MAT 312/AMS 351
Solutions of Midterm II.
1. (a) (10 points) How many () injections, () surjections, and () bijections are there from
the set cfw_1, 2, 3 to the set cfw_a, b?
Answers:
no injections, no bijections, 6 surjections.
Solution:
The number of ele
MAT 312/AMS 351
Solutions of Midterm I.
1. Find a pair of integers (s, t) or show that such a pair does not exists such that
(a) (10 points) 153s + 87t = 1,
(b) (10 points) 153s + 87t = 3,
(c) (10 points) 153s + 87t = 6.
Answers:
(a) no integer solutions
MAT 312/AMS 351, Fall 2012
Solutions to Homework Assignment 11
Maximal grade for HW11: points
Section 6.2:
1. (10 points) For each of the following pairs of polynomials, f , g , write f in the form qg + r
with either r = 0 or the degree of r is less than
MAT 312/AMS 351, Fall 2012
Solutions to Homework Assignment 10
Maximal grade for HW10: 50 points
Section 4.4:
1 Which of the following sets are semigroups under the given operation:
(i) The set Z under the operation a b := s, where s is the smaller of a a
MAT 312/AMS 351, Fall 2012
Solutions to Homework Assignment 9
Maximal grade for HW9: 100 points
Section 5.2.
5. (15 points) Let G be the group Z . What, according to Corollary 5.2.4, are the possible
20
orders of elements of G and which of these integers
MAT 312/AMS 351, Fall 2012
Solutions to Homework Assignment 8
Maximal grade for HW8: 100 points
Section 5.1
4. (20 points) Use Theorem 5.1.1 to decide which of the following subsets of the given
groups are subgroups:
(i) The subset of symmetries of a squa