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]