HOMEWORK:
Updated Wed, Mar 20, 1996
Alg.464. Fall 1996.
Michael Boshernitzan.
- #1, due Jan 24, 1996. p.379: 1,2,3,7,8,9,10,12,13.
- #2, due Jan 31, 1996. p.381: 4,7,8,9,14,15,17,18,23, p.382:27,29,30.
- #3, due Feb 7, 1996. p.382: 33, Sect.4: 2, 3(b),6, p.383: Sect.5: 1,2,16,
Sect.6: 5, Sect.7: 2,3,10,11. Read: p.384: Sect.6: 1-7; Sect.7: 1.
- #4, due Feb 14, 1996. p.384: Sect.7: 4, 6, 7, 14; p. 386: 1, 2(b,c) (you
can use (a)).
p.441 (Section 1): 15, 16. Sect.2: 1, 3, 4, 5, 8, 11(a,b - try it!).
Read: p.442: (Sect.2) 7, 9, 12, 13, 15.
- #5, due Feb 28, 1996. p.443-444: Sect.3: 4, 10. Sect.4: 1, 2, 3, 4, 7, 8, 16;
p.444-445: Sect. 5: 1, 7 (either Zp*Zp or a field).
- #6, due Mar 13, 1996. p. 530-531: Sect. 1: 1, 3, 4; Sect. 2: 3, 4, 5, 6;
Sect. 3: 1, 2, 3, 5, 6, 10.
- #7. Due Mar 20, 1996. p. 531-532. Sect. 3: #14, 15; Sect. 4: #1, 4, 5;
Sect. 5: #1, 2, 3; p.533. Sect. 6: #10, 11;
Read: p.531-532. Sect.4: #2,3,6,7,8,10,11.
- #8. Due Mar 27, 1996. p. 532-533. Sect. 5: #4; Sect. 6: #1,3,7;
p.535. Misc. Exercises: #2, 3 (difficult problem!); p. 575 # 1,2,5,6,7,9.
Read: p.534-535. Sect.8: #1.
- #9. Due Apr 3, 1996. p. 575. Sect. 1: #3,8,12,13,16.
- #10. Due Apr 10, 1996.
p. 576-577: Sect. 2: #1, 7, 9; Sect. 3: #4, 7; Sect. 4: #2, 3, 5.
p. 578-579: Sect. 5: #12; Sect. 6: #1, 4.
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- #11. Due Apr 17, 1996.
Very Short: p. 575: #10,11,19;
p. 578: Sect. 5: #2, 3, 4.
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- #12. Read only: Pages 537-547, 565-568, 570-574.
Also: Distributed page: Main Thm of Galois Theory (p. 542, & 558-559)
and the sketch of the proof.
Prove that the p-th root of a positive rational is either a rational or
an algebraic number of deg p (where p>1 is a prime).
Prove: If an algebraic number is constructible then all its algebraic conjugates are.
