Math 403 A: Introduction to Modern Algebra
Winter 2017
Instructor: Alexandru Chirvasitu

Class times and location: Office: C-417 Padelford
Office hours: Mo 1 - 2:30, Tu 3:30 - 5, We 8 - 9 or by appointment
Email: chirva AT uw.edu

TA: Li Li
Office: Padelford C-430
Office hours: Tu 10:30 - 12
Email: lil37 AT uw.edu

This is a continuation of the abstract algebra sequence beginning with Math 402, which focused on group theory.

In 403 we will be focusing on the general theory of a different type of mathematical structure: that of a ring. While groups were sets equipped with a binary operation meant to capture the abstract properties of composition for symmetries, a ring is a set equipped with two operations, mimicking addition and multiplication for any number of examples you have seen ``in nature'': the set of integers, or rational, or real, or complex numbers, the set of nxn matrices, the set of polynomials with real or complex coefficients, etc. etc.

There are several reasons why this is not a complete change of subject:

Textbook

We are (still) using Dan Saracino's Abstract Algebra (2nd edition). The textbook is absolutely necessary, both for the reading and in order to do the assignments.
Reading

It's essential that you do the reading. I won't have time to go over every relevant example in class, and you'll need a good grasp of the material in order to do the homework. In fact, I encourage you to regard the reading as part of your homework.

The phrase 'Section x', page numbers and result numbering (such as 'Theorem a.b') always refer to our textbook.

Due date Assignment Remarks
1 Fri Jan 06 Section 16 before
Theorem 16.1		 We're not meeting that day.
Please do the reading!
2 Mon Jan 09 Finish Section 16
3 Wed Jan 11 Section 17
Stop on page 167 before
'In dealing with groups [...]'
4 Fri Jan 13 Continue Section 17
Stop on page 170
after Example 13.
5 Fri Jan 20 Finish Section 17
6 Wed Jan 25 Section 18
Stop before Theorem 18.3		 Eeverything up to here
is your midterm material.
7 Mon Jan 30 study for the midterm; treat this
meeting as extended office hours / Q&A for the test
There will be no classes during the entire week of Feb 06.
8 Mon Feb 13 Continue Section 18
Stop before Theorem 18.8
9 Wed Feb 15 Finish Section 18
10 Fri Feb 17 Section 19
Stop before Theorem 19.2
11 Mon Feb 20 Continue Section 19
Stop after Example 3. on page 196		 This is a university-observed
holiday; we're not meeting.
12 Wed Feb 22 Continue Section 19
Stop after Example 4. on page 198
13 Fri Feb 24 Finish Section 19
14 Mon Feb 27 Section 20
Stop before Theorem 20.3
15 Wed Mar 01 Finish Section 20
Use the rest of the quarter to study for the (cumulative) final.
16 Fri Mar 03 No meeting
17 Mon Mar 06
Wed Mar 08		 In-class Q&A session for final
18 Fri Mar 10 Office hours in PDL C-417
instead of regular class


Supplementary material

On occasion, I'll post extra notes, comments, etc. in this space.
Homework

I am denoting the problems by x.y, as the textbook does (to mean problem y from Section x). Whenever you solve a problem, you can cite any preceding problem or theorem in your solution.

Unless specified otherwise, always assume that justification is required for your answers (that is, give a proof for your answer).

You have to turn in the assignment at the beginning of class, before the lecture. No late homework for any reason, but I will drop the lowest score.

Because of time constraints your TA will grade a couple of problems (tops) for correctness and the rest for completeness. I won't be telling you in advance which problems are graded for correctness though..

Due date Assignment Remarks
1 Wed Jan 11 16.1, 16.2, 16.3, 16.7, 16.12, 16.14
2 Wed Jan 18 16.16, 16.20, 16.23, 16.25
17.1, 17.2, 17.3, 17.5
3 Wed Jan 25 17.14, 17.19, 17.21, 17.27, 17.34, 17.35
18.1, 18.2, 18.3		 Your homework problems up to here
are midterm prep.
No hw on Feb 01
because of the midterm
4 Wed Feb 15 18.5, 18.6, 18.14, 18.15
18.16, 18.18, 18.22, 18.25
5 Wed Feb 22 19.1, 19.4, 19.5, 19.6
19.10, 19.11, 19.16 (just parts (a) and (b) )
6 Wed Mar 01 19.2, 19.12, 19.13, 19.14
20.1, 20.2, 20.3, 20.4
7 Wed Mar 08 All remaining problems from Section 20
Midterm

It's happening in class (usual time and place): The test is open book.

Final

The date and time are set by the department and I cannot change it. Early / late exams are not an option, so please plan accordingly. Both the midterm and the final are open book exams. You get to bring your book, class notes, past homework, whatever (just do not collaborate with anyone during the tests).

Grading
As mentioned above, we'll drop the lowest homework score.
Overloading

"Overloading" means allowing more students in class than the limit (which in our case is 40). Because 40 is also our room limit, there will be no overloading.
Disability Resources

If you need special accommodations please go to DRS (Disability Resources for Students) for more information. You should meet with a DRS counselor and get a letter attesting your need for academic accomodations. Once you have such a letter, please see me so that we can arrange for those.
If you have any questions, don't hesitate to email me.

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