MAT 301, Groups and Symmetries, Fall 2012

Instructor

Prof. Kasra Rafi
Office: BA 6188 (Bahen Centre)
Email: rafi@math.toronto.edu

Meetings

Wednesdays 6-9pm in LM 158.

Office hours

Tuesdays and Wednesdays 5-6pm or by appointment.

Teaching Assistant

Mikhail Gudim
Email: mgudim@gmail.com
Mikhail is available on Thursdays 6-7pm in the math lounge.

Textbook

Contemporary Abstract Algebra, Joseph A. Gallian.
You can use either the 7th or the 8th edition.

Course description

This course is an introduction to groups theory. We will cover the first 11 sections of the textbook. You need to be comfortable with using the language of set theory, like defining a set, function, relation, etc. Familiarity with Linear Algebra, elementary number theory and modular arithmetic is also seful for some of the examples we will discuss.

Prerequisite

MAT 224H1, MAT 235Y1 / MAT 237Y1, MAT 246H1 / CSC 236H1 / CSC 240H1.

Exams

There will be one midterm and one final exam.

The midterm will take place on Wednsday, October 24, 6-9pm in MP 203.

The format of the midterm will be as follows:

• Definitions
• A theorem from the book
• Computational problems
• Proof problems

The best way to prepare for the midterm is to study the definitions and theorems first and then go over the quizzes and homework assignments or problems similar to those from the textbook. The following problem set is from a previous class and provides a good review or the topics covered:

• Problem set from a previous course.

The final exam is tentitively scheduled for Tuesday, Decembert 18, 7-10pm.

Homework and quizzes:

There will be weekly homework assignments. However the homework will not be collected. Instead, there will be weekly quizzes based on the homework problems (10 quizzes in total). Only the grades of the best 8 quizzes will count towards the final grade. Students are encouraged to work together on the homework problems.

Solutions

Quiz 1, Quiz 2, Quiz 3, Quiz 4, Quiz 5, Quiz 6, Quiz 7, Quiz 8, Quiz 9

Midterm

Suggested problems

7th Edition:

• Chapter 1: 2, 3, 7, 9, 15, 17, 22.
• Chapter 2: 2, 3, 4, 5, 12, 15, 19, 20, 23, 26, 27, 28, 29, 33, 34.
• Chapter 3: 3, 7, 11, 14, 16, 17, 27, 30, 31, 33, 47, 49, 60, 62.
• Chapter 4: 1, 5, 9, 13, 22, 23, 29, 33, 40, 45, 49, 60, 62.
• Chapter 5: 1, 2, 3, 5, 7, 9, 11, 15, 18, 23, 25, 37, 38, 41, 42.
• Chapter 6: 1, 2, 3, 4, 5, 10, 11, 23, 25, 27, 32, 37, 39.
• Chapter 7: 1, 2, 3, 5, 9, 11, 13, 15, 17, 21, 29, 30, 39, 40, 42.
• Chapter 8: 1, 2, 5, 7, 11, 12, 21, 26, 30, 31, 41, 49, 61.
• Chapter 9: 1, 2, 4, 6, 7, 8, 9, 10, 14, 19, 37, 41, 47, 48.
• Chapter 10: 5, 6, 7, 9, 11, 17, 18, 22, 24, 29, 38, 49, 55.
• Chapter 11: 1, 4, 5, 7, 9, 10, 11, 19, 20, 29, 30.

8th Edition:

• Chapter 1: 2, 7, 9, 15, 17, 24.
• Chapter 2: 7, 8, 9, 11, 20, 23, 27, 28, 31, 34, 35, 37, 39, 45, 46.
• Chapter 3: 3, 11, 19, 23, 28, 30, 31, 43, 46, 49, 63, 65, 67.
• Chapter 4: 1, 5, 9, 13, 22, 23, 29, 33, 40, 55, 59, 70, 72.
• Chapter 5: 2, 3, 4, 5, 7, 9, 11, 15, 19, 27, 29, 41, 42, 45, 52.
• Chapter 6: 1, 2, 3, 4, 5, 10, 11, 33, 35, 37, 42, 53, 55.
• Chapter 7: 1, 2, 3, 5, 9, 13, 15, 17, 19, 23, 31, 32, 34, 42, 48.
• Chapter 8: 1, 2, 5, 7, 11, 23, 28, 34, 35, 49, 59, 71.
• Chapter 9: 1, 2, 6, 8, 9, 10, 11, 12, 14, 19, 37, 43, 49, 50.
• Chapter 10: 5, 6, 7, 9, 11, 17, 18, 22, 24, 29, 38, 49, 55.
• Chapter 11: 1, 4, 5, 7, 9, 10, 11, 21, 22, 31, 32.

Marking scheme

Your course grade is computed as follows:

• Quizzes 25%
• Midterm 30%
• Final exam 45%

Study hints

Before each class, you should both review the material from recent sections and read the section to be discussed that day. This will allow you to both understand the presentation of new material and identify questions that you need to resolve during class.

Policy on missed quizzes or exams:

There are no make up exams or quizzes. If you miss more than two quizzes or the midterm for a legitimate reason which you can document, your grading scheme will be adjusted by increasing the final exam component of your mark. The documentation must be submitted no later than 7 days after the date of the exam/quiz. You can find the University of Toronto Medical Certificate form here.

Academic integrity

The University of Toronto Code of Behaviour on Academic Matters can be found here.

Accessibility needs

The University of Toronto is committed to accessibility. If you require accommodations for a disability, or have any accessibility concerns about the course, the classroom or course materials, please contact Accessibility Services as soon as possible: email disability.services@utoronto.ca or visit here.