Elementary Modern Algebra I, MA 361 Spring 2012
Homework set # 8 (Section 8)
(due on April 4 (Wednesday), 2012)
In Exercises 1 through 5, compute the indicated product involving the following
permutations in S6 :
=
1
3
2
1
3
4
4
5
5
6
6
2
=
1
2
2
4
3
1
4
Elementary Modern Algebra I, MA 361 Spring 2012
Homework set # 4 (Section 3)
(due on February 17 (Friday), 2012)
1. (#1 on page 34) What three things must we check to determine whether a function
: S S is an isomorphism of a binary structure (S, ) with (
Elementary Modern Algebra I, MA 361 Spring 2012
Homework set # 5 (Section 4)
(due on February 24 (Friday), 2012)
1. (#8 on page 45) We can also consider multiplication n modulo n in Zn . For example,
5 7 6 = 2 in Z7 because 5 6 = 30 = 4(7) + 2. The set cf
Elementary Modern Algebra I, MA 361 Spring 2012
Homework set # 6 (Section 5)
(due on March 9 (Friday), 2012)
In Exercises 1 through 3, determine whether the given set of invertible n n matrices
with real number entries is a subgroup of GL(n, R).
1. (#8 on
Elementary Modern Algebra I, MA 361 Spring 2012
Homework set # 7 (Section 6)
(due on March 28 (Wednesday), 2012)
An isomorphism of a group with itself is an automorphism of the group. In
Exercises 1 through 5, nd the number of automorphisms of the given g
Elementary Modern Algebra I, MA 361 Spring 2012
Homework set # 3 (Section 2)
(due on February 10 (Friday), 2012)
Exercises 1 through 4 concern the binary operation dened on S = cfw_a, b, c, d, e by
means of the table below:
a
b
c
d
e
a
a
b
c
b
d
b
b
c
a
e
MA 361 - 05/05/2003
FINAL EXAM
Spring 2003
A. Corso
Name:
PLEASE, BE NEAT AND SHOW ALL YOUR WORK; JUSTIFY YOUR ANSWER.
Problem Possible Points
Number Points Earned
1
20
2
20
3
15
4
15
5
15
6
15
TOTAL
100
1
2
1. (i ) Compute the indicated product of cycles
MA 361 - 02/24/2010
FIRST MIDTERM
Spring 2010
A. Corso
Name:
PLEASE, BE NEAT AND SHOW ALL YOUR WORK; JUSTIFY YOUR ANSWER.
Problem Possible
Number Points
1
8
2
7
3
15
4
10
5
10
Bonus
5
TOTAL
Points
Earned
55
/50
1
2
1. If P = cfw_1, 3, cfw_2, cfw_4, 5, the
MA 361 - 02/27/2012
FIRST MIDTERM
Spring 2012
A. Corso
Name:
PLEASE, BE NEAT AND SHOW ALL YOUR WORK; JUSTIFY YOUR ANSWER.
Problem Possible
Number Points
1
10
2
10
3
10
4
10
5
10
Bonus
5
TOTAL
Points
Earned
55
/50
1
2
1. (a ) Write the arithmetic expressio
MA 361 - 04/20/2012
THIRD MIDTERM (take home)
Spring 2012
A. Corso 1. Let go : G > G be a group homomorphism.
Show that if [0 l is nite, then [90(G)| is nite and is a divisor of |G"
MM 2 WCwlf CW3
W Mama) owab 9" 2. Find all left cosets of the subgroup
MA 361 - 04/20/2012
THIRD MIDTERM (take home)
Spring 2012
A. Corso
Name:
PLEASE, BE NEAT AND SHOW ALL YOUR WORK; JUSTIFY YOUR ANSWER.
Problem Possible
Number Points
1.
10
2.
10
3.
10
4.
10
5.
10
TOTAL
Points
Earned
50
/50
1
2
1. Let : G G be a group homom
Elementary Modern Algebra I, MA 361 Spring 2012
Homework set # 1 (Section 0)
(due on January 27 (Friday), 2012)
1. (#4 on page 8) Describe the set cfw_m Z | m2 m < 115 by listing its elements.
2. (#5 on page 8) Decide whether the object described
cfw_n Z+
Elementary Modern Algebra I, MA 361 Spring 2012
Homework set # 2 (Section 1)
(due on January 27 (Friday), 2012)
1. (#3 on page 19) Compute the given arithmetic expression
i23
and give the answer in the form a + ib for a, b R.
2. (#15 on page 19) Write the