# MATH 322: Introduction to Algebra.

### Text: N. Lauritzen, "Concrete Abstract Algebra".

Section 101, Instructor: Julia Gordon.

REVIEW SESSION FOR THE FINAL: Friday December 18, 4-6pm, room Math 104 (our usual room).
My office: Math 217.

e-mail:
gor at math dot ubc dot ca
Office Hours AFTER THE END OF TERM: Friday December 11: 2-4pm, Saturday December 19, 11am -2pm, and by appointment. TO GET INTO THE BUILDING on Saturday: TRY THE ENTRANCE THAT FACES MATH ANNEX.

• List of topics to review
Course outline: We will cover approximately the first four chapters of the textbook. The three big topics are groups, rings, and specifically rings of polynomials.
We will start with the notion of divisibility of numbers, Euclidean algorithm, Fermat's little theorem; and this will lead us to a more abstract notion of a group. We will discuss such topics as normal subgroups, cosets, quotient groups, and actions of a group on a set. Permutation groups will be an important example.
Further, we will explore what we really need in order to do addition and multiplication (that is, we'll introduce a concept of a ring), and discuss ideals, and the questions of unique factorization.
Finally, we'll study rings of polynomials, and possibly finite fields. All these concepts will of course be defined in the lectures, so stay tuned.
This course will emphasize proofs, so please be ready to start reading and writing proofs from the first week. If you are not comfortable with the concept of a proof, please come talk to me right away, do not wait for the midterm!

There will be weekly homework assignments, due Tuesdays (this changed to Thursdays in the first week of October) at the beginning of class. You should attempt the problems as soon as we cover the relevant material; do not wait until Monday night to do the homework! In fact, doing the readings before class, and trying to the homework right after the lecture is one of the best strategies to succeed in this challenging course.
The first assignment is due Tuesday September 15.

Evaluation:
Course mark will be based on the homework (20%), one midterm and the final exam. The midterm and final scores will be weighted at 5%-75% or 35%-45%, whichever gives you a better mark. The lowest homework score will be dropped. Late homework will not be accepted.
The midterm will be on Tuesday October 20.
Please be sure to make no travel plans for that date. There will be no make-up midterm under any circumstances, and travel of any kind is not a valid excuse for missing a test.
Missed final: If for any reason you have to miss the final exam, it is the university-wide policy that you need to apply for "standing deferred" status through your faculty. Missed finals are not handled by me or the Mathematics Department.

A word on academic integrity: You are allowed to collaborate on homework, but it is definitely not acceptable to copy someone's solution, or to ask for a solution without having tried the problem yourself. If you are inclined to collaborate, it is best to work on the problems alone at first, develop some ideas and questions, and only then discuss them; after that, you are responsible for writing all the solutions in your own words (you should do the final write-up on your own). Whether you collaborate or not, you have to turn in your own assignment, with the solution to every problem written by yourself in your own words, expressing your own understanding of each problem. Identical solutions will be noticed, and treated as cheating, by the university's standards (that is, will have very serious consequences). I hope no-one needs reminders about cheating in exams. If copying or "collaboration" occurs during a test, it will be taken very seriously.

## HOMEWORK

• Problem set 1 (due 15/09): Section 1.12: Problems 3, 6, 8, 11.

• For Tuesday Sept. 22:
• Reading: Sections 1.1-1.6 (this covers the first two lectures), and 2.1.1--2.1.6, example 2.1.13 (Thursday, Sept. 17 lecture). Read the rest of Chapter 1 for fun!
• Problem set 2, due Tuesday September 22. Section 1.12: Problems 14, 19. Section 2.11: Problem 2. Plus, two more problems
• Solutions to problem set 2.

• For Tuesday September 29:
• Reading: Tuesday, 22/09 lecture: Section 2.3.2, Section 2.4 only up to example 2.4.8; Section 1.7; Section 2.8.1.
• Problem set 3: Section 1.12: Problem 29. Section 2.11: Problems 4, 10, 11, 19, 20, 23.
• Solutions to Problem Set 3.

• For Thursday, October 8:
• Reading: All of Sections 2.2, 2.3, 2.4, and 2.8.1; also Sections 2.5-2.6 (covered in Lecutre on Tuesday Oct. 6)
• Problem set 4: Section 2.11: Problems 7, 12, 13, 14, 15, 21.
• Solutions.

• For Thursday, October 15:
• For Tuesday, October 27:
• Midterm was on Tuesday October 20.
• For Thursday, November 5:
• Reading: Sections 2.9.1 - 2.9.2, 2.10.1 (except Examples 2.10.9, 2.10.10 which you can ignore); 2.10.2, 2.10.3; 3.1.
• Problem Set 7 .
• Solutions .

• For Thursday, November 12:
• Reading: Sections 3.1, 3.3 up to 3.3.1 (covers the lectures October 29- November 5); 3.2 -- this covers the lectures on November 10-12.
• Problem Set 8.
• Solutions.

• For Thursday, November 19:
• For Thursday, November 26:
• For Thursday, December 3:
• Some extra credit problems (some are realtively easy, some are very hard). Each part of each problem is worth 1 point in your "extra points" bank, redeemable towards the increase of your overall homework score.