MATH 4000/6000
Fall, 2012
T. Shifrin
PROBLEM SET #1
DUE Monday, August 20, 2012.
Problems to work but not hand in :
1.1: #1, 2, 4b,e, 5.
1.2: #2, 4, 5, 6.
Problems to turn in :
1.1: #4i, 6, 8.
A. For any n N, n 2, nd a formula for
1
1
22
1
1
32
1
1
n2
an
MATH 4000/6000
T. Shifrin
Fall, 2012
PROBLEM SET #15
DUE Monday, December 3, 2012.
Problems to work but not hand in :
Chapter 5, 2: #1, 2, 3, 5, 6, 9, 10.
Problems to turn in :
Chapter 5, 2: #7 (3), 13 (2), 16 (2).
A. (3) Let = arcsin(6/13).
(i) Explain w
MATH 4000/6000
Fall, 2012
PROBLEM SET #14
DUE Monday, November 26, 2012.
Problems to work but not hand in :
Chapter 4, 3: #1, 2, 3, 6, 8.
Problems to turn in :
A. (2) Find the multiplicative inverse of x3 + 2x + 1 in F [x]/ x2 x 1
for
(i) F = Q
(ii) F = Z
MATH 4000/6000
PROBLEM SET #13
Fall, 2012
DUE Monday, November 12, 2012.
Problems to work but not hand in :
Chapter 4, 3: #1a, 2a,b.
Problems to turn in :
Chapter 4, 2: #11 (5), 12 (3), 23 (4).
A. (4) Dene : Z Z Z2 Z15 by
(a, b) = a (mod 2), 5a + 6b (mod
MATH 4000/6000
Fall, 2012
PROBLEM SET #12
DUE Monday, November 5, 2012.
Problems to work but not hand in :
Chapter 4, 1: #1, 2, 6, 9, 10.
Chapter 4, 2: #1, 2, 4.
Problems to turn in :
Chapter 4, 1: #11 (3), 12 (2), 15 (4), 16 (3).
Chapter 4, 2: #5 (2).
A.
MATH 4000/6000
PROBLEM SET #11
Fall, 2012
DUE Monday, October 29, 2012.
Problems to work but not hand in :
Chapter 4, 1: #1, 2, 4.
Problems to turn in :
Chapter 3, 2: #14 (3).
A. (4) Find the splitting elds K of the following polynomials in Q[x]
and deter
MATH 4000/6000
Fall, 2012
PROBLEM SET #10
DUE Monday, October 22, 2012.
Problems to work but not hand in :
A. True/False. Provide justications.
(i) 2 Q 4 2, i
(ii) 3 2 Q 4 2, i
(iii) 3 Q 6i, 2i
(iv) 3 Q 6, 2i
(v) Q 6 5 = Q 5, 3 5
Chapter 5: 1: #17.
Proble
MATH 4000/6000
PROBLEM SET #9
Fall, 2012
DUE Monday, October 15, 2012.
Problems to work but not hand in :
Chapter 3, 3: #3b,c.
Chapter 5, 1: #1, 2, 7.
A. Consider the linear independence issue.
(i) Are the vectors (1, 0, 1), (1, 1, 0), (0, 1, 1) Q3 linear
MATH 4000/6000
Fall, 2012
PROBLEM SET #8
DUE Monday, October 8, 2012.
Problems to work but not hand in :
Chapter 3, 1: #1a,c, 2a,d,e, 8.
Chapter 3, 2: #1, 4, 6a,b.
Problems to turn in :
Chapter 3, 1: #4 (3), 15 (3).
A. (4) Suppose F is a eld and f (x) F [
MATH 4000/6000
Fall, 2012
PROBLEM SET #7
DUE Monday, October 1, 2012.
Problems to work but not hand in :
Chapter 2, 5: #8, 9, 11.
Chapter 3, 1: #1a,c, 2a,d,e, 5, 8, 10, 11.
Problems to turn in :
Chapter 2, 5: #6 (2), 7a,c (3), 10a,c (3).
Chapter 3, 1: #14
MATH 4000/6000
Fall, 2012
PROBLEM SET #6
T. Shifrin
DUE Monday, September 24, 2012.
Problems to work but not hand in :
Chapter 2, 3: #1, 2, 3, 9a,c, 15a, 22.
Chapter 2, 4: #1a,c,d, 2b.
Problems to turn in :
A. (4) Express the following roots in closed for
MATH 4000/6000
Fall, 2012
T. Shifrin
PROBLEM SET #5
DUE Monday, September 17, 2012.
Problems to work but not hand in :
Chapter 2, 2: #5, 6b,c, 7.
Problems to turn in :
Chapter 1, 3: #34 (4).
Chapter 2, 2: #2 (2), 3 (2).
A. (4)
(i) Prove that if a real num
MATH 4000/6000
Fall, 2012
PROBLEM SET #4
T. Shifrin
DUE Monday, September 10, 2012.
Problems to work but not hand in :
Chapter 1, 4: #1, 2, 3, 4, 8.
A. Consider R =
a
b
b a+b
: a, b, Z2 . Using the usual matrix addi-
tion and multiplication, check that R
MATH 4000/6000
Fall, 2012
PROBLEM SET #3
DUE Wednesday, September 5, 2012.
(Note the one-time change because of the Labor Day holiday.)
Problems to work but not hand in :
Chapter 1, 3: #7, 9, 12, 13, 19, 20a,d,e, 21a,c.
Problems to turn in :
A. Prove that
MATH 4000/6000
PROBLEM SET #2
Fall, 2012
T. Shifrin
DUE Monday, August 27, 2012.
Problems to work but not hand in :
Chapter 1, 2: #8, 9, 10, 16.
Chapter 1, 3: #1, 2, 3, 4, 5.
Problems to turn in :
Chapter 1, 2: #7, 13.
A. Prove: gcd(a, b) = gcd(a + kb, b)
Fall 2012
MATH 4000/6000
SYLLABUS
T. Shifrin
Text: T. Shifrin, Abstract Algebra: A Geometric Approach, Prentice Hall, 1996. (Up-to-date
list of typos at http:/math.uga.edu/~ shifrin/AlgebraErrata.pdf )
Oce: 444 Boyd Graduate Studies Building, 542-2556.
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