Course Guidelines

Abstract Algebra I

University of Puget Sound
Math 433
Fall 2014
Dr. Beezer

We will be using Abstract Algebra: Theory and Applications, by Thomas W. Judson as our textbook. We will cover material from the first fifteen chapters (excluding Chapter 12), 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 The “2014 Annual Edition” will be the version I will follow for this course — it is your responsibility to be careful about numbering of chapters and exercises if you use an old edition, since several years ago the chapter numbers were slightly different and the exercise numbers have changed slightly.

The book's website has links to help you with the purchase of a physical copy of the book, should you desire one. I will have news in-class about the availability of the 2014 edition.

There will be a highly experimental, but very usable, web version of the text available online via the book's website. I will say more in class as this evolves rapidly through the semester.

Office Hours

My office is in Thompson 303. Making appointments or simple, non-mathematical questions can be handled via email — my address is Do not confuse this address with the one used for submitting homework (I only look at the homework address when something is due). 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 Monday, Tuesday, Thursday, 2:00–3:50 PM, and Friday 2:00–2:50 PM. 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 at other times 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 posted on the course webpage, as a single PDF for the entire semester. The course page also includes careful directions about submitting your responses. These are due to me by 6:00 AM the morning of the day when we begin discussing a new chapter, as indicated on the schedule and announced in class. Under no circumstances will they be accepted late. These should be submitted to the email address announced in class, not my address.


Abstract algebra has become increasingly important for applications to digital technologies. We will cover efficient digital communication in Chapter 8 (“Algebraic Coding Theory”) and cryptography (a key component of the Internet) in Chapter 7 (“Introduction to Cryptography”). 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. Your default installation is the on-campus server at which will be running the latest version of Sage (6.3) within the Sage Notebook interface. If you want to access it from off-campus, learn to use the university's vDesk software or virtual private network (VPN). You might like using the (experimental) SageMath Cloud at for experimenting, but you will need to submit Sage exercises as Sage worksheets generated by the Sage Notebook. Availability, version incompatibility or convenience of other sites is not an excuse for not being able to use Sage.

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 Sage worksheet attached to an email sent to the same address as for the reading questions. We will discuss this procedure in class. Exact due dates will be announced in class. Under no circumstances will they be accepted late.


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 eleven 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.
I hear, I forget.
I see, I remember.
I do, I understand.
Chinese Proverb
An education is not received. It is achieved.


There will be seven 50-minute timed examinations. Planned dates are all listed on the tentative schedule. The lowest of your examination scores will be dropped. The comprehensive final examination will be given at 8 AM on Monday, 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: 10% each

  • Sage: 15% total

  • Reading Questions: 5% total

  • Final Examination: 20%

Attendance and improvement will be considered for borderline grades. Scores will be posted anonymously on the web at a link off the course page.


Here are three reminders about important university policies contained in the Academic Handbook. These are described thoroughly online at, or a printed copy may be requested from the Registrar's Office (basement of Jones Hall).

“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.” (Registration for Courses of Instruction, Non-Attendance)

Withdrawal grades are often misunderstood. A Withdrawal grade (W) can only be given during the third through sixth weeks of the semester, 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'. (Grade Information and Policy, Withdrawal Grades)

All of your graded work is expected to be entirely your own work, this includes Reading Questions and Sage. 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. (Academic Integrity)


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.

Read the book before the lectures, work the exercises 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.

Many consider group theory (the branch of Abstract Algebra that we will concentrate on this semester) one of the most fascinating areas of mathematics. The investment of your time and energy applied to studying it will be amply repaid by a full understanding of its deeper ideas.


