Syllabus for the second midterm exam:

 7-1  7-2      (see notes on primitive roots)
 9-1  9-2  9-3 (see notes on quadratic reciprocity)
11-1 11-2      (see notes on sums of squares)
12-1 12-2 12-3 (see notes on partitions)

Be prepared to calculate:

1. Primitive roots for small primes
2. Legendre symbols for prime modulus
3. Expression of a composite number as 
    a sum of two and four squares
4. Partitions of integers


Be prepared to prove:

1. Existence theorem for primitive root (assuming 
   the fundamental theorem of algebra) from notes
2. Euler's criterion
3. Theorem 9-5 from Andrews
4. The 2 square theorem for a prime p=4k+1
5. Theorems 12-2 12-3 from Andrews

Additionally be prepared to solve problems
similar to homework problems.