Course Guidelines

Linear Algebra

University of Puget Sound

Math 290B

Spring 2019

Dr. Beezer


We will be using A First Course in Linear Algebra, by Robert A. Beezer as our textbook. We will follow Version 3.50 throughout the semester as the official version for the course. This version may be found as a PDF on the book's site at, where it is made freely available with an open license. If you prefer, you can use the hardcover version, which is Version 3.00, and has only minor differences. See the book's site for information on ordering a physical copy.

The latest online version of the textbook is at This has the subtitle “(Beta Version)” presently, and is not the older green-themed version. You may find this version the most useful, and it will also perform well on a mobile device.

The course web page has some recommendations for open textbooks about proof techniques, which will augment the shorter discussions in the textbook.

Course Web Page

Off of 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 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 10:00–10:50 on Monday and Friday, 8:00–8:20, 10:20–10:50 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.


Linear algebra is at the heart of many large computations in computer science, physics, chemistry, economics, statistics, and other disciplines. So it is useful to become familiar with relevant software. Futhermore, freed from doing error-prone numerical computations you can concentrate on new ideas and concepts.

For both reasons, we will make extensive use of Sage. Since Sage is open source software, it is available freely in many places. We will be relying this semester on hosted versions at CoCalc, You already have a course project associated to your UPS email address and by the “last day to drop” you will need to pay $14 for the entire semester so you can move your course project to a members-only server.

There are thorough discussions about Sage integrated into the web version of your textbook. We will discuss in class the use of Sage during examinations. In particular, if you do not own a laptop, investigate procedures now for borrowing one from the library.


There is a nearly complete collection of exercises in the text. Any (or all) of the problems will be good practice as you learn this material. Many of these problems have complete solutions in the text to further aid your understanding. Of course, you are not limited to working just these problems.

None of these problems will be collected, but instead they will form the basis for our eleven “Problem Sessions” and for discussions in Office Hours. It is your responsibility to be certain that you are learning from these exercises. The best ways to do this are to work the problems diligently as we work through the sections (see attached schedule) and to participate in the classroom discussions. If you are unsure about a problem, then a visit to my office is in order. Making a consistent effort outside of the classroom is the easiest 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 exams—they are all listed on the tentative schedule. The lowest of your seven exam scores will be dropped. The comprehensive final exam will be given on Wednesday, May 15 at Noon. The final exam cannot be given at any other time and also be aware that I may allow you to work longer on the final exam than just the two-hour scheduled block of time. In other words, plan your travel arrangements accordingly.

As a study aid, I have posted copies of old exams on the course web site. These are offered with no guarantees, since techniques, approaches, emphases, and even notation will change slightly or radically from semester to semester. Some of the solutions contain mistakes, and some of the problem statements have typos. In other words, they are not officially part of this semester's course and I do not maintain them. In particular, I do not advocate working old exams as a primary, or exclusive, technique for learning the material in this course. Use at your own risk: they have not been reviewed for minor mistakes or inconsistencies with this semester's course. I will not entertain questions about the correctness of these materials via email.

Come to examinations prepared to remain in the room for the entire length of the exam. Leave all networked devices at home (this includes phones), or place them into a purse or book bag, POWERED OFF (not simply on silent or hibernating). As an alternative, you may check your device(s) with me if you wish. Violations will be treated as cases of Academic Dishonesty. In this course, an exception to this policy will be the use of laptops for Sage computations during examinations, which will be discussed further in class.


This course has been designated as part of the University's Writing in the Major requirement. Thus, there will be two proofs assigned for each chapter. You will be expected to formulate a proof, and write it up clearly. These will be graded on a pass/fail basis. Each chapter's questions will be returned to you with careful comments, and if you do not earn a pass, then you can resubmit them at the close of the next chapter. You may resubmit a problem for several consecutive chapters in a row, so long as you make a serious effort on each outstanding problem at each opportunity. Once you miss an opportunity to resubmit, or a retry does not contain any new work, or significant comments and hints are ignored, then it will be scored as a fail. Failure to follow the directions for submitting these can result in a retry with no feedback from me. Please read the instructions and details provided with these problems very carefully.

These will be due the day of the problem session prior to the chapter exam, and submitted prior to the start of class. Under no circumstances, including an inability to print, will they be accepted late. During the first part of the course, we will learn the mathematical typesetting software, , and you will be required to use this tool appropriately when writing your proofs, and you may be required to do a retry soley on the basis of incomplete use of . I might request your source as part of grading your exercises, so make sure you retain these.

