Department of Mathematics - SUNY Geneseo

#### Course Description

A study of the basic properties of groups, rings, and integral domains, including the fundamental theorem of group homomorphisms. The concepts basic to the development of algebraic systems are studied initially.

#### Instructor

Cesar Aguilar, South Hall 325A

#### Office Hours

MF 1:30 - 2:30, W 9:30 - 10:30

#### Class Meetings

MWF 2:30-3:20 PM, Welles 123

#### Software

1. Intro to LaTeX Video
2. LaTeX Online: Overleaf or LaTeX Base
3. LaTeX Tutorial
4. LaTeX Homework Template
5. You can also install LaTeX on your machine:
1. For Mac: MacTeX, MiKTeX
2. For Windows: MiKTeX

#### Final Exam

Wednesday, May 17, 3:30-6:00 PM

#### Textbook and Resources

Abstract Algebra: Theory and Applications, by Thomas W. Judson. This is a FREE textbook. Use the current annual edition. Hardcopy available on Amazon.

### This Week

Week 10: Mar 27 - Mar 31 | Today: Mar 27
Isomorphisms, Direct Products
Topics: Isomorphisms, Direct Products
HW DUE HW 6DUE: Mar 27
NEXT WEEK Test 2 on Apr 7, 2:30 PM – 3:20 PM

### Last Week

Week 9: Mar 20 - Mar 24
Cosets, Lagrange's Thm, Fermat's & Euler's Thm
Topics: Cosets, Lagrange's Thm, Fermat's & Euler's Thm
What to Read: 6.1, 6.2, 6.3
HOMEWORK HW 6DUE: Mar 27

### Homework

Title Due Date Week No.
Homework 1 - Preliminaries Feb 5, 2023 2
Homework 2 - The Integers Feb 15, 2023 3
Homework 3 - Groups Feb 23, 2023 4
Homework 4 - Subgroups Feb 28, 2023 5
Homework 5 - Cyclic Groups Mar 10, 2023 6
Homework 6 - Permutation Groups Mar 27, 2023 9

### Schedule

Week 1:  Jan 23 - Jan 27
Sets & Equivalence Relations
Topics: Sets & Equivalence Relations
First Day: Welcome video
Jan 24 First day of classes
Week 2:  Jan 30 - Feb 03
Induction, Division Algorithm, $$\mathbb{Z}$$ mod $$n$$
Topics: Induction, Division Algorithm, $$\mathbb{Z}$$ mod $$n$$
What to Read: 2.1, 2.2, 3.1
HOMEWORK HW 1DUE: Feb 05
Week 3:  Feb 06 - Feb 10
Groups, Subgroups
Topics: Groups, Subgroups
HW DUE HW 1DUE: Feb 05
HOMEWORK HW 2DUE: Feb 15
Week 4:  Feb 13 - Feb 17
Subgroups
Topics: Subgroups
HW DUE HW 2DUE: Feb 15
HOMEWORK HW 3DUE: Feb 23
Week 5:  Feb 20 - Feb 24
Cyclic subgroups, $$\mathbb{C}^*$$
Topics: Cyclic subgroups, $$\mathbb{C}^*$$
HW DUE HW 3DUE: Feb 23
HOMEWORK HW 4DUE: Feb 28
NEXT WEEK Test 1 on Mar 1, 2:30 PM – 3:20 PM
Week 6:  Feb 27 - Mar 03
Review, Test 1
Topics: Review, Test 1
Feb 28 Diversity Summit - No Classes
HW DUE HW 4DUE: Feb 28
HOMEWORK HW 5DUE: Mar 10
TEST 1 Mar 1, 2:30 PM – 3:20 PM
Week 7:  Mar 06 - Mar 10
Permutations, Dihedral groups
Topics: Permutations, Dihedral groups
HW DUE HW 5DUE: Mar 10
Week 8:  Mar 13 - Mar 17
Rest, recover, & enjoy the turning of the season
Topics: Rest, recover, & enjoy the turning of the season
Mar 13-17 Spring Break - No Classes
Week 9:  Mar 20 - Mar 24
Cosets, Lagrange's Thm, Fermat's & Euler's Thm
Topics: Cosets, Lagrange's Thm, Fermat's & Euler's Thm
What to Read: 6.1, 6.2, 6.3
HOMEWORK HW 6DUE: Mar 27
Week 10:  Mar 27 - Mar 31 | Today: Mar 27
Isomorphisms, Direct Products
Topics: Isomorphisms, Direct Products
HW DUE HW 6DUE: Mar 27
NEXT WEEK Test 2 on Apr 7, 2:30 PM – 3:20 PM
Week 11:  Apr 03 - Apr 07
Review, Test 2
Topics: Review, Test 2
TEST 2 Apr 7, 2:30 PM – 3:20 PM
Week 12:  Apr 10 - Apr 14
Normal Subgroups, Simplicity of $$A_n$$
Topics: Normal Subgroups, Simplicity of $$A_n$$
Week 13:  Apr 17 - Apr 21
Homomorphisms, Isomorphism Thms
Topics: Homomorphisms, Isomorphism Thms
Week 14:  Apr 24 - Apr 28
Fundamental Theorem of Finite Abelian Groups
Topics: Fundamental Theorem of Finite Abelian Groups
Apr 26 GREAT Day - No Classes
Week 15:  May 01 - May 05
Rings, Integral Domains
Topics: Rings, Integral Domains
Week 16:  May 08 - May 12
Integral Domains, Fields
Topics: Integral Domains, Fields
May 10 Last day of classes

