## Abstract Algebra I

#### Dr. Beezer

##### Texts

We will be using Abstract Algebra: Theory and Applications, by Thomas W. Judson as our textbook. We will cover material from Chapters 1–15, as described on the attached calendar. This is an open source textbook, which in part means you are free to make unlimited copies. The book's website is abstract.pugetsound.edu. The “2021 Annual Edition” will be the version I will follow for this course. Older editions can have substantial changes in how theorems and examples are numbered, and it will be difficult to follow along with an older copy. Plus, there is not much money to be saved over a new copy.

We will be using an “enhanced” online version this semester hosted at Runestone, more about that in class.

The book's website has links to help you with the purchase of a physical copy of the book, should you desire one. You may also download a PDF that is nearly identical to the hard copy, or another PDF which contains the extra material about Sage. Additionally, the online version has all the same content and the Sage examples are executable and editable, via the Sage Cell server, so is a far superior way to use the book.

As you begin working with Sage, you could find Gregory Bard's Sage for Undergraduates very useful. It is freely and legally available for download as a full-color PDF. (See links in electronic versions of this syllabus, or on the course page).

##### Course Web Page

Off of buzzard.ups.edu/courses.html you can find the link to the course web page.

##### Office Hours

My office is in Thompson 303. Making appointments or simple, non-mathematical questions can be handled via email — my address is beezer@ups.edu. I rarely do not receive your email, and I read all of my email all of the time, usually very shortly after receiving it. Urgency of replying varies by the hour, day, and nature of the message. Office Hours are 9:00–10:50 on Monday and Friday, 9:30–10:50 on Tuesday and Thursday. Office Hours are first-come, first-served, so I do not make appointments for these times, nor do you need to ask me if I will be present at these times. You may assume I will be there, unless I have announced otherwise in class or by email. You may make an appointment for other times, or just drop by my office to see if I am in. Office Hours are your opportunity to receive extra help or clarification on material from class, or to discuss any other aspect of the course.

##### Class Preparation

Reading questions will help you prepare for the lectures on each chapter. They are available in our enhanced online version of the textbook.

1. These are due to be completed by 6:00 AM the morning of the day when we begin discussing a new chapter, as indicated on the schedule and/or announced in class.

2. Under no circumstances will they be accepted late.

3. You can expect a reply that morning, or within 30 hours at the latest. After that time, an email inquiry is appropriate.

##### Computation

Abstract algebra has become increasingly important for its application to digital technologies. For example, we will cover cryptography (a key component of the Internet) in Chapter 7 (Introduction to Cryptography). Your textbook contains an interesting exposition on efficient digital communication in Chapter 8 (Algebraic Coding Theory). Conversely, digital technologies are an ideal assistant for studying the subject. So computation will be a feature of the course.

For this reason, we will make extensive use of Sage. Since Sage is open source software, it is available freely in many places. You will need to purchase an account at CoCalc where we will have access to a powerful servers via your web browser and we can efficiently manage homework assignments. (Details on accounts will be provided in class, cost is \$14 for the semester.) The assumption is that you have a paid membership on CoCalc for doing these assignments, so availability, version incompatibility, or convenience of other sites is not an excuse for not being able to complete the Sage assignments on-time.

For each chapter there will be assigned exercises to work in Sage. These will be due roughly on the discussion day following the lectures for each chapter, as a CoCalc worksheet or Jupyter notebook. We will discuss the exact procedure in class. Exact due dates will be announced in class. Under no circumstances will these assignments be accepted late.

##### Practice

Exercises from the text will be suggested for each chapter. Of course, you are not limited to working just these assigned problems and you can find many more in textbooks in the library (ask me for suggestions). We have twelve class days reserved for discussions when we can talk about these problems. It is your responsibility to be certain that you are learning from the homework exercises. The best ways to do this are to work the problems diligently, start studying them early, and participate in the classroom discussion. If at this point you are still unsure about a problem, then a visit to my office is in order, since you are obviously not prepared for the examination questions. Making a consistent effort outside of the classroom is the easiest way (only way?) to do well in this course.

