Math 411: Abstact Algebra I: Section 1 (#58690)

This is a one semester introduction to group theory through a series of concrete examples. Among the topics covered by the course are subgroups, quotient groups, cyclic, permutation, and linear groups, homomorphisms, and group actions. Numerous applications to number theory, geometry, and symmetries will be derived. Some attention will be given to development of careful mathematical reasoning.

Text: Algebra: Pure and Applied by A. Papantonopoulou

Class meetings: MWF 10:10-11:00 in LGRT 204

Policy Sheet

Instructor

Dan Yasaki, LGRT 1116, (413) 545-6016, yasaki@math.umass.edu

Office hours: Mondays and Tuesdays 9:00-10:00 AM in LGRT 1116

Useful Links

• Farshid's Math 300 Notes: Everything you will need to know about number theory, equivalence relations, partitions, etc for this course. All the definitions and theorems are here.
• TUG: Getting started in LaTeX. A nice way to typeset mathematics and more.
  Short reference for math symbols.
• UMASS: More LaTeX documentation:
• SPARK: Check grades, chat with peers.
• SPIRE: Register.

Grading

• Problem Sets:
  HW 1: 1.1 and 1.2
  • 1.1 (6,14,16,18,19,22,29) Hints and optional problems tex file Solutions tex file
  • 1.2 (14,16,20,24,28,29,30,32,36) Hints tex file Solutions tex file
    HW 2: 1.3 and 1.4
  • 1.3 (1,10,11,20,23) Hints tex file Due Tuesday 2/18 (Accepted Wednesday) Solutions tex file
  • Part 1: 1.4 (2,4,5,7,11,12) Hints tex file Due Tuesday 2/18 (Accepted Wednesday) Solutions tex file
  • Part 2: 1.4 (16,17,28,35) Optional: 1.4 (38) Hints tex file Due Wednesday 2/18 (Accepted Friday) Solutions
    HW 3: 2.1
  • Part 1: 2.1 (2,3,4,5,8) Hints tex file Due Wednesday 2/26 (Accepted Friday)Solutions
  • Part 2: 2.1(21,22,23,26,31,32) Hints tex file Due Wednesday 2/26 (Accepted Friday)Solutions
    HW 4: 2.2-2.4 Due Wednesday 3/26 (accepted Friday)
  • Part 1: 2.2 (1,3,6,8,14,18) Hints tex file Solutions
  • Part 2: 2.2 (34,40,43,48) Hints tex file Solutions
  • 2.3 (3,8,12,14,18,29) Hints tex file Solutions
  • 2.4 (3,8,23) Hints tex file Solutions
    HW 5: 3.1, 3.2 Due Friday 4/4 (accepted Monday)
  • 3.1 (3,4,6) Hints tex file Solutions
  • 3.2 (1,2,4,18,21) Hints tex file Solutions
    HW 6: 3.3-3.4 Due Wednesday 4/9 (accepted Friday)
  • 3.3 (3,7,19) Hints tex file Solutions
  • 3.4 (8,14,15,17) Hints tex file Solutions
    HW 7: 4.1-4.2 Due Wednesday 4/16 (accepted Friday)
  • 4.1 (10,11,15) Hints tex file Solutions
  • 4.2 (3,4,6,8,11): On 3,4,6,8, only answer for a=1 Hints tex file Solutions
    HW 8: 4.3-4.5 Due Wednesday 5/7 (accepted Friday)
  • 4.3 (2,8):
  • 4.4 (3,9,12):
  • 4.5 (7,8):
    Hints tex file Solutions
• Tests/Quizzes:
  • Quiz 1: If the Patriots lose, we will have a quiz in class covering 1.1-1.2 on the Monday following the Super Bowl.
    Quiz 1 tex file (I was shocked.)Solutions tex file
  • Test 1: Wednesday, March 12. in-class test covering first 2 chapters of the text. Practice SolutionsTest 1 Solutions
  • Test 2: Friday, April 18. in-class test covering 3.1-4.4 of the text. Practice test with solutions posted. Practice SolutionsTest 1 Solutions
• The final exam is cumulative. Start reviewing.
  Take home final is due Monday 5/19 in my mailbox on the 16th floor of LGRT Final Exam