### Syllabus

#### Learning Outcomes

Upon successful completion of MATH 330 - Abstract Algebra, a student will be able to:

Below is the tentative course grading scheme. The grading scheme may change during the semester at the discretion of the instructor. Any changes to the grading scheme will be announced in class before the final exam. If homework assignments are done in groups, then a student must achieve a passing grade in all individual assessments (e.g., tests and final exam) to pass the course.

ItemPercentage
Homework30
Tests40
Final30
A94-100
A−90-93
B+87-89
B83-86
B−80-82
C+77-79
C73-76
C−70-72
D60-69
E< 60

#### Tests and Exam

There will be 3-4 tests scheduled evenly throughout the semester. The final exam is scheduled for Wednesday, May 17, 3:30-6:00 PM. The final exam will be cumulative, that is, any topic covered in the course could be tested in the final exam. There will be no make-up for a missed test or final exam under any circumstances. If a student misses a test and can present evidence of an extenuating circumstance then the weight of the missed test will be redistributed to the final exam weight. Having the cold or flu is not an extenuating circumstance. Examples of extenuating circumstances include a medical emergency, a serious prolonged illness, or the death of a member of your immediate family.

#### Homework

There will be approximately one homework assignment per week. Students will be given approximately one week to complete a homework assignment. All homework assignments must be written in LaTeX (not Word). Instructions will be given on the first day of class on how to obtain and use the LaTeX program. The quickest way to get started with LaTeX is to use the online application called Overleaf and by reading the Learn LaTeX in 30 Minutes tutorial. If homework assignments are done in groups, then a student must achieve a passing grade in all individual assessments (e.g., tests and final exam) to pass the course. I encourage you to collaborate with your colleagues on your assignments/labs but your final submitted work should be your own (see Academic Dishonesty statement below).

#### Technology

Calculators are not permitted during the tests or final exam. However, I encourage you to use your calculator, Maple and other math software, WolframAlpha, and other forms of technology as you study and do your assignments. Both Maple and Mathematica can be downloaded from SUNY Geneseo Software page.

#### Office Hours and Math Learning Center

I encourage you to come to my office (South Hall 325A) whenever you are having trouble with any part of the course material, seeking academic advice, or you just want to chat about mathematics in general. If you want to meet with me outside of my office hours, you will need to make an appointment, preferably via email. I also encourage you to visit the Math Learning Center located in South Hall 332 where you can receive free tutoring on a walk-in basis by highly qualified upper level students. Access to in-person office hours and to the MLC will depend on social distancing guidelines set by the College.

#### Email Communication

I will do my best to reply to student email regarding the logistics of the course within 24 hours during the working week (Mon-Fri). However, due to the potential large volume of emails, inquiries regarding homework problems and/or specific course content should be made during office hours or after class.

Please read, and follow, Geneseo's Academic Dishonesty and Plagiarism policy. Below is the definition of plagiarism and its consequences as described in SUNY Geneseo's Academic Dishonesty and Plagiarism statement:

Plagiarism is the representation of someone else's words or ideas as one's own, or the arrangement of someone else's material(s) as one's own. Such misrepresentation may be sufficient grounds for a student's receiving a grade of E for the paper or presentation involved or may result in an E being assigned as the final grade for the course.

If there is sufficient evidence of academic dishonesty on a homework assignment, all students involved will receive a zero score on the homework assignment and I will provide the department chairperson, the dean of academic planning and advising, and the student(s) with a written report of the violation, the penalty imposed and the counseling provided to the students involved. A second instance of academic dishonesty on a homework assignment will result in a final grade of E for the course for all students involved. Academic dishonesty on a test/final exam will result in a final grade of E for the course.