Daily attendance is required, expected, and overall a pretty good idea. Class will begin on-time, so be here, settled-in and ready to go. In other words, walking in the door at the exact time class is to begin is not acceptable. Repeated tardieness and absences will result in grade penalties, in accordance with university policies. Do not leave class during the lecture unless there is a real emergency — fill your water bottles, use the toilet, and so on, in advance. I do not care how much food or drink you bring to class, so long as it does not distract others or make me hungry. Please do not offer me sweets. Please keep phones in your pocket or bag, unless you are using them to read course material. In short, we are here to learn and discuss mathematics and it is your responsibility to not distract your peers who are serious about their education or distract me as I endeavor to make the best use of the class time for everybody.

Student Accessibility and Accommodation

“If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Peggy Perno, Director of the Office of Accessibility and Accommodation, 105 Howarth, 253.879.3395. She will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.”

I request that you give me at least two full working days to respond to any requests from this office.

Student Beravement Policy

“Upon approval from the Dean of Students Office, students who experience a death in the family, including parent, grandparent, sibling, or persons living in the same household, are allowed three consecutive weekdays of excused absences, as negotiated with the Dean of Students. For more information, please see the Academic Handbook.”

Classroom Emergency Response Guidance

Please review university emergency preparedness and response procedures posted at 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.

Tentative Daily Schedule
Monday Tuesday Thursday Friday
Sep 1
Labor Day
Sep 2
Chapter 1
Sep 4
Chapter 1
Sep 5
Chapter 2
Sep 8
Chapter 2
Sep 9
Chapter 2
Sep 11
Problem Session
Sep 12
Exam 1
Chapters 1, 2
Sep 15
Chapter 3
Sep 16
Chapter 3
Sep 18
Chapters 3, 4
Sep 19
Problem Session
Sep 22
Chapter 4
Sep 23
Chapter 4
Sep 25
Problem Session
Sep 26
Exam 2
Chapters 3, 4
Sep 29
Chapter 5
Sep 30
Chapter 5
Oct 2
Chapters 5, 6
Oct 3
Problem Session
Oct 6
Chapter 6
Oct 7
Chapter 6
Oct 9
Problem Session
Oct 10
Exam 3
Chapters 5, 6
Oct 13
Last Day to Drop
Oct 14
Chapter 7
Oct 16
Chapters 7, 9
Oct 17
Chapter 9
Oct 20
Fall Break
Oct 21
Fall Break
Oct 23
Problem Session
Oct 24
Exam 4
Chapters 7, 9
Oct 27
Chapter 10
Oct 28
Chapter 10
Oct 30
Chapters 10, 11
Oct 31
Problem Session
Nov 3
Chapter 11
Nov 4
Chapter 11
Nov 6
Problem Session
Nov 7
Exam 5
Chapters 10, 11
Nov 10
Chapter 13
Nov 11
Chapter 13
Nov 13
Chapters 13, 14
Nov 14
Problem Session
Nov 17
Chapter 14
Nov 18
Chapter 14
Nov 20
Problem Session
Nov 21
Exam 6
Chapters 13, 14
Nov 24
Chapter 8
Nov 25
Chapter 8
Nov 27
Nov 28
Dec 1
Chapters 8, 15
Dec 2
Chapter 15
Dec 4
Chapter 15
Dec 5
Chapter 15
Dec 8
Problem Session
Dec 9
Exam 7
Chapters 8, 15
Dec 10
Reading Period
Dec 11
Reading Period
Final Examination: Monday, December 15, 8 AM
Suggested Exercises

Chapter Computational Theoretical

1 18, 25 8, 9, 22c, 28, 29
2 15 5, 10, 16, 18, 27
3 1, 3, 5, 6, 10, 17, 32 29, 30, 31, 38, 43, 44, 45, 46, 53, 55
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, 17, 19, 20, 23, 23
7 7, 8, 10
9 3, 5, 10, 12, 14, 16, 17 20, 21, 22, 24, 25, 29, 34, 35, 38, 48
10 1bcd, 2, 3, 4 5, 6, 7, 9, 11, 12, 13, 14, 15
11 2, 3, 4, 5, 6; Additional: 7, 8 8, 15, 16, 17, 20; 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