MAT 150A: Modern Algebra

[Course Information]

[Homework]

[Exams]

[Lectures and Materials]

Course information

Class Meetings

CRN	Lecture	Discussion
30765	OLSON 158, MWF 0110-0200 PM	BAINER 1134, R 0610-0700 PM
30766	OLSON 158, MWF 0110-0200 PM	BAINER 1134, R 0510-0600 PM

[MAT 150A Class Calendar]

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, Fridays 3:30--4:30 pm
No instructor office hour on Friday, February 23rd; I will be giving a colloquium talk.
My office hour this week will be Thursday, February 22nd from 3:30--4:30 pm.

Teaching assistant (TA): Ian Sullivan

TA office hours: ACAD SURGE 1029, Mondays and Tuesdays 10--11 am

Homework

HW09 due 3/12/24

Here is the TeX template for you to fill in: [150A-HW09.tex]
Here is a PDF of the homework, provided for your convenience: [150A-HW09.pdf]

HW08 due 3/5/24

Here is the TeX template for you to fill in: [150A-HW08.tex]
Here is a PDF of the homework, provided for your convenience: [150A-HW08.pdf]

HW07 due 2/27/24

Here is the TeX template for you to fill in: [150A-HW07.tex]
Here is a PDF of the homework, provided for your convenience: [150A-HW07.pdf]

HW06 due 2/20/24

There were some typos in Exercise 3 of the HW. The following are updated files. After clicking on the link, press "refresh" to make sure your browser fetches the new files.
Here is the TeX template for you to fill in: [150A-HW06.tex]
Here is a PDF of the homework, provided for your convenience: [150A-HW06.pdf]

HW05 due 2/13/24

Here is the TeX template for you to fill in: [150A-HW05.tex]
Here is a PDF of the homework, provided for your convenience: [150A-HW05.pdf]

HW04 due 2/6/24

Here is the TeX template for you to fill in: [150A-HW04.tex]
Here is a PDF of the homework, provided for your convenience: [150A-HW04.pdf]

HW03 due 1/30/24

Here is the TeX template for you to fill in: [150A-HW03.tex]
Here is a PDF of the homework, provided for your convenience: [150A-HW03.pdf]

HW02 due 1/23/24

Jan 19: Exercise 1 has been updated to include the definition of "even" and "odd" permutations. Also, as a hint, you can describe a permutation matrix P=(P_{ij}) by saying that the only nonzero entries are P_{i, p(i)} = 1.
Here is the TeX template for you to fill in: [150A-HW02.tex]
Here is a PDF of the homework, provided for your convenience: [150A-HW02.pdf]

HW01 due 1/16/24

Here is the TeX template for you to fill in: [150A-HW01.tex]
Here is a PDF of the homework, provided for your convenience: [150A-HW01.pdf]
These serve as an example of roughly the amount of detail you should show in your solutions. In the future, solutions may be abridged.

HW00 (Optional, not graded)

This is not graded, though I encourage you to make sure you can do it. The purpose of this homework is just to get you set up to TeX your future homework solutions, and to make sure you can upload your homeworks to Gradescope.

Here is the TeX file for HW00: [HW00.tex]
Here is a PDF of the homework, provided for your convenience (there is no reason to print this out): [HW00.pdf]

You'll find a version of the following instructions at the top of the HW00 PDF:

Instructions. Create a free Overleaf account, and create a new project (e.g. "MAT150A-hw"). Upload the provided "HW00.tex" file for HW00, and click on it on the sidebar. Then, press the big green "compile" or "recompile" button at the top of the right half of your screen. You should then see the HW01 PDF show up on the right half of your screen.
There are two exercises in this HW. Type your solutions directly into the code, compiling every once in a while to admire your work. When you are done, press the download icon next to the recompile button to download your solutions as a PDF. Submit this PDF to Gradescope.

Reminder. Your homework submission must be typed up in full sentences, with proper mathematical formatting. The following resources may be useful as you learn to use TeX and Overleaf:

Exam Information

Final Exam

The final exam for this course is scheduled for Wednesday, March 20, 2024 at 3:30 pm in our usual classroom.

Here's a study guide for the final exam: [150A/FinalExamInfo.pdf]

Here are the cumulative lecture notes (sans Sylow Theorems): [Algebra Notes]

Exam 2

Exam 2 will focus on material discussed in Lectures 9--18 and HW04--HW07. This corresponds to the latter half of Chapter 2, and parts of the beginning of Chapter 6. Note that our notation for isometries of the plane differs from the textbook. Also, the book doesn't describe the structure of O(2) or Isom(R^2) in terms of semi-direct products. Also be aware that the material in this class is naturally cumulative.

Here are my cumulative notes from Lectures 01-18: [150A-Lect01-Lect18.pdf]

There are some exercises in these notes that we have not covered in class or lecture; you can try these if you are still looking for more practice problems in addition to the practice Exam 2 problems that appear on HW08.

[150A-Midterm02-solns.pdf]

Exam 1

[150A-Midterm01.pdf]
[150A-Midterm01-solns.pdf]