Course Guidelines Math
290A
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 masspurchase as a class in the ﬁrst couple of days. Electronic copies of the textbook can be found at the book’s website (linear.ups.edu). 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 http://buzzard.ups.edu/courses.html 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, nonmathematical questions can be handled via electronic mail — my address is beezer@ups.edu. Oﬃce Hours are Monday, Tuesday, Thursday and Friday mornings. Normally I arrive oncampus 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 atlarge in Thompson/Harned, I’ll leave a note with my cellphone 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 opensource software (free), which is on the rise (and maybe a bit rough to install), whereas Octave is also opensource (free), more mature, but limited to numerical work in linear algebra. SAGE may include Octave as a component. Limitedtime 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 TI83 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 nearweekly “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 50minute 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 Wednesday, May 14 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 twohour 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 inclass discussion, submit your responses to the reading questions via electronic mail as follows. Do not send your responses to my regular email address (beezer@ups.edu), but instead use the address lineara@beezer.privacyport.com. 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 http://buzzard.ups.edu/courses.html. 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 http://www.ups.edu/x4727.xml#withdrawal 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 http://www.ups.edu/x4718.xml.
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 upperdivision 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 indepth knowledge of some very interesting and fundamental ideas, in addition to beginning to learn to think like a mathematician.
Monday  Tuesday  Thursday  Friday  
Jan 21
MLK Day  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  