Math 371: Algebra
- Lectures: MTWR 1:00-3:10pm in DRL 2C4
- Instructor: Tobias Dyckerhoff
- Office: DRL 3E6A
- Office hours: MW 3:10-4:00pm
- Phone: 215-898-5980
- Email: tdyckerh AT math upenn edu
Announcements
Homework
| Section |
Problems |
| 2.1 |
Read Chapter 2/Section 1 |
| 2.1 |
1-11 |
Quiz 1 |
| 2.2 |
Read Chapter 2/Section 2 |
| 2.2 |
1-5,8+subgroups,10,12,16,17,21 |
| 2.Miscellaneous Problems |
1,3 |
| 2.3 |
Read Chapter 2/Section 3 |
| 2.3 |
1,2,5,9,10,12,13 |
| 2.4 |
Read Chapter 2/Section 4 |
| 2.4 |
3,4,7,8,11,15,16,22,23 |
Midterm 1 |
| 2.5 |
Read Chapter 2/Section 5 |
| 2.5 |
2,5,7,9 |
| 2.6 |
Read Chapter 2/Section 6 |
| 2.6 |
3,4,5,7,10,11 |
| 2.9 |
Read Chapter 2/Section 9 |
| 2.9 |
2,4,7 |
Quiz 2 |
| 2.10 |
Read Chapter 2/Section 10 |
| 2.10 |
1,3,5,6,7,8,11 |
| 2.misc |
4,7,8 |
| 5.5-7 |
Read Chapter 5/Section 5-7 |
| 5.5 |
4,8,10 |
| 5.6 |
1,3,4,5 |
| 5.7 |
1,2,3 |
| 5.9 |
Read Chapter 5/Section 9 |
| 5.9 |
1,3,5,6 |
Midterm 2 |
| 3.1,2 |
Read Chapter 3/Section 1 and 2 |
| 3.1 |
1,2,3,4,5 |
3.3,4 |
Read Chapter 3/Section 3 and 4 |
| 3.3 |
1,4,5,6,7,9 |
| 3.4 |
1,2,3 |
Quiz 3 |
| 4.2 |
1,2,4,5 |
| 4.4 |
5,11,13 |
| 4.5 |
1,2,4 |
| Quotient Spaces |
problem1.pdf |
| 9.1 |
1,2,3,5,9,10 |
| 9.4 |
1,2,3 |
Final |
Course policies
The syllabus will include the study of basic algebraic
structures like groups, rings, modules, etc. After laying the
foundations, we will focus on representation theory. This abstract
study of symmetries has many applications in other scientific fields,
the most prominent one being its fundamental role in modern particle
physics.
The syllabus will be roughly as follows.
- Groups
- Vector spaces and linear transformations
- Symmetries
- Rings and modules
- Representation theory
We will use Algebra by Michael Artin
as a textbook for the course.
Other useful books are
- Topics in Algebra (Herstein)
- Algebra (Lang)
Math 240.
The course runs for 6 weeks.
In the odd weeks we will write
quizzes (Thursdays), in the even weeks we will write exams (on
Thursdays).
- Homework.
I will assign homework at least once a week. You do not have to submit your
work. BUT: The set of problems on the quizzes will literally be a
subset of the assigned homework problems. So, if you do your homework you will
automatically be well prepared for the quizzes. Selected homework problems will be discussed in the office hours.
- Quizzes.
In the odd weeks (1,3,5) on Thursdays, I will take a short quiz in
the first 10 minutes of class.
- Exams.
In the even weeks (2,4,6) on Thursdays, we will write exams. In weeks 2 and 4
we will write midterms, in the last week we will write the final exam.
Grading
Your final grade will be computed using the following weights
- Quizzes: 20 %
- Midterm 1: 25 %
- Midterm 2: 25 %
- Final Exam: 30 %
Grades will be posted on
blackboard.
The final grade distribution should be around 33% A, 33% B and 33% C, though in
case of a general good performance I am willing to shift this distribution.