Mathematics 504: Abstract Algebra

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

e-mail: jdhsmithATmathDOTiastateDOTedu (substitute punctuation)

Office Hours: Mon. 11 am, 3.10 pm, 5.30 pm; Wed., Fri. 11am

Finals Week Office Hours: Tue. 1 - 2pm, Wed. 11am - noon

Grading: based on three graded homework assignments (45%), mid-term (25%), and final (30%, Fri. 12/19, 9.45-11.45am). 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.


  • 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.


Click here for practice final in Portable Document Format

12/5 for 12/8: Read pp. 104-108, do Ch.I, EXX 4.4A, 4.4B, 4.4H, 4.4I.

12/1 for 12/5: Read pp. 101-103, do Ch.I, EXX 4.3B, 4.3D, 4.3H.

Third graded homework (due 12/1): Three questions from Ch.I, EXX 2.4I, 2.5D, 3H, 3.1F, 3.2L.

11/17 for 11/19: Read pp. 82-83, do Ch.I, EXX 3.3A, 3.3B, 3.3C, 3.3E.

11/14 for 11/17: Read pp. 78-81, do Ch.I, EXX 3.2A, 3.2D, 3.2E, 3.2J, 3.2K.

11/12 for 11/14: Read pp. 75-77, do Ch.I, EXX 3.1A, 3.1B, 3.1C, 3.1L.

11/10 for 11/12: Read pp. 72-73, do Ch.I, EXX 3B, 3D, 3J, 3L.

11/7 for 11/10: Read pp. 68-71, do Ch.I, EXX 2.5A, 2.5C, 2.5E, 2.5G.

11/3 for 11/5: Read pp. 65-67, do Ch.I, EXX 2.4A, 2.4C, 2.4H, 2.4K.

Second graded homework (due 11/3): Three questions from Ch.I, EXX 1.5B, 2.1F, 2.1K, 2.2K, 2.3C.

10/27 for 10/29: Read pp. 63-64, do Ch.I, EXX 2.3A, 2.3B, 2.3F.

10/24 for 10/27: Read pp. 59-62, do Ch.I, EXX 2.2C, 2.2E, 2.2H, 2.2L.

10/22 for 10/24: Read pp. 55-58, do Ch.I, EXX 2.1A, 2.1E, 2.1G.

10/20 for 10/22: Read pp. 52-54, do Ch.I, EXX 2A, 2D, 2E.

10/17 for 10/20: Read pp. 45-48, do Ch.I, EXX 1.4A, 1.4B, 1.4E.

10/15 for 10/20: Read pp. 49-51, do Ch.I, EXX 1.5A, 1.5E, 1.5G, 1.5H.

Click here for practice mid-term in Portable Document Format

10/6 for 10/8: Read pp. 41-43, do Ch.I, EXX 1.3C, 1.3G.

10/3 for 10/6: Read pp. 34-35, do Ch.I, EXX 1.1C, 1.1E.

10/1 for 10/3: Read pp. 31-32, do Ch.I, EXX 1K, 1L, 1T, 1U.

9/26 for 9/29: Read pp. 29-31, do Ch.I, EXX 1A, 1B, 1C, 1D. Try EX 1G. Also Ch. O, EX 4.4H

First graded homework (due 9/26): Three questions from Ch.O, EXX 4N, 4Q 4.1D, 4.1H, 4.2B.

9/19 for 9/22: Read p. 23, do Ch.O, EXX 4.2D.

9/17 for 9/19: Read pp. 20-22, do Ch.O, EXX 4.1A, 4.1C, 4.1J.

9/15 for 9/17: Read p. 19, do Ch.O, EXX 4M (note the correction for line 20+5), 4P, 4R.

9/10 for 9/12: Read pp. 17-19, do Ch.O, EXX 4B, 4D, 4G.

Zero-th graded homework (due 9/10): Three questions from Ch.O, EXX 3.1D, 3.1G, 3.2H, 3.3D, 3.4A.

9/8 for 9/12: Read pp. 15-16, do Ch.O, EXX 3.5C, 3.5D, 3.5E.

9/5 for 9/8: Read pp. 12-14, do Ch.O, EXX 3.4E, 3.4G.

9/3 for 9/5: Read pp. 10-12, do Ch.O, EXX 3.3A, 3.3C.

8/29 for 9/3: Read pp. 7-9, do Ch.O, EXX 3.2C, 3.2G.

8/27 for 8/29: Read pp. 4-6, do Ch.O, EXX 3.1C, 3.1E.

8/25 for 8/27: Read pp. 1-3, do Ch.O, EXX 3.