M302: Algebra

Mathematics 302: Abstract Algebra

Instructor: Jonathan Smith, 496 Carver, 4-8172

e-mail: jdhsmithATmathDOTiastateDOTedu (substitute punctuation)

Grading: 10% for each of 2 graded homework assignments,
20% for each of 2 in-class 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 0-471-32147-8

Syllabus: Rings and Fields - most of Chapters VI - XI.

Homework Assignments

1/8 for 1/10: Section 24: 3, 4, 8, 9, 10, 11, 20, 22.
1/10 for 1/12: Section 24: 14, 15. Section 25: 5, 6, 7, 8, 16, 22, 23.
1/12 for 1/17: Section 25: 1 - 4, 10, 12, 14, 25.
1/17 for 1/19: Section 26: 1 - 10.
1/17 for 1/22 (hand-in): Section 24: 16. Section 26: 11, 12, 23.
1/19 for 1/22: Section 27: 2, 3, 10.
1/22 for 1/24: Section 38: 1-3, 10, 17, 18.
1/26 for 1/29: Section 39: 1, 3, 4, 7, 8, 12.
1/26 for 1/31 (graded): 24.17, 27.20(a), 38.22, 39.2.
1/31 for 2/2: Section 27: 14, 18, 19, 20(b), 21, 25.
2/5 for 2/7: Section 28: 1 - 6, 8, 12 - 14.
2/7 for 2/12: Section 29: 3, 4, 8.
2/12 for 2/14: Section 30: 6, 8, 9, 11.
Practice Test #1: 24.18, 24.21, 38.24, 29.6.
Click here for Test #1 in Portable Document Format
2/19 for 2/21: Section 31: 1 - 4, 8.
2/21 for 2/23: Section 31: 16, 14, 17 - 19.
2/23 for 2/26: Section 32: 1, 15, 16, 13, 17, 19.
2/26 for 2/28: Section 33: 19, 20, 22, 23, 28, 31.
2/28 for 3/2: Section 33: 24, 25, 34, 35. Section 54: 14, 15.
3/2 for 3/5: Section 25: 11, 21. Section 26: 14. Section 27: 23. Section 30: 3. (Subtract 3 to get section # in 3rd Ed.)
3/5 for 3/7: Section 34 (Defn. & elem. props. of polynomials): 1, 3(a)(c), 5(a)(d), 6, 9, 10, 14.
3/7 for 3/9: Section 35: 1 - 6, 16, 15.
3/9 for 3/19: Section 35: 7, 8, 12, 19, 20.
3/19 for 3/21: Section 36: 1 - 4.
3/19 for 3/23 (graded): 31.5, 31.13, 34.8, 35.14.
3/21 for 3/23: Section 36: 5 - 8.
3/23 for 3/26: Section 36: 9, 11, 19, 20.
3/28 for 3/30: Section 40 (Quotient rings of F[x] ) : 7, 8, 12 - 15.
3/30 for 4/2: Section 40: 2, 3, 16.
4/2 for 4/4: Section 43 (Finite fields) : 6 - 8.
4/4 for 4/6: Section 42: 4 - 7, 9.
4/6 for 4/9: Catch up with earlier assignments. Also:
Show there is no rational number l with 3l² = 2.
4/9 for 4/11: Section 42: 1, 8, 11.
Practice Test #2: 35.17, 39.12, 40.10, 43.7(b).
Click here for Test #2 in Portable Document Format
4/16 for 4/18: Section 44 (Roots of a polynomial) : 1 - 6.
4/18 for 4/20: Section 58 (Introduction to algebraic coding) : 2 - 6.
4/20 for 4/23: Section 59: 1, 3, 4, 7.
Review problems part II: 34.12, 35.9, 36.12, 40.4, 43.3, 42.2, 44.7, 59.8.
Review problems part I: 24.13(d), 25.13, 26.13, 27.13, 38.11, 39.6, 28.10, 31.26.
Click here for Final in Portable Document Format