## Mathematics 504: Abstract Algebra

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

e-mail: jdhsmithATmathDOTiastateDOTedu (substitute punctuation)

Grading: based on three graded homework assignments (45 points = 64%) and mid-term (25 points = 36%). 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/math504smith.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, split extensions, presentations, Boolean rings and algebras, Galois theory, tensor products, etc.

### Assignments

Click here for practice final in Portable Document Format

12/5 for 12/10: Read pp. 83 - 85, do Ch. I, EXERCISES 3.3G, 3.3I, 3.3J (p. 86).

Third graded homework due 12/5:
Three questions from Ch. I, EXERCISES 2.2M, 2.4I, 2.5D, 3H, 3L.

12/3 for 12/10: Read pp. 82 - 83, do Ch. I, EXERCISES 3.3C, 3.3E, 3.3B, 3.3A (pp. 85 - 86).
12/1 for 12/3: Read pp. 80 - 81, do Ch. I, EXERCISES 3.2H, 3.2J, 3.2K, 3.2M, 3.2L (pp. 81 - 82).
11/21 for 12/1: Read pp. 78 - 79, do Ch. I, EXERCISES 3.2A, 3.2B, 3.2D, 3.2E, 3.2O (pp. 81 - 82).
11/19 for 11/21: Read pp. 74 - 77, do Ch. I, EXERCISES 3.1A, 3.1B, 3.1C, 3.1D, 3.1H (p. 77).
11/17 for 11/19: Read pp. 72 - 73, do Ch. I, EXERCISES 3B, 3C, 3D, 3I, 3J (p. 71).

Second graded homework due 11/12:
Three questions from Ch. I, EXERCISES 1.3L(a)-(b), 1.3M, 2E, 2.1G, 2.1K.

11/12 for 11/17: Read pp. 68 - 71, do Ch. I, EXERCISES 2.5G, 2.5A, 2.5C, 2.5E (p. 71).
11/10 for 11/12: Read pp. 65 - 67, do Ch. I, EXERCISES 2.4A, 2.4F, 2.4G, 2.4K (pp. 67 - 68).
11/7 for 11/10: Read pp. 59 - 62, do Ch. I, EXERCISES 2.2A, 2.2B, 2.2C, 2.2E, 2.2H, 2.2K (pp. 62 - 63).
11/5 for 11/7: Read p. 58, do Ch. I, EXERCISES 2.1I, 2.1J (p. 59).
11/3 for 11/5: Read pp. 55 - 56, do Ch. I, EXERCISES 2.1A, 2.1B, 2.1E (pp. 56 - 57).
10/31 for 11/3: Read pp. 52 - 54, do Ch. I, EXERCISES 2B, 2D, 2A, 2F (pp. 54 - 55).
10/29 for 10/31: Read pp. 49 - 51, do Ch. I, EXERCISES 1.5A, 1.5B, 1.5D, 1.5G, 1.5F (p. 51).
10/27 for 10/29: Read pp. 45 - 48, do Ch. I, EXERCISES 1.4A, 1.4E, 1.4B, 1.4D (pp. 48 - 49).

Click here for actual mid-term in Portable Document Format
Click here for practice mid-term in Portable Document Format

10/17 for 10/20: Read pp. 42 - 43, do Ch. I, EXERCISES 1.3D, 1.3G, 1.3J (p. 44).
10/15 for 10/17: Read pp. 41 - 42 (except last paragraph of p.42), do Ch. 1, EXERCISES 1.3A, 1.3B, 1.3C, 1.3E, 1.3I (p. 44).
10/13 for 10/15: Read pp. 37 - 39, do Ch. I, EXERCISES 1.2A, 1.2C, 1.2D (p. 39).
10/10 for 10/13: Read pp. 34 - 35, do Ch. I, EXERCISES 1.1A, 1.1B, 1.1C, 1.1E (pp. 35 - 36).
10/6 for 10/8: Read pp. 29 - 32, do Ch. I, EXERCISES 1E, 1F, 1G, 1K, 1U (pp. 29, 32 - 33).

First graded homework due 10/6:
Three questions from Ch. O, EXERCISES 3.2G, 3.5B, 4C, 4.1J, 4.4H.
[ NOTE: The grading will focus on careful exposition. ]

10/3 for 10/6: Ch. O, EXERCISE 4.4J (pp. 26 - 27).
10/1 for 10/6: Ch. O, EXERCISES 4.4E, 4.4F, 4.4G (p. 26).
9/29 for 10/1: Ch. O, EXERCISES 4.4D, 4.4B, 4.4A, 4.4C (p. 26).
9/26 for 9/29: Ch. O, EXERCISES 4.3A - 4.3F (p. 24).
9/24 for 9/26: Ch. O, EXERCISES 4.2A, 4.2B, 4.2C, 4.2D (p. 23).
9/22 for 9/24: Ch. O, EXERCISES 4O, 4Q, 4S, 4T, 4U (p. 20).
Also:
For a function f : X —Y, define the graph to be the subset
{ ( x, xf ) | x in X }
of X x Y. Show that for monoids M and N, a function
f : M —N
is a monoid homomorphism if and only if its graph is a submonoid of M x N.
9/17 for 9/19: Read pp. 20 - 22, do Ch. O, EXERCISES 4.1A, 4.1B, 4.1C, 4M, 4.1H (pp. 20 - 22).
9/15 for 9/17: Read pp. 17 - 19, do Ch. O, EXERCISES 4A, 4B, 4G, 4J, 4K, 4P (pp. 17, 19).
9/12 for 9/15:
Ch. O, EXERCISES 3.5B, 3.5C, 3.5D (first part P({1,2}) only), 3.5E (pp. 16 - 17).
9/8 for 9/10: Ch. O, EXERCISES 3.4A, 3.4C, 3.4E, 3.4G (pp. 14 - 15).

Zeroth graded homework due 9/8:
Three questions from Ch. O, EXERCISES 3.1D, 3.1G, 3.2D, 3.2H, 3.2Q.

8/29 for 9/3: Ch. O, EXERCISES 3.2E, C (p. 8), 3.1H (p. 6), 3.2A, B (p. 8).
8/27 for 8/29: Ch. O, EXERCISES 3.1A, B, C, G (pp. 5 - 6).
8/25 for 8/27: Ch. O, EXERCISE 3 (p. 4).