Math 3140 Fall 21

## MATH 3140: Abstract Algebra 1 (Fall 2021)

Syllabus

### Schedule

Numbers are for orientation and refer to sections with related material in Goodman, Algebra: Abstract and Concrete.
1. 08/23: symmetries, multiplication table (1.1-1.3)
2. 08/25: linear maps, symmetries of the square as matrices (1.4)
3. 08/27: symmetries of the square as permutations, Sym(X), S_n (1.5)
4. 08/30: cycle notation of permutations (1.5), groups, matrix groups, permutation groups (1.10)
5. 09/01: uniqueness of identity, inverses in groups (2.1), modular arithmetic, equivalence relation, Z_n (1.7)
6. 09/03: symmetries of a regular n-gon, dihedral group D_2n, +,. on Z_n welldefined (1.7)
7. 09/08: Euclidean algorithm for gcd, Bezout's coefficients, multiplicative inverses in Z_n (1.7)
8. 09/10: subgroups (2.2), center of a group
9. 09/13: center of D_2n, cyclic subgroups, generators (2.2)
10. 09/15: order of groups and elements, homomorphisms (2.4)
11. 09/17: properties of homomorphisms (2.4), isomorphisms, cyclic subgroup are isomorphic to Z or Z_n (2.2.20)
12. 09/20: subgroups of cyclic groups (2.2.21, 2.2.30), permutation groups
13. 09/22: Cayley's Theorem, cosets of subgroups
14. 09/24: Lagrange's Theorem 2.5.6, index of subgroups, Euler's Theorem
15. 09/27: REVIEW
16. 09/29: MIDTERM 1

### Assignments

1. due 08/25 [pdf]
2. due 09/01 [pdf]
3. due 09/10 [pdf] [tex]
4. due 09/15 [pdf] [tex]
5. due 09/22 [pdf] [tex]
6. due 09/27 [pdf] [tex] Practice Exam due Monday!

### Handouts

1. Integers mod n [pdf]