Mathematics not only demands straight thinking, it grants the student the satisfaction of knowing when he [or she] is thinking straight.

―D. Jackson

Mathematics is not a spectator sport.

―Anonymous

I hear, I forget. I see, I remember. I do, I understand.

―Chinese Proverb

An education is not received. It is achieved.

―Anonymous
##### Examinations

There will be six 50-minute timed examinations. Planned dates are all listed on the tentative schedule. The comprehensive final examination will be given at 8 AM on Wednesday, December 15. The final exam cannot be given at any other time, so be certain that you do not make any travel plans that conflict, and also be aware that I will allow you to work longer on the final exam than just the two-hour scheduled block of time.

Grades will be based on the following breakdown:

• Examinations: 50%

• Sage: 25%

• Final Examination: 20%

The lowest of your six examination scores will be dropped. Attendance and improvement will be considered for borderline grades, while excessive attendance and late-arrival problems will result in grade penalties. Scores will be posted anonymously on the web at a link off the course page.

Here are three reminders about important academic policies which are described thoroughly in the “Academic Policies” section of the University Bulletin. The online version is off of

www.pugetsound.edu/academics/academic-resources/university-bulletins/

or a printed copy may be requested from the Registrar's Office (basement of Jones Hall).

• Registration for Courses of Instruction, Non-Attendance.

“Regular class attendance is expected of all students. Absence from class for any reason does not excuse the student from completing all course assignments and requirements.”

Withdrawal grades are often misunderstood. A Withdrawal grade (W) can only be given prior to the university deadline listed on our course schedule, and after that time (barring unusual circumstances), the appropriate grade is a Withdrawal Failing (WF), even if your work has been of passing quality. See the attached schedule for the last day to drop with an automatic ‘W’.

All of your graded work is expected to be entirely your own work, this includes Reading Questions and Writing Exercises. Anything to the contrary is a violation of the university's comprehensive policy on Academic Integrity (cheating and plagiarism). Discovered incidents will be handled strictly, in accordance with this policy. Penalties can include failing the course and range up to being expelled from the university.

##### Purpose

At this point in your college career, you should be well on your way to being an independent scholar, who appreciates the beauty of mathematics and understands the effort needed to master new and difficult ideas. Consistent with that, I will be giving you a fair degree of freedom to learn this material in a manner that suits you. Of course, with freedom comes responsibility.

Read the book before the lectures, work the exercises early and diligently, tidy up your class notes each evening, and ask questions. Arriving late to class, or having conversations with others during class, not only disrupts your peers, but tells me you are not serious about your education.

“Modern” algebra is the basis of one of the two main branches of mathematics (analysis being the other). So every mathematician should have a basic understanding of its principal concepts. The investment of your time and energy applied mastering its basic concepts will be amply repaid by a full understanding of its deeper ideas.

##### University Notices

These are multiple notices the university administration requests we duplicate for you.

• Classroom Emergency Response Guidance.

Please review university emergency preparedness, response procedures and a training video posted at www.pugetsound.edu/emergency/. There is a link on the university home page. Familiarize yourself with hall exit doors and the designated gathering area for your class and laboratory buildings.

If building evacuation becomes necessary (e.g. earthquake), meet your instructor at the designated gathering area so she/he can account for your presence. Then wait for further instructions. Do not return to the building or classroom until advised by a university emergency response representative.

If confronted by an act of violence, be prepared to make quick decisions to protect your safety. Flee the area by running away from the source of danger if you can safely do so. If this is not possible, shelter in place by securing classroom or lab doors and windows, closing blinds, and turning off room lights. Lie on the floor out of sight and away from windows and doors. Place cell phones or pagers on vibrate so that you can receive messages quietly. Wait for further instructions.

• Student Religious Accommodation.

The university provides reasonable religious accommodations for academic courses and programs, and the university policy is found at this location 1 . If you need a reasonable accommodation due to a religious holiday or organized religious activity, you must give me written notice within the first two weeks of class so that we can coordinate the accommodation. If you have questions about the policy, you may contact the University Chaplain. If you have a grievance about the application of the policy or the handling of your request for an accommodation, you may contact the Dean of the Faculty.

www.pugetsound.edu/about/offices-services/human-resources/policies/campus-policies/ student-religious-accommodations-in-academic-courses-or-programs
##### Learning Outcomes

The University Curriculum Committee and accrediting agencies expect to see a list of learning outcomes.