These problems ARE YOUR OWN WORK. In other words, no collaboration on formulating the proof, no collaboration on writing the proof, no copying content from the book's source, and no discussion whatsoever with classmates or others familiar with the subject. In particular, I do not provide consultation in advance of submission, but rather will provide careful comments on your written submitted work. Late submissions will not be accepted and forfeit your opportunity to submit retries.

Reading Questions

Each section of the textbook contains three reading questions at the end. Once you have read the section prior to our in-class discussion, it will be time to consider these questions. Responses will be due by 6 AM of the day we discuss the section in class, and will not be accepted late. If a question asks for a computation, then provide a complete answer, perhaps with some relevant intermediate computations. If the question requests a yes/no answer, or asks “Why?” then give a thorough explanation using correct English grammar, syntax, and punctuation along with appropriate use of . Cutting and pasting from the textbook without a citation is always plagiarism. And even providing a verbatim quote along with a citation will always get you zero credit.


Grades will be based on the following breakdown:

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

Academic Policy Reminders

Here are three reminders about important academic policies which are described thoroughly in the Academic Handbook. You can find a link to a PDF version at, 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.”

Grade Information and Policy, Withdrawal Grades

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’.

Academic Integrity

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.


This course is much different from most any mathematics course you have had recently, in particular it is much different than calculus courses. We will begin with a simple idea—a linear function—and build up an impressive, beautiful, abstract theory. We will begin computationally, but soon shift to concentrating on theorems and their proofs. By the end of the course you will be at ease reading and understanding complicated proofs. You will also be very good at writing routine proofs and will have begun the process of learning how to create complicated proofs yourself.

You will see this material applied in subsequent courses in mathematics, computer science, chemistry, physics, economics and other disciplines (though we will not have much time for applications this semester). You will gain a “mathematical maturity” that will be helpful as you pursue upper-division coursework and in any logical, rational, or argumentative activity you might engage in throughout your lifetime. It is not easy material, but your attention and hard work will be amply repaid with an in-depth knowledge of some very interesting and fundamental ideas, in addition to beginning to learn to think like a mathematician.


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 considered being on-time. Repeated tardieness and absences will result in grade penalties, in accordance with university policies. Do not leave class during the lecture unless remaining would be a greater distraction—fill your water bottles, use the toilet, and so on, IN ADVANCE. Come to class prepared to be attentive for 50 minutes. 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 right before lunch. 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. 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.

University Notices

These are two notices the university administration requests we relay to you.

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.

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
Jan 21
Jan 22
Section WILA
Jan 24
Section SSLE
Jan 25
Section RREF
Jan 28
Section TSS
Jan 29
Section HSE
Jan 31
Section NM
Feb 1
Problem Session
Feb 4
Exam SLE
Last Day to Drop
without Record
Feb 5
Section VO
Feb 7
Section LC
Feb 8
Section SS
Feb 11
Problem Session
Feb 12
Section LI
Feb 14
Section LDS
Feb 15
Section O
Feb 18
Problem Session
Feb 19
Exam V
Feb 21
Section MO
Feb 22
Section MM
Feb 25
Section MISLE
Feb 26
Section MINM
Feb 28
Problem Session
Mar 1
Section CRS
Mar 4
Section FS
Mar 5
Problem Session
Mar 7
Exam M
Mar 8
Section VS
Mar 11
Section S
Mar 12
Section LISS
WED (3/13)
Mar 14
Section B
Mar 15
Section D
Tentative Daily Schedule
Monday Tuesday Thursday Friday
Mar 25
Section PD
Mar 26
Problem Session
Mar 28
Exam VS
Mar 29
Apr 1
Section E1
Apr 2
Section E2
Apr 4
Section E3
Apr 5
Section E4
Last Day to
Drop with ‘W’
Apr 8
Problem Session
Apr 9
Exam E
Apr 11
Section LT
Apr 12
Apr 15
Section ILT
Apr 16
Section SLT
Apr 18
Problem Session
YVR (?)
Apr 19
Section IVLT
Apr 22
Problem Session
Apr 23
Exam LT
Apr 25
Section VR
Apr 26
Section MR
Apr 29
Problem Session
Apr 30
Section CB
May 2
Section D1
May 3
Problem Session
May 6
Exam R
May 7
May 9
Reading Period
May 10
Reading Period
Final Examination: Wednesday, May 15, Noon