Course Guidelines Math 290B
Dr. R. Beezer Spring 2008

Text We will be using A First Course in Linear Algebra, (Version 1.30) by Robert A. Beezer as our textbook. We will be doing a mass-purchase as a class in the first couple of days. Electronic copies of the textbook can be found at the book’s website ( These may be updated weekly, usually on Wednesday evenings, but Version 1.30 will be the canonical text for the entire semester. The Bookstore also has a highly recommended optional text: The Nuts and Bolts of Proofs by Antonella Cupillari (Third Edition). The course WWW page has some recommendations for similar books about proof techniques.

Home Page Start at to locate the WWW page for this course.

Office Hours My office is in Thompson 390A; the telephone number is 879–3564. Making appointments or simple, non-mathematical questions can be handled via electronic mail — my address is Office Hours are Monday, Tuesday, Thursday and Friday mornings. Normally I arrive on-campus at about 8:00 AM, and every other Tuesday I have a 9:30 AM construction meeting. If I am not in my office, and at-large in Thompson/Harned, I’ll leave a note with my cell-phone number. You are also welcome to drop by my office in the afternoon. Office hours are your opportunity to receive extra help or clarification on material from class, or to discuss any other aspect of the course.

Calculators This course requires the use of a calculator. It should be capable of doing matrix operations — specifically “reduced row echelon form,” “determinants” and “eigenvalues and eigenvectors.” I am most familar with the Texas Instruments series. If you no longer have a manual for your calculator, there is a good chance you can locate one on the Internet. You may also opt to use mathematical software, such as SAGE, Octave, Mathematica or Matlab on a laptop computer during exams. SAGE is open-source software (free), which is on the rise (and maybe a bit rough to install), whereas Octave is also open-source (free), more mature, but limited to numerical work in linear algebra. SAGE may include Octave as a component. Limited-time student copies of Mathematica are available at good prices, and Matlab is also commercial. See the course web page for links. My recommendation is to get involved with SAGE if you are adventurous, or opt for a student version of Mathematica if you are cautious.

Being unfamiliar with your calculator, using an insufficient model, forgetting to install fresh batteries, or forgetting your calculator all together are not excuses for poor performance on examinations. In particular, I have seen students have trouble making the TI-83 perform all the functions required for this course.

Homework There is a fairly 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 the classes where we will have near-weekly “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.
   — Anonymous

I hear, I forget.
I see, I remember.
I do, I understand.
   — Chinese Proverb

An education is not received. It is achieved.
   — Anonymous

Quizzes There will be seven 50-minute timed quizzes — they are all listed on the tentative schedule. The lowest of your seven quiz scores will be dropped. The comprehensive final exam will be given on Friday, May 16 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 quizzes 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 statments have typos. In other words, they are not officially part of this semester’s course. 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.

Writing 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 comments, and if you do not earn a pass, then you can resubmit them the next week. You may resubmit a problem for several consecutive chapters in a row, so long as you make a serious effort each chapter on an old problem. Once you miss submitting a retry, it will be marked as a fail. These will be due the day of the chapter quiz, in class. These problems are your own work (i.e. no collaboration on formulating the proof, or writing it), and will not be accepted late.

Reading Questions Each section of the textbook contains reading questions at the end. Once you have read the section prior to our in-class discussion, submit your responses to the reading questions via electronic mail as follows. Do not send your responses to my regular email address (, but instead use the address Your responses are due at 6 AM of the day we discuss the section in class, and will not be accepted late, i.e. 6 AM is a firm deadline. Use a subject that is only the acronym for the section. So for example, your first response will be simply titled: WILA. Do not include anything else in the subject line. In the first line of your response, please put your real name, then answer the questions in order. If you are not getting replies from me within 24 hours of submission, something is amiss and we will need to figure out where your responses are going. In particular, notice that the email address does not include the word “report.” If a question asks for a computation, you can just give the numerical answer, no need to show your work in the email. If the question requests a yes/no answer, or asks “Why?” then give an explanation. Do your best with mathematical notation, but do not fret if it is a bit sloppy or weird, I can usually decipher any reasonable attempt. Please send only straight text — no attachments, no Word files, no graphics, no HTML if you can help it. Please pay careful attention to these procedures and deadlines.

Grades Grades will be based on the following breakdown: Quizzes — 55%; Reading Questions — 10%; Writing — 15%; Final — 20%. Attendance and improvement will be considered for borderline grades. Scores will be posted on the Internet at A reminder about withdrawals — a Withdrawal Passing 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’ and please read Academic Handbook at about these often misunderstood grades.

Adademic Honesty All of your graded work is expected to be entirely your own work — this includes reading questions and writing assignments. Anything to the contrary is a violation of the University’s Academic Honesty policy, which can be read at

Attendance Daily attendance is required, expected, and overall a pretty good idea.

Purpose 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.

Tentative Daily Schedule

Monday Tuesday Thursday Friday
Jan 21
Jan 22
Section WILA
Jan 24
Section SSLE
Jan 25
Section RREF
Jan 28
Problem Session
Jan 29
Section TSS
Jan 31
Section HSE
Feb 1
Section NM
Feb 4
Problem Session
Feb 5
Quiz SLE
Feb 7
Section VO
Feb 9
Section LC
Feb 11
Section SS
Feb 12
Section LI
Feb 14
Problem Session
Feb 15
Section LDS
Feb 18
Section O
Feb 19
Problem Session
Feb 21
Quiz V
Feb 22
Section MO
Feb 25
Section MM
Feb 26
Section MISLE
Feb 28
Problem Session
Feb 29
Section MINM
Mar 3
Section CRS
Last day to drop
Mar 4
Section FS
Mar 6
Problem Session
Mar 7
Quiz M
Mar 10
Section VS
Mar 11
Section S
Mar 13
Section LISS
Mar 14
Problem Session
Mar 24
Section B
Mar 25
Section D
Mar 27
Section PD
Mar 28
Problem Session
Mar 31
Quiz VS
Apr 1
Section DM
Apr 3
Section PDM
Apr 4
Section EE
Apr 7
Problem Session
Apr 8
Section PEE
Apr 10
Section SD
Apr 11
Problem Session
Apr 14
Quiz D&E
Apr 15
Section LT
Apr 17
Section ILT
Apr 18
Section SLT
Apr 21
Problem Session
Apr 22
Section IVLT
Apr 24
Problem Session
Apr 25
Quiz LT
Apr 28
Section VR
Apr 29
Section MR
May 1
Section R
May 2
Section R
May 5
Problem Session
May 6
Quiz R