Math 791 ABSTRACT ALGEBRA
MIDTERM EXAM I (Take-Home)
March 17 (Thu), 2011
Instructor:
Yasuyuki Kachi
Line #: 57808.
Name :
ID :
This take-home part of Midterm Exam I is worth 60 points and is
due in class Thursday, March 31st, 2011. Submission after 2:15p
Math 791 ABSTRACT ALGEBRA
SOLUTION FOR REVIEW EXAM I (03/10)
March 10 (Thu), 2011
Instructor:
Yasuyuki Kachi
Line #: 57808.
[I] (8pts)
(1)
a+
=
(2)
2+
[II] (8pts)
1 b
1 5
(1)
1 +
a+
+
ac bd
c+
1 b
1 d
1
a, b, c, d R .
ad + bc
1 2
=
12 +
1
1
a
+
=
a 2 + b
Math 791 ABSTRACT ALGEBRA
MIDTERM EXAM I (Take-Home) SOME HINTS
March 29 (Tue), 2011
Revised Due date: April 5 (Tue), 2011
Instructor:
Yasuyuki Kachi
Line #: 57808.
As for problem [I] :
As for problem [II] :
Covered in class.
5
z=
5
4 1
.
You are asked to
Math 791 ABSTRACT ALGEBRA
MIDTERM EXAM I (Take-Home) MORE HINTS
March 29 (Tue), 2011
Revised Due date: April 5 (Tue), 2011
Instructor:
Yasuyuki Kachi
Line #: 57808.
As for problem [III] :
Covered in class, except part (7).
Let
Q 7
=
0 + 1 7 + 2 7
2
3
+ 3
Math 791 ABSTRACT ALGEBRA
SOLUTION FOR QUIZ I (02/10)
February 17 (Thu), 2011
Instructor:
Yasuyuki Kachi
Line #: 57808.
[I] (10pts)
We may nd one algebraic equation with integer coecients which has
x=
3+
5
x=
3+
5
as one of its roots, as follows:
Step 0.
Math 791 ABSTRACT ALGEBRA
SOLUTION FOR MIDTERM EXAM I (03/15)
March 29 (Tue), 2011
Instructor:
Yasuyuki Kachi
Line #: 57808.
[I] (8pts)
(1)
a+
=
(2)
3+
[II] (8pts)
1 b
1 5
(1)
2 +
a+
+
ac bd
c+
1 b
1 d
1
ad + bc
1 4
=
a, b, c, d R .
26 +
1 2.
1
a
+
=
a 2