IOWA STATE UNIVERSITY

Mathematics 505: Abstract Algebra

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

e-mail: jdhsmithATmathDOTiastateDOTedu (substitute punctuation)

Office Hours: Mon. 11 am, 2.10 pm, 3.10 pm; Wed., Fri. 11am, (subject to change).

Grading: based on three graded homework assignments (45%), mid-term (25%), and final (30%).

Click here for information about special accommodations.

Click here for tally of points earned.

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

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.

Communication devices must remain switched off during the class periods and final.

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, split extensions, presentations, Boolean rings and algebras, Galois theory, tensor products, etc.

Assignments

4/27 for 4/29: Read pp. 260 - 264, do Ch. III, EXX 3.3A, 3.3H(a), 3.3J.

4/22 for 4/27: Read pp. 254 - 258 (skip the proof of Thm. 3.2.3), do Ch. III, EXX 3.1J(a)-(e), 3.2C, 3.2J, 3.2N, 3.2O.

Third graded homework due 4/22: Three questions from Ch. III, EXERCISES 1J, 1.3F, 1.4B, 2M, 2.1H.

4/15 for 4/17: Read pp. 228 - 229, 232, do Ch. III, EXX 2.3B, 2,3E, 2.3F, 2.3O.

4/13 for 4/15: Read pp. 223 - 226, do Ch. III, EXX 2.2B, 2.2C, 2.2I.

4/10 for 4/13: Read pp. 218 - 222, do Ch. III, EXX 2.1B, 2.1D, 2.1E.

4/8 for 4/10: Read pp. 213 - 216, do Ch. III, EXX 2A, 2C, 2F, 2K.

4/6 for 4/8: Read pp. 209 - 212, do Ch. III, EXX 1.4C, 1.4D, 1.4F, 1.4G.

4/3 for 4/6: Read pp. 205 - 208, do Ch. III, EXX 1.3D, 1.3E, 1.3I, 1.3J.

3/30 for 4/3: Read pp. 191 - 203, do Ch. III, EXX 1A, 1E, 1.1A, 1.1F, 1.2A, 1.2C, 1.2G, 1.2M.

Second graded homework due 3/30: Three questions from Ch. II, EXERCISES 3.5F, 3.5G, 3.5I, 3.5J, Ch. III, EXERCISE 1B.

3/13 for 3/23: Read pp. 188 - 190, do Ch. II, EXX 3.5C, 3.5D, 3.5H.

3/11 for 3/13: Read pp. 187 - 188, do Ch. II, EXX 3.5A, 3.5B.

3/9 for 3/11: Read pp. 183 - 185, do Ch. II, EXX 3.4D, 3.4E, 3.4F, 3.4I.

3/6 for 3/9: Read pp. 181 - 182, do Ch. II, EXX 3.4A, 3.4C.

Click here for Practice Mid-Term in Portable Document Format

2/23 for 2/25: Read pp. 174 - 179, do Ch. II, EXX 3.3D, 3.3J, 3.3L, 3.3M.

2/20 for 2/23: Read pp. 174 - 175, do Ch. II, EXX 3.3A, 3.3F, 3.3K.

2/18 for 2/20: Read pp. 170 - 172, do Ch. II, EXX 3.2I, 3.2K (a),(c, see errata), (d) (f), 3.2L.

2/16 for 2/18: Read pp. 168 - 170, do Ch. II, EXX 3.2A, 3.2C, 3.1D, 3.2F.

2/13 for 2/16: Read pp. 164 - 166, do Ch. II, EXX 3.1B, 3.1E, 3.1G, 3.1H, 3.1K.

2/11 for 2/13: Read pp. 158 - 162, do Ch. II, EXX 3A, 3B (see errata), 3D, 3G, 3O.

2/9 for 2/11: Read pp. 150 - 155, do Ch. II, EXX 2.4H, 2.4K, 2.4L, 2.4Q.

2/6 for 2/9: Read pp. 146 - 148, do Ch. II, EXX 2.3H, 2.3I, 2.3J, 2.3L.

2/4 for 2/6: Read pp. 137 - 146, do Ch. II, EXX 1.1L, 1.1M (see errata), 2H, 2.1E, 2.3A.

1/28 for 1/30: Read pp. 133 - 134 (including Example 2.1.5, but omitting Example 2.1.4), do Ch. II, EXX 2.1A, 2.1C, 2.1D. If you are an analyst, try 2.1H, 2.1I.

1/26 for 1/28: Read pp. 126 - 131, do Ch. II, EXX 2A, 2B, 2G.

First graded homework due 1/30: Three questions from Ch. II, EXERCISES 1F, 1.1I, 1.2I (see errata), 1.3G, 1.4K (see errata).

1/21 for 1/23: Read pp. 122 - 124, do Ch. II, EXX 1.3A, 1.3B, 1.3D.

1/16 for 1/21: Read pp. 119 - 121, do Ch. II, EXX 1.2C, 1.2E, 1.2K.

1/14 for 1/16: Read pp. 114 - 117, do Ch. II, EXX 1.1D, 1.1J, 1.1K.

1/12 for 1/14: Read pp. 111 - 113, do Ch. II, EXX 1B, 1C, 1E.