Midterm 2 was held on Monday, November 14. Solutions to it to many of the homework problems are available at ELMS.
I plan to cover chapter 1-3 of Herstein's book, Topics in Algebra.
Chapter 1 is a review chapter on sets and elementary number theory.
The main result is the fundamental theorem of arithmetic which states
that you can factor a positive number into prime factors in a unique
way. This is something everyone learns in school, but hardly anyone learns
how to prove it in school. Another important notion from Chaper 1 is the
concept of an
Chapter 2 is about finite groups and their subgroups. The main result is Sylow's theorem on subgroups of prime power order. This is a very important result for determining the structure of finite groups. We will also discuss important concepts like normal subgroups, quotient groups and the isomorphism theorems for finite groups. If time permits, I will prove another important result which classifies finite abelian groups.
Chapter 3 is about ring theory. Here a central notion is that of an ideal inside a ring. These play the role similar to that of the normal subgroups of a group.
For a more complete list of topics covered, please consult the section headings in Herstein's book.
There will be two midterm held in class. The tentative dates for these are as follows.
| Midterm 1 | Monday, October 17 |
|---|---|
| Midterm 2 | Monday, November 14 |
You must let me know immediately during the first week of class if you plan to be absent during the exam due to a religious holiday or for another valid reason.
Course grades will be computed as follows.
| Homework | 20% |
|---|---|
| Midterms | 40% |
| Final | 40% |
Homework will be assigned weekly and due on Friday's. It will be assigned on the homework web page linked here and at the top of this syllabus web page. Late homework will not be accepted but the lowest homework grade will be dropped.
M. Bhatia will be running a tutoring session at various times each week. Click the link above to find the time.
I want every student to feel free to questions in class. Without student questions, even ones that might sometimes seem silly, lectures can become very dry and monotonous. So questions and comments are more than welcome!
On the other hand, please be courteous to other students by paying attention to the lecture and not carrying on conversations with each other. These kind of private conversations can be distracting both to me and everyone else.
Please make sure that your cell phone does not ring during the lecture, and please do not use headphones. Please do not use laptops for anything not related to the class, and, if you do bring a laptop, please sit in the back so that your screen is not distracting to others.