exam will cover material from the following sections: Garrett's notes 1.1-1.5, 6.1-6.3,
6.5, 6.7-6.8, 8.1, 9.1, 9.3 and from Roman's book 0.1-0.2, and 1.1-1.2. Be prepared to
answer questions on calculating probability of events in a probability
space, as well as calculating the expected value of a random variable, and its variance.
The case of a finite probability space is our primary focus although some elementary
infinite and even continuous examples were gone over. We also considered with some care the
rings Z(mod N) and considered the nature of a group, ring and field from the abstract
axiomatic point of view. Be prepared to use Euclid's algorithm to calculate the greatest
common divisor of two integers, and to find the multiplicative inverse of an element in the
field Z(mod p) when p is a prime (or even more generally the inverse of any invertible
element in Z(mod N) in the general case). Also be prepared to use Euclid's algorithm
to express the gcd as a linear combination of the given integers. Also if prime
factorization of two integers is known, know how to find the gcd and lcm. These were
the major topics and will be the primary focus of the exam. Related questions in the
homework were also considered and you are responsible for these as well.