Mat 301F: Groups and Symmetries

Instructors: Henrique Bursztyn and Kyu-Hwan Lee

Textbook : Contemporary Abstract Algebra, by J. Gallian (fifth edition)
Lectures: Wed 6-9pm in SS1085 (HB) and SS1073 (Lee).
Office hours: HB: Wed 1-2pm or by appointment; Lee: Tu 4-5pm, Wed 10-12.
Course outline: We will try to cover most of Part 1 (Chapters 1 - 11) and, time permitting, some topics in Part 5 (Chapters 24, 27, 29 ...). Here is a brief outline:
- Groups: definition and examples: symmetries of plane figures, cyclic groups, permutation groups, finite groups etc.
- Subgroups, examples; group isomorphisms and homomorphisms.
- Cosets and Lagrange's theorem.
- Normal subgroups, quotients.
- Fundamental theorem of finite abelian groups.
- Sylow theorems.
- Symmetry groups, group actions.
Exams: We will have one midterm on October 22, and a final in December.
Quizzes: We will have 4 or 5 quizzes throughout the semester, dates to be announced. These are very short tests (around 20 min) based on HW problems.
- Quiz #1: Sep. 24, in class. It covers Chapters 1,2,3.
- Quiz #2: Oct. 8, in class. It covers Chapters 4,5.
- Quiz #3: Nov. 5, in class. It covers Chapters 6,7.
- Quiz #4: Nov. 26, in class, covering Chapters 8,9 and 10.
Midterm-I Info:
- Date: Oct. 22
- Time: 7-8:30pm
- Place: SS1069 for HB, and SS1085 for Lee (NOTE ROOM CHANGE!)
Homework: Problems will be assigned every lecture to be collected on the following one. The TA will be grading some (but probably not all) of the questions. Late homeworks will not be accepted. Your lowest HW grade will be dropped.
Grades: Homework + quizzes: 30%, Midterm: 20%, Final: 50%. There will be no make-up exams.
Homework Problems:
- Chapter 2: 1, 3, 4, 5, 7, 22, 34. (Due Sep. 17.)
- Chapter 3: 4, 5, 6, 8, 14, 15, 47, 52; Chapter 4: 4 (Due Sep. 24)
- Chapter 4: 7, 10, 11, 40, 45; Chapter 5: 4 (Due Oct. 1)
- Chapter 5: 9, 10, 13, 18, 30; Chapter 6: 2, 3, 15, 17 (Due Oct. 8)
- Chapter 6: 4, 20, 27, 30, 33; Chapter 7: 1,6 (Due Oct. 15)
- Chapter 7: 8, 14, 15, 20 26, 29 (Due Oct. 29) (Not Oct. 22 due to Midterm I !)
- Chapter 8: 1, 4, 10, 17, 18, 20, 22, 40, 52 (Due Nov. 5)
- Chapter 9: 3, 4, 8, 9, 10, 16, 20, 46, 48 (Due Nov. 12)
- Chapter 10: 8, 9, 16, 20, 24, 34, 44 (Due Nov. 19)
- Chapter 11: 2, 6, 11, 16, 19, 20, 24, 32 (Due Nov. 26)
- Chapter 24: 5, 11, 12, 17, 25 (Suggested, not to be handed in)
Final Homework (optional):
- Write a sample final exam, consisting of 7 questions covering the entire course, including solutions. You should hand in your sample final by Tuesday, Dec. 2, 5pm, in your instructor's mailbox (next to SS 4072). If you do a good job, this could replace your second lowest HW mark (the lowest one will be dropped). We will select some of your questions for a review sheet which we will work on in class, on Wed. Dec 3.