| Time | Mon, Wed 11:40am–12:55pm |
| Place | Room 312, Math building |
| Instructor | Anand Deopurkar (anandrd at math) |
| TAs |
Rob Castellano (castellano at math),
Philip Engel (engel at math)
|
| Office hours | Mon, Wed 5pm–6pm in Math 413 |
| Textbook | Algebra (2nd edition) by Michael Artin |
The final grades are on Courseworks. The letter grade is based on the cumulative score, which is calculated by taking a weighted average of the final (40%), midterms (20% each), and homework (20%). I have dropped the two lowest homework scores.
Thank you for a great semester! Enjoy winter break.
Here is a classification of groups of order up to 30 with some exceptions. (Solution to Homework 11).
The final is on Friday, Dec 13 from 9 to 12 in the morning. Here are some practice exams.
The last homework, homework 11, is up. It is due by next Monday, December 9. It is slightly unusual; it contains only one but extended problem. I have added a few useful lemmas as hints.
We have finished grading the second midterm. The mean was 33 with a standard deviation of 9. The median was 34. Here are the solutions.
Homework 9 is up and due on Nov 20.
Midterm 2 will be on Monday, Nov 11 in class.
I will have office hours on Sunday, Nov 10 (5pm–7pm).
Since you are unlikely to get HW8 back before the midterm, I have sketched out the solutions.
To prepare for the exam, know the definitions and proofs of everything we have done in class. Make sure you can do all homework problems. For more practice, here are some old midterms
Here is a proof that a rigid motion fixing the origin is given by multiplication by an orthogonal matrix (taken from Artin's Algebra (1 ed)).
I am considering moving the second midterm to Nov 11 from Nov 6. If you have an opinion on this change, let me know.
The optional problems are challenging problems for you to think about. You do not have to write their solutions and turn them in.
As promised, here are the notes for the correspondence theorems. To reduce notation, I switched from the perspective of a surjective homomorphism to that of a quotient. I apologize for the changes in notation caused by this.
Here are the solutions of Midterm 1. I encourage you to come and talk to me about the midterm. I will be in my office today from 4pm to 7pm and tomorrow from 10am to 6pm (except 12 to 1). Email me to schedule some other time. I will be out of town starting Wednesday afternoon, so I won't have my usual office hours on Wednesday.
The first midterm is on October 2 (Wednesday). It will be a closed-book, closed-notes, in-class exam. You will be responsible for the material covered until (and including) September 25. This corresponds to sections 2.1 – 2.6 of the text along with the associated background material in Chapter 1 and the appendices.
For preparation, make sure you understand the statements, their proofs, and the examples in the book and can apply them to solve the exercises. Also review all the homework problems. You may want to look at past midterms here, here, or here. But be aware that the material covered on those exams may not be the same as ours. So skip the problems that involve unfamiliar concepts.
For the next week, I am moving my Mon, Wed office hours to Mon, Tue (5 – 6 pm).
Homework 2 has been graded. You can view your score on CourseWorks and pick up the homework from the shelf in the math help room (Math 406).
Homework 1 has been graded. You can view your score on CourseWorks and pick up the homework from the shelf in the math help room (Math 406).
| Week of | Reading | Homework |
| Sept 2 | How to write proofs by Eugenia Cheng, Introduction to mathematical arguments by Michael Hutchings, Artin A.1, A.2, Artin (1E) A1. | Homework 1 (Due Wed, Sept 11) |
| Sept 9 | Artin Chapter 1 (for review), 2.1, 2.2. | Homework 2 (Due Wed, Sept 18) |
| Sept 16 | Artin 2.3, 2.4, 2.6 | Homework 3 (Due Wed, Sept 25) |
| Sept 23 | Artin 1.5 (permutation matrices), 2.5, 2.6, Subgroups of a finite cyclic group | Homework 4 (Due Wed, Oct 2) |
| Sept 30 | Midterm 1 on Wednesday, Oct 2. | No homework |
| Oct 7 | Artin 2.7, 2.8, 2.12 | Homework 5 (Due Wed, Oct 16) |
| Oct 14 | Artin 2.9, 2.10, 2.12, Correspondence theorems | Homework 6 (Due Wed, Oct 23) |
| Oct 21 | Artin 5.1 up to Theorem 5.1.17, 6.1, 6.2, 6.4, Rigid motions | Homework 7 (Due Wed, Oct 30) |
| Oct 28 | Artin 6.7, 6.8, 6.9 | Homework 8 (Due Wed, Nov 6) |
| Nov 4 | Midterm 2 on Nov 11. | No homework |
| Nov 11 | Artin 7.2, 7.5 | Homework 9 (Due Wed, Nov 20) |
| Nov 18 | Artin 7.2, 7.3, Semidirect products | Homework 10 (Due Wed, Nov 27) |
| Nov 25 | Artin 7.7, 7.8 | |
| Dec 2 | Artin 14.7.3–14.7.7 Classification of (finitely generated) abelian groups | Homework 11 (Due Mon, Dec 9) |
This is the first in a sequence of two courses in which we will study fundamental algebraic structures such as groups, rings, and fields. Our focus in the fall semester will be the theory of groups. A parallel goal will be to hone the skills of reading and writing rigorous mathematical proofs.
I plan to cover Chapter 2, Chapter 6, Chapter 7, and some topics from Chapter 9 (depending on time and interest) from the book.
Expected background: Calculus, basic linear algebra (matrices and matrix operations) as taught in MATH V2010 or Honors Mathematics A-B. Familiarity with basic mathematical vocabulary (sets, functions). Familiarity with proofs as taught in MATH V2000 (Introduction to Higher Mathematics) will be helpful (but not required). Please contact me if you are unsure about your background.
The final grade will be based on homework (20%), two in-class midterms (20% each), and a final (40%). The exams are scheduled as follows:
It is impossible to learn algebra without working through examples, so the homework forms an essential part of the course. It will be announced weekly on the website and will be due in a week (usually on Wednesday). No late homeworks will be accepted. To compensate, I will drop the two lowest homework scores.
Collaboration: You may work on the homework problems in groups, but you must write up the solutions by yourself. Do not copy anyone else's written work. As a matter of academic honesty, write the names of your collaborators on top of your submission (this will not affect your grade).