• Understand the techniques used for the classification of the groups of order less than 16.

• Understand the structure of a finite abelian group.

• Better understand the general concept of an algebraic structure.

Please review these at the end of the semester when they will be easier to understand.

Tentative Daily Schedule
Monday Tuesday Thursday Friday
Aug 30
Syllabus
Runestone
CoCalc
Aug 31
Chapter 1
Sep 2
Chapter 1
Sep 3
Chapter 1/2
Sep 6
Labor Day
Holiday
Sep 7
Problem Session
Sep 9
Chapter 2
Sep 10
Chapter 2
Sep 13
Problem Session
Drop w/o Record
Sep 14
Exam 1
Chapters 1, 2
Sep 16
Chapter 3
Sep 17
Chapter 3
Sep 20
Chapter 3/4
Sep 21
Problem Session
Sep 23
Chapter 4
Sep 24
Chapter 4
Sep 27
Problem Session
Sep 28
Exam 2
Chapters 3, 4
Sep 30
Chapter 5
Oct 1
Chapter 5
Oct 4
Chapter 5/6
Oct 5
Problem Session
Oct 7
Chapter 6
Oct 8
Chapter 6
Oct 11
Problem Session
Oct 12
Exam 3
Chapters 5, 6
Oct 14
Chapter 7
Oct 15
Chapter 7
Mid-Term
Tentative Daily Schedule
Monday Tuesday Thursday Friday
Oct 18
Fall Break
Oct 19
Fall Break
Oct 21
Chapter 9
Oct 22
Chapter 9
Oct 35
Chapter 9/10
Oct 26
Problem Session
Oct 28
Chapter 10
Oct 29
Chapter 10
Nov 1
Problem Session
Nov 2
Exam 4
Chapters 7, 9, 10
Nov 4
Chapter 11
Nov 5
Chapter 11
Last Day for
Automatic W
Nov 8
Chapter 11
Nov 9
Problem Session
Nov 11
Chapter 13
Nov 12
Chapter 13
Nov 16
Chapter 13
Nov 17
Problem Session
Nov 19
Exam 5
Chapters 11, 13
Nov 20
Chapter 14
Nov 22
Chapter 14
Nov 23
Chapter 14
Nov 25
Thanksgiving
Nov 26
Thanksgiving
Nov 29
Problem Session
Nov 30
Chapter 15
Dec 2
Chapter 15
Dec 3
Chapter 15
Dec 6
Problem Session
Dec 7
Exam 6
Chapters 14, 15
Dec 9
 Suggested Exercises Chapter Computational Theoretical 1 18, 25 8, 9, 22c, 28, 29 2 15 5, 10, 15, 16, 18, 27, 28 3 1, 3, 5, 6, 10, 17, 32 29, 30, 31, 38, 43, 44, 45, 46, 53, 54* 4 3, 4, 5, 6, 7, 8, 9, 11, 20, 21, 22b 24, 26, 27, 28, 30, 34, 37 5 2, 3, 5, 7, 9, 10, 15 4, 18, 20, 23, 25, 27, 30*, 33, 35 6 1, 2, 5 3, 6, 11, 12, 15*, 17, 19, 20, 21, 23 7 7, 8, 9 9 3, 5, 10, 12, 14, 16, 17 21, 22, 25, 29, 34, 35, 38, 48, 55* 10 1bcd, 2, 3, 4 5, 6, 7, 9, 11, 12, 13, 14 11 2, 3, 4, 5, 6; Additional: 7, 8 8, 14, 15, 16, 19; Additional: 2, 3, 9, 10 13 1, 2, 3, 4bc 6, 9, 11, 12, 13 14 2, 3, 4, 6, 9, 11, 13, 17 ($$S_3$$ only) 20, 22, 24 15 1, 2, 3, 5, 6, 9, 15, 16, 17, 24 4, 7, 8, 10, 12, 14, 21