Math 419: Abstract Algebra II, Spring 2012
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- Due 1/20: Solve these problems
- Due 1/27: p. 232 #26; p. 239 #12; p. 250 #34
- Due 2/3: p. 257 #15, 16
- Due 2/10: p. 259 #33; p. 264 #3; and the following problem:
- (From Brahmagupta, 7th century A.D.) A girl was carrying a basket of eggs, and a man driving a horse hit the basket and broke all the eggs. Wishing to pay for the damage, he asked the girl how many eggs there were. The girl said she did not know, but she remembered that when she counted them by twos, there was one left over; when she counted them by threes, there were two left over; when she counted them by fours, there were three left over; when she counted them by fives, there were four left; and when she counted them by sixes, there were five left over. Finally, when she counted them by sevens, there were none left over. `Well,' said the man, `I can tell you how many you had.' What was his answer?
- Due 2/24: p. 278 #8; p. 293 #7; p. 302 #12
- Due 3/2: p. 306 #1; p. 311 #3
- Due 3/9: p. 423 #8; p. 519 #3; and classify, up to
isomorphism, all degree 1 extensions of the rational field.
- Due 3/30: p. 529 #1; Prove that the cosine of 20 degrees
has degree 3 over the rationals.
- Due 4/13: p. 545 #2; p. 566 #1
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