Course Guidelines Math 232B
Dr. R. Beezer Spring 2005

Text We will be using A First Course in Linear Algebra, version 0.30, as our primary textbook. This text is nearly complete, and will be expanded and modified as the course progresses. I would suggest keeping your copy in a (big) 3-ring binder, especially as new pages become available. You may download copies of the text off the Internet, but I will be taking orders at the beginning of the course for a mass purchase of printed copies. The textbook will be updated weekly on the course WWW page. The text Introduction to Linear Algebra by Lee W. Johnson, R. Dean Riess, Jimmy T. Arnold (Fourth or Fifth Edition) will be used as a backup source of homework exercises. The Bookstore also has a highly recommended text: The Nuts and Bolts of Proofs by Antonella Cupillari. 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 Thompson 321G; the telephone number is 879-3564. Making appointments or simple, non-mathematical questions can be handled via electronic mail -- my address is Office hours will be 1:00-1:50 on Monday, Tuesday, Wednesday and Friday. I will always be available during these times on a first-come, first-served basis. If these times are not convenient, please do not hesitate to make an appointment with me for another time. You are also welcome to drop by my office without an appointment at any time that I am in (roughly 3 P.M. - 4:30 P.M. is a good time to try). 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 highly recommend the Texas Instruments TI-86, which is what I will be using, since this is the model currently used in our calculus courses. These are available at the bookstore, though you must ask for them at the checkout counter. It is not required that you use this exact model, but whatever you use should have the capabilities listed above. If you no longer have a manual for the TI-86, check the course WWW page for a link to an electronic version (you will especially want Chapter 13, and possibly Chapter 12). 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 I will be expanding the collections of exercises in the text during the semester. It is expected that you will work all of these problems. Additional exercises from Johnson/Riess/Arnold are posted on the course WWW page. 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 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 when assigned 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 at on Friday, May 13 at 8 AM. The final exam cannot be given at any other time 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. In other words, plan your travel arrangements accordingly, especially since this exam is at the end of the final exam period. 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 and emphases will change slightly from semester to semester. 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.

Writing This course has been designated as part of the University’s Writing in the Major requirement. Thus, there will be an emphasis on the quality of the mathematical exposition in your written work, and there will be two assignments that will be primarily graded on the basis of the exposition. These assignments 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 I will announce in class. They are due at 9 PM of the day prior to the day we discuss the section in class, and will not be accepted late. Use a subject that is exactly like“Math 232 XXX,” where XXX is the acronym for the section. So for example, your first response will be titled: Math 232 WILA. In the first line of your response, please put your real name, then answer the questions in order. Do your best with mathematical notation, but do not fret if it is a bit sloppy or weird. Please send only 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 -- 60%; Reading Questions -- 5%, Writing -- 15%; Final -- 20%. Attendance and improvement will be considered for borderline grades. Scores will be posted on the World Wide Web at A reminder about withdrawals -- a Withdrawal Passing grade (W) can only be given during the third or fourth 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 The Logger about these often misunderstood grades.

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 Wednesday Friday
Jan 17
Jan 18
Chapter SLE
Section WILA
Jan 19
Section SSSLE
Jan 21
Section RREF
Jan 24
Problem Session
Jan 25
Section TSS
Jan 26
Section HSE
Jan 28
Section NSM
Jan 31
Problem Session
Feb 1
Quiz SLE
Feb 2
Chapter V
Section VO
Feb 4
Section LC
Feb 7
Section SS
Feb 8
Problem Session
Feb 9
Section LI
Feb 11
Section O
Feb 14
Problem Session
Last day to drop
Feb 15
Quiz V
Feb 16
Chapter M
Section MO
Feb 18
Section RM
Feb 21
Section RSM
Feb 22
Writing #1
Feb 23
Problem Session
Feb 25
Section MM
Feb 28
Section MISLE
Mar 1
Section MINSM
Mar 2
Problem Session
Mar 4
Quiz M
Mar 7
Chapter VS
Section VS
Mar 8
Section S
Mar 9
Problem Session
Writing #1 Due
Mar 11
Section B

Monday Tuesday Wednesday Friday
Mar 21
Section D
Mar 22
Section PD
Mar 23
Problem Session
Mar 25
Quiz VS
Mar 28
Chapter D
Section DM
Mar 29
Chapter E
Section EE
Mar 30
Section PEE
Apr 1
Devlin Lecture
MAA Meeting
Apr 4
Section SD
Apr 5
Writing #2
Apr 6
Problem Session
Apr 8
Quiz D & E
Apr 11
Chapter LT
Section LT
Apr 12
Section ILT
Apr 13
Problem Session
Apr 15
Section SLT
Apr 18
Section IVLT
Apr 19
Problem Session
Writing #2 Due
Apr 20
Quiz LT
Apr 22
Chapter R
Section VR
Apr 25
Section MR
Apr 26
Problem Session
Apr 27
Section CB
Apr 29
Problem Session
May 2
Quiz LT
May 3
May 4
Snow Day
Final Examinations
Friday, May 13 at 8 AM