IOWA STATE UNIVERSITY

Mathematics 505: Abstract Algebra

Instructor: Jonathan Smith, 496 Carver, 4-8172 (voice mail)

e-mail: jdhsmith<AT>math<DOT>iastate<DOT>edu (substitute punctuation)

Office Hours: Monday 2:10 - 3, 5:25 - 6:15; Tuesday 11 - 11:50, 1:35 - 2; Thursday 11 - 11:50, 1:35 - 2 (subject to change).

Grading: based on five graded homework assignments. Click here for information about special accommodations.

Textbook: J.D.H. Smith and A.B. Romanowska, Post-Modern Algebra, Wiley, ISBN 0-471-12738-8. Click here for errata in Portable Document Format.

Library Reserve: http://www.lib.iastate.edu/class/ers/list/math505smith.html

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.

Syllabus:

  • Mathematics 504:
    • Ch. O: Set constructions, First Isomorphism Theorem, proof techniques, ordered sets, monoids - codes and free monoids, dynamical systems, semilattices, relations
    • Ch. I: Groups and quasigroups, monoid actions, symmetry, graphs
  • Mathematics 505:
    • Ch. II: Linear algebra, rings, modules, fields, commutative algebra
    • Ch. III: Categories and lattices, diagonalization, Tarski Fixed Point Theorem, Cantor-Schröder-Bernstein Theorem, limits, presentations, adjoint functors, Galois theory, tensor products.

Assignments



Fifth graded homework due 4/29:
Three questions from Ch. III, EXERCISES 1.3F, 2.1F (give a "careful proof"), 2.3A, 2.3J, 3.2J.

4/22 for 4/27: Read pp. 260 - 262 (middle), do Ch. III, EXERCISES 3.3A, 3.3B, 3.3D, 3.3E, 3.3F (p. 264).
4/20 for 4/22: Read pp. 250, 256 - 258, do Ch. III, EXERCISES 3.1F, 3.1J(a) - (d) (p. 253); 3.2I, 3.2L(a), 3.2R (pp. 259 - 260).
4/15 for 4/20: Read pp. 228 - 229, 232, do Ch. III, EXERCISES 2.3E, 2.3F, 2.3K, 2.3N, 2.3O (pp. 233 - 235).
4/8 for 4/13: Read pp. 213 - 216, 218 - 221, do Ch. III, EXERCISES 2C, 2E, 2F, 2K (pp. 217 - 218); 2.1B, 2.1D, 2.1E (p. 223).
4/6 for 4/8: Read pp. 205 - 208, 209 - 211, do Ch. III, EXERCISES 1.3D, 1.3J, 1.3L (pp. 208 - 209); 1.4C, 1.4D(a)(b) (p. 211).

Fourth graded homework due 4/8:
Three questions from Ch. II, EXERCISES 3.4H, 3.5I; Ch. III, EXERCISES 1.1B, 1.2C, 1.2F.

4/1 for 4/6: Read pp. 196 - 198, 200 - 203, do Ch. III, EXERCISES 1.1A, 1.1C (p. 198); 1.2A, 1.2B, 1.2M (pp. 203 - 204).
3/30 for 4/1: Read pp. 191 - 195, do Ch. III, EXERCISES 1C, 1A, 1B, 1F, 1H, 1J (pp. 195 - 196).
3/25 for 3/30: Read pp. 189 - 190, do Ch. II, EXERCISES 3.5G, 3.5H, 3.5J (p. 190).
3/23 for 3/25: Read pp. 188 - 189, do Ch. II, EXERCISES 3.5C, 3.5D, 3.5F (p. 190).
3/9 for 3/23: Read pp. 187 - 188, do Ch. II, EXERCISES 3.5A, 3.5B, 3.5E (p. 190).

Third graded homework due 3/9:
Three questions from Ch. II, EXERCISES 3K, 3.1D, 3.2E(b)[just (3.5)],(c)(i), 3.3I, 3.3M.

3/4 for 3/9: Read pp. 183 - 185, do Ch. II, EXERCISES 3.4A, 3.4C, 3.4D, 3.4F, 3.4J (pp. 185 - 186).
3/2 for 3/4: Read pp. 181 - 183, do Ch. II, EXERCISE 3.4I (p. 186).
2/26 for 3/2: Read pp. 177 - 180, do Ch. II, EXERCISES 3.3E, 3.3F, 3.3G, 3.3H (just Z21), 3.3L (pp. 180 - 181).
2/24 for 2/26: Read pp. 174 - 177, then (re)do Ch. II, EXERCISE 2G (p. 132), do Ch. II, EXERCISES 3.3D(a), 3.3A, 3.3K (pp. 180 - 181).
2/19 for 2/24: Read pp. 170 - 173, do Ch. II, EXERCISES 3.2E(a), 3.2G, 3.2I, 3.2L (pp. 173 - 174).
2/12 for 2/17: Read pp. 168 - 170, do Ch. II, EXERCISES 3.2A, 3.2C, 3.2J (p. 173), 3.1D (p. 167), 3.2F (p. 173).

Second graded homework due 2/12:
Three questions from Ch. II, EXERCISES 2.1G, 2.2H, 2.3M, 2.3O, 2.4L.

2/10 for 2/12: Read pp. 164 - 166, do Ch. II, EXERCISES 3.1B, 3.1E, 3.1G, 3.1H, 3.1K (pp. 166 - 167). For analysts: 3.1F, 3.1L (pp. 167 - 168).
2/5 for 2/10: Read pp. 158 - 162, do Ch. II, EXERCISES 3B, 3D, 3C, 3G, 3O (pp. 162 - 163). For analysts: 3J (p. 163).
2/3 for 2/5: Read pp. 150 - 155, do Ch. II, EXERCISES 2.4F, 2.4M, 2.4Q, 2.4R, 2.4S (pp. 156 - 157).
1/29 for 2/3: Read pp. 144 - 148, do Ch. II, EXERCISES 2.3E, 2.3D, 2.3J, 2.3L, 2.3N(a) (pp. 148 - 149).
1/27 for 1/29: Read pp. 133 - 143, do Ch. II, EXERCISES 2.1A, 2.1C, 2.1D, 2.1E (pp. 136 - 137), 2.2A, 2.2B, 2.2E (p. 144). For analysts: 2.1H, 2.1I (p.137).

First graded homework due 1/27:
Three questions from Ch. II, EXERCISES 1F, 1.3D, 1.4K, 1.4Q, 1.4S.

1/22 for 1/27: Read pp. 129 - 133, do Ch. II, EXERCISES 2D, 2A, 2F, 2G, 2K (pp. 131 - 132).
1/20 for 1/22: Read pp. 126 - 128, do Ch. II, EXERCISES 1.4C, 1.4J, 1.4L, 1.4M (pp. 128 - 129).
1/15 for 1/20: Read pp. 119 - 124, do Ch. II, EXERCISES 1.2C, 1.2K (pp. 121 - 122), 1.3A, 1.3B, 1.3E, 1.3F (p. 125).
1/13 for 1/15: Read pp. 111 - 117, do Ch. II, EXERCISES 1B, 1C, 1E (p. 113), 1.1D, 1.1J, 1.1K (pp. 117 - 8).