Mat 301F: Groups and Symmetries
Instructors: Henrique Bursztyn and Michael Shub
- Textbook : Contemporary Abstract Algebra, by J. Gallian (fifth edition)
- Lectures: Wed 6-9pm in SS1085 (HB) and SS1073 (MS).
- Office hours: M. Shub: Tuesday 4-5pm in SS4057,
H. Bursztyn: Wed 10-11am in SS5017B.
- Teaching Assistants: Andrew Douglas (adouglas@math) and Guangyu Fu (gyfu@math).
- 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 exam on October 27, and a final in December.
- Midterm-I Info:
- Date: Oct. 27
- Time: 7-8:45pm
- The exam covers chapters 2 to 7.
- Quizzes: We will have 4 quizzes throughout the semester. Tentative dates are:
- Quiz #1: Sep. 29. (It covers Chapters 2,3)
- Quiz #2: Oct. 13. (It covers Chapters 4,5)
- Quiz #3: Nov. 10. (It covers Chapter 7)
- Quiz #4: Nov. 24. (It covers Chapters 8,9 -- bonus question from Chapter 10)
These are very short tests (around 20 min, in the beginning of the class) based on HW
problems.
- Homework: Problems will be assigned every lecture to be collected
on the following one. The TAs will be grading them. Late homeworks will not be accepted.
Your lowest HW grade will be dropped.
- Grades: Homework:15%, Quizzes: 15%, Midterm: 20%,
Final: 50%.
There will be no make-up exams.
- Assigned Homework Problems :
- Chapter 2: 26, 34, 36. (Due Sep. 22). Other suggested problems (not to be marked, no need to hand them in):
Chapter 0: 39,40; Chapter 1: 2,3; Chapter 2: 8, 22, 30.
- Chapter 3: 28, 52; Chapter 4: 38 (Due Sep. 29). Other suggested problems:
Chapter 3: 14, 20, 24; Chapter 4: 14, 26.
- Chapter 4: 10, 54; Chapter 5: 18 (Due Oct. 6). Other suggested problems:
Chapter 4: 9, 40; Suppl. Exercises: 10 (pp. 90); Chapter 5: 4.
- Chapter 5: 32, 34; Chapter 6: 4 (Due Oct. 13). Other suggested problems: Chapter 5: 10, 17, 36; Chapter 6: 8, 24, 27.
- Chapter 6: 36; Chapter 7: 8, 20 (Due Oct. 20). Other suggested problems: Chapter 6: 12, 22, 32; Chapter 7: 10, 12, 34.
- Chapter 7: 28, 38, 42 (Due Nov. 3 due to Midterm on Oct. 27).
- Chapter 8: 18, 22, 30 (Due Nov. 10); Other suggested problems: Chapter 8: 4, 27; Chapter 9: 1, 3.
- Chapter 9: 4, 10, 22 (Due Nov. 17); Other suggested problems: Chapter 8: 15, 32;
Chapter 9: 49; Chapter 10: 21, 24.
- Chapter 10: 12, 18, 42 (Due Nov. 24);
Other suggested problems: Chapter 9: 30, 32, 55;
Chapter 10: 27, 52.
- Chapter 11: 4, 20, 24 (Due Dec. 01);
Other suggested problems: Chapter 10: 52;
Chapter 11: 11, 28.
- Final Worksheet: Click here to get it. Make sure to
try to solve all the problems before our last meeting (on Dec. 08).
Click for information on the
Norten Institute Undergraduate Scholarship (deadline is Nov. 1, 2004).
Back to the main page