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In 2020-2021, I taught the Graduate Algebra sequence at UC
Irvine, Math 206ABC. (This course has since been re-numbered
and is now known as Math 230ABC.) In Fall 2022 and Winter
2023, I taught Math 230A and Math 230B. One major goal of
this course is to prepare students for success on the Qualifying
Exam in Algebra. On this page I will collect some materials
that I created for Math 206 and Math 230 that may be useful
resources for students taking similar courses and for students
preparing for Algebra Qualifying Exams.
Syllabi
Math
206A Syllabus
Math
206B Syllabus
Math
206C Syllabus
Here
is the syllabus for the UC Irvine Algebra Qualifying Exam.
Here
is the UCI Graduate Examinations page, which contains many
examples of recent Algebra Qualifying Exams.
Textbook
The primary textbook for Math 206 was Abstract
Algebra, Third Edition by Dummit and Foote.
In many places, I supplemented the textbook with material from
notes of Keith Conrad available on this page.
Lecture Videos
I recorded asynchronous lecture videos for Math 206 and
have posted them on my YouTube Channel: nckaplan
math. Most videos are around 10-15 minutes and there
were usually 3-4 videos per lecture. Each video contains a
description with a summary of what was covered in that lecture
along with suggested reading.
The videos are divided into playlists by topic. These are:
Introduction
to Groups (Math 206A)
Group
Actions (Math 206A)
Direct
Products, Semidirect Products, and Classification of Groups of
Given Order (Math 206A)
Introduction
to Rings (Math 206A)
Rings
of Fractions and the Chinese Remainder Theorem (Math 206B)
Euclidean
Domains, PIDs, and UFDs (Math 206B)
Polynomial
Rings (Math 206B)
Introduction
to Modules (Math 206B)
Vector
Spaces (Math 206B)
Tensor
Products (Math 206B)
The
Classification of Modules over a PID (Math 206B)
Canonical
Forms (Math 206C)
Introduction
to Field Theory (Math 206C)
Galois
Theory (Math 206C)
Exams
Each quarter of the algebra sequence had two Midterms and a
Final Exam. Here are these exams together with solutions.
Fall 2020
Math
206A Midterm 1
Math
206A Midterm 1 Solutions
Math
206A Midterm 2
Math
206A Midterm 2 Solutions
Math
206A Final Exam
Math
206A Final Exam Solutions
Fall 2022
Math
230A Midterm 1
Math
230A Midterm 1 Solutions
Math
230A Midterm 2
Math
230A Midterm 2 Solutions
Math
230A Final Exam
Math
230A Final Exam Solutions
Winter 2021
Math
206B Midterm 1
Math
206B Midterm 1 Solutions
Math
206B Midterm 2
Math
206B Midterm 2 Solutions
Math
206B Final Exam
Math
206B Final Exam Solutions
Winter 2023
Math
230B Midterm 1
Math
230B Midterm 1 Solutions
Math
230B Midterm 2
Math
230B Midterm 2 Solutions
Math
230B Final Exam
Math
230B Final Exam Solutions
Spring 2021
Math
206C Midterm 1
Math
206C Midterm 1 Solutions
Math
206C Midterm 2
Math
206C Midterm 2 Solutions
Math
206C Final Exam
Math
206C Final Exam Solutions
Review Materials
I created review materials for Math 206 and Math 230
exams listing important definitions, examples, and theorems:
Math
206A Summary: Groups
Math
206A Summary: Rings
Math
206B Midterm 1 Things to Know
Math
206B Midterm 2 Things to Know
Math
206B Final Exam Things to Know
Math
206C Midterm 1 Things to Know: Canonical Forms
Math
206C Midterm 1 Things to Know: Fields
Math
206C Midterm 2 Things to Know: Fields
Math
206C Midterm 2 Things to Know: Galois Theory
Math
206C Final Exam Things to Know: Galois Theory
I also created documents containing practice problems for the
exams. Some of these problems comes from the textbook, but
most are from UC Irvine Algebra Qualifying and Comprehensive
Exams.
Math
206A Midterm 1 Practice Problems
Math
206A Midterm 2 Practice Problems
Math
206A Qualifying Exam Problems: Groups
Math
206A Final Exam Practice Problems: Rings
Math
206B Midterm 1 Practice Problems
Math
206B Midterm 2 Practice Problems
Math
206B Final Exam Practice Problems
Math
206B Tensor Product Problems
Math
206C Midterm 1 Practice Problems: Canonical Forms
Math
206C Midterm 1 Practice Problems: Fields
Math
206C Midterm 2 Practice Problems: Fields
Math
206C Midterm 2 Practice Problems: Galois Theory
Math
206C Practice Problems Week 9
Math
206C Practice Problems: Cyclotomic Fields
Math
206C Final Exam Practice Problems
Here are some exams from when I taught Math 230A and Math230B, in
2015-2016.
Math
230A Midterm 1
Math
230A Midterm 1 Solutions
Math
230A Midterm 2
Math
230A Final Exam
Math
230B Midterm
Math
230B Final Exam
Homework
Here are the homework assignments for Math 206:
Math
206A Homework 1
Math
206A Homework 2
Math
206A Homework 3
Math
206A Homework 4
Math
206A Homework 5
Math
206A Homework 6
Math
206A Homework 7
Math
206B Homework 1
Math
206B Homework 2
Math
206B Homework 3
Math
206B Homework 4
Math
206B Homework 5
Math
206B Homework 6
Math
206C Homework 1
Math
206C Homework 2
Math
206C Homework 3
Math
206C Homework 4
Math
206C Homework 5
Please feel free to contact me if you have questions about any of
these materials or notice any mistakes that should be corrected.
Do not post any of these materials online (CourseHero, Chegg,
etc.) without my permission.