MATH 4550 - Modern Algebra I

Class information:

Notes:

  • Notes on the dihedral group can be found here.
  • Lemma about the identity element and inverses in subgroups.
  • Lemma about what cyclic subgroups look like.
  • The division algorithm statement and proof
  • Classification of homomorphisms from cyclic groups: lemma and main theorem.
  • A proof that the set of permutations of a set is a group under composition.

Homework:

  • Homework #1: problems and solutions 
    See this for a better way to do the solutions for 2,3,13
    Typos: The solutions on problem 5 should say "Thus, e = 2 and e = 1.   This is a contradition."
     
  • Homework #2: problems and solutions 
    See this for a better way to do #2,9,10 and for two extra problems to do

     
  • Homework #3: problems and solutions.
    Typo: At the end of the proof 5(a) it says "By the lemma, k divides the order of phi(x)."   It should say "By the lemma, the order of phi(x) divides k."  

     
  • Homework #4: problems and solutions.
    Typos: In the solutions for problem 6 I found the homomorphisms from Z_6 to Z_8.   It should have been Z_8 to Z_6 as stated in the problem set.   But my solution is correct for the Z_6 to Z_8 problem.   Try doing Z_8 to Z_6 in the same way.

     
  • Homework #5: problems and solutions.
  • Homework #6: problems and solutions.
  • Homework #7: problems and solutions.
  • Homework #8: problems and solutions.
  • Homework #9: problems and solutions.

Student notes from F16 (Thanks Cynthia!):

week 1, week 2, week 3, week 4, week 5,
week 6, week 7, week 8, week 9, week 10,
week 11, week 12, week 13, week 14, week 15

Test solutions:

  • Fall 2017: Test 1 solutions are here.
  • Fall 2017: Test 2 solutions are here.
  • Fall 2016: Test 1 solutions are here.
  • Fall 2016: Test 2 solutions are here.