#
MAT 250B: (Graduate) Algebra

###

## Course information

### Class Meetings

CRN 30858

Lectures: Olson 158, MWF 2:10 -- 3:00 pm

Discussion: Hunt 110, T 2:10 -- 3:00 pm

Edits:

(1) On schedule builder, it shows that this course has a 20-day drop. The class calendar has been updated to reflect this.

(2) The midterm exam is scheduled for **Wednesday, February 14**, as shown on the class calendar. (There's a typo on the syllabus.)
**The class calendar is my personal lesson planning calendar. Lesson plans are subject to change.**
Course instructor:
Dr. Melissa Zhang, MSB 2145

Instructor office hours:
MSB 2145, Tuesdays 3:30--4:30 pm

Teaching assistant (TA):
Colby Brown

TA office hours: Wednesdays 11-12, Thursdays 3-4 in MSB 3123

## Homework

Homeworks are posted by Saturday at noon.
### HW10 due 3/15/24

[HW10 PDF]
[HW10 TeX template]
[HW10 Solutions]

### HW09 due 3/8/24

[HW09 PDF]
[HW09 TeX template]
[HW09 Solutions]

Update: For Exercise 6, in irreducibility proof is nonsensical (specifically the parenthetical part).
Here's a way to finish the proof.
We've already shown (in the solutions) that f(x) has no linear factors.
Now suppose by way of contradiction that f(x)=g(x)h(x) where g(x) is irreducible of degree k where 1 < k < p.
Then g(x) is the product of k factors of the form (x-β+i_j) where 1 ≤ j ≤ k.
The coefficient of x^{k-1} of g(x) is then kβ + t where t is some number mod p.
But if kβ+ t is in F, then so is alpha, which is a contradiction.
### HW08 due 3/1/24

[HW08 PDF]
[HW08 TeX template]
[HW08 Solutions]

### HW07 due 2/23/24

[HW07 PDF]
[HW07 TeX template]
[HW07 Solutions]

### HW06 due 2/16/24

[HW06 PDF]
[HW06 TeX template]
[HW06 Solutions]

### HW05 due 2/9/24

[HW05 PDF]
[HW05 TeX template]
[HW05 Solutions]

Notes:
- The 5-lemma problem won't be graded for "correctness", but rather for completion. The purpose is for you to practice "diagram chasing".
Your main goal should be to figure out why the hypotheses were needed to prove the conclusion.
- Hint for 7(d): Your example will probably involve two short exact sequences (i.e. there are 0s on the ends).

### HW04 due 2/2/24

[HW04 PDF]
[HW04 TeX template]
[HW04 Solutions]

### HW03 due 1/26/24

[HW03 PDF]
[HW03 TeX template]
[HW03 Solutions]

Corrections:

For Exercise 4, you are allowed to use the characterization of injective modules in terms of split exact sequences (that we haven't proven is equivalent to the definition yet!). This is not a dependency for that proof. Your solution to Exercise 4 should be short and sweet. :)

On Exercise 7, the indexing set should be the natural numbers. Also, the solution is too involved... So just write down whatever your first thoughts are and submit the solution. Just note that even if F is free, F^* might not be free!

For Exercise 8, my intended solution is about two sentences long, for reference.
### HW02 due 1/19/24

[HW02 PDF]
[HW02 TeX template]
[HW02 Solutions]
### HW01

[HW01 PDF]
[HW01 TeX template]
If you feel so inclined, feel free to add your own macros. Submit the PDF of your completed homework to Gradescope.

If you are unfamiliar with using LaTeX, you can try working on HW00 for my 150A course:
HW00 for the 150A students

## Exam Information

### Final Exam

The final exam will be held from 10:30--12:30 on Wednesday, March 20, 2024 in our usual classroom.
The structure will be similar to that of the midterm, but you'll have 2 hours to complete the exam.

Here is some more information: [Final Information]
Here are the final exam and final exam solutions:

### Midterm Exam

[Midterm]
[Midterm Solutions]

## Materials

Calculation for the random example we came up with (x^5+2x^3+3) is in Lecture 27 notes.
Here is the video lecture: [Lecture 25 (Youtube)]
There was a hole in the proof from class; we will discuss this in more detail in Lecture 14.