Mathematics 301: Abstract Algebra
Instructor: Jonathan Smith, 496 Carver, 48172
email: jdhsmithATmathDOTiastateDOTedu (substitute punctuation)
Grading: 10% for each of 2 graded homework assignments,
20% for each of 2 inclass tests,
40% for the final examination.
Study plan: reserve 1  2 hours for homework between each pair
of classes. Successful
performance in the class depends critically on completion of the homework
assignments.
Textbook: J.R. Durbin, Modern Algebra, 4th ed., Wiley, ISBN 0471321478
Syllabus: Group theory  most of Chapters I  V and XIII.
Homework Assignments
8/21 for 8/23: Section 1: 1  6, 21.
8/23 for 8/25: Section 2: 9(a), 9(b), 10(a), 10(b), 22, 24,
26, 27(a).
8/25 for 8/28: Section 3: 1  7, 10, 11, 13, 21, 27, 31.
8/28 for 8/30: Section 4: 1, 4, 11.
8/28 for handin 8/30, returned 9/1: 2.27(b), 3.30, 3.31, 4.1(c).
8/30 for 9/1: Section 5: 1  12, 17, 23.
9/1 for 9/6: Section 4: 6. Section 5: 19.
9/6 for 9/8: Section 6: 3, 5, 7, 6.
9/8, graded work due 9/13: 4#13, 6#4, 6#13, 14#22(a).
9/11 for 9/15: Section 14: 12, 11.
9/13 for 9/15: Section 7: 1, 4, 11  14, 24.
9/18 for 9/20: Section 7: 7, 8.
9/20 for 9/22: Section 9: 1  4, 7, 9, 13.
9/22 for 9/25: Section 10: 1, 2, 13, 26.
9/25 for 9/27: Section 10: 11, 12, 27, 28, 14.
9/27 for 9/29: Section 10: 3, 6  8, 16  18, 22  24.
9/29 for 10/2: Section 11: 2, 7, 14, 15.
Practice Test #1: 5#21, 7#9, 14#17, 14#18, 10#23.
Click here for Test #1 in Portable
Document Format
10/6 for 10/9: Section 12: 1, 2, 13.
10/9 for 10/11: Section 12: 5, 6, 9  12, 15, 21.
10/11 for 10/13: Section 12: 23. Also:

Prove by induction: 1+2+...+n = n(n+1)/2.

Prove 2^{n} < n! for all sufficiently large n.
How large must n be?
10/13 for 10/16: Section 13: 1  6, 17.
10/16 for 10/18: Section 14: 5  7, 23, 29, 33.
10/18 for 10/20: Section 15: 1  4, 13  15, 24.
10/20 for 10/23: Section 16: 1, 2, 5, 6, 14.
10/20, graded work due 10/25: 12#13, 14#24, 15#26, 16#9.
10/23 for 10/25: Section 17: 1  4, 7, 10, 24.
10/25 for 10/27: Section 18: 1, 3, 5, 6, 9, 11, 12.
10/27 for 10/30: Section 15: 22, 17, 18. Section 18: 24,
10, 13, 14.
10/30 for 11/1: Section 21: 2, 5, 8  10, 26, 27, 34.
11/1 for 11/3: Section 22: 1, 2, 7, 12, 14, 9, 15.
11/3 for 11/8: Section 23: 5, 19(a)(b), 20, 22, 21, 13.
11/8 for 11/10: Section 19: 25  27, 29. Section 20: 3
 6.
11/10 for 11/13: Section 19: 1  3, 6, 7, 17  24.
11/13 for 11/15: Section 19: 5, 8, 13, 14.
Practice Test #2: 11#17(a), 17#25, 19#30, 23#16.
Click here for Test #2 in Portable
Document Format
11/27 for 11/29: Section 51: 9(a)(f), 10.
11/29 for 12/1: Section 51: 5, 6, 8, 11, 13, 14.
Note 51.13 should read: G_{s} = a^{1}G_{t}
a.
12/1 for 12/4: Section17: 28. Section 53: 1, 2, 5, 6,
7, 11.
12/4 for 12/6: Section 53: 10, 12  14.
Note 53.13 should read: ... must have a normal subgroup
of order 3 or 25.
Practice Final: 17#32, 19#32, 23#12, 51#12(e), 51#17(a)(b),
53#12.
Click here for Final in Portable
Document Format