Welcome to Math 340! Here some facts about how the
course will run. Check the course web site for the latest information.
Math
340, Elementary Matrix and Linear Algebra, is a course serving several
functions at the same time. The actual content material is of great use in many
applications, but we will not spend much time on the applications. As we
proceed through the course, we will move from relatively concrete,
calculational, content to much more abstract material. Since essentially all
higher level math courses are much more on the abstract side, a critical function
of this course is to prepare you to survive in that world.
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Grading:
There will be two midterm exams and a final exam. Your grade will depend upon
those exams as well as the grade from your TA-led discussion section. Each
midterm exam will be “worth” 100 points and the final exam 200 points. Your TA
will have a grade 0-100 based on your work in the discussion section. We will
at the end of the semester construct final grades based on your totals from
that possible 500 points. After each exam I will give a “curve” for translating
numbers to letter grades, but that will be just for your guidance as to how you
did compared to the rest of the class. The final grade will not just come from
putting together the exam letter grades.
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Exams:
Midterm exams will take place in the evenings, so you can have more time and
more room than in the regular class: 5:30-7:00 PM on Thursday, February 24, and
Thursday, April 14. We do not yet know the rooms for those exams. Since you
know the exam schedule now you should clear these times well in advance rather
than waiting until the last minute! (I will not be giving midterm exams on
other days. I may be able to work around a few conflicts for time-of-day only.)
Rooms for those exams (and for the final) have not yet been assigned. The final
exam time, 7:45-9:45 AM on Thursday, May 12, is the time given in the UW
timetable, and again the room is yet to be determined. There should be no
conflicts with that time. Requests for alternate final exam times will not be
normally granted and, in keeping with UW policy, will never be granted for
times earlier than the official time.
As you can see on the class schedule,
exam 1 is planned to go through the material we will have covered through
section 3.3 and exam 2 through 5.4. We will have reached those sections a
couple of days before the exam, but I will continue going through a bit of new
material after that point and before the exam! We have to keep moving to get
through all that is required, but at the same time I want you to have a bit of
time to “digest” the information, as well as at least one discussion section
where you can ask questions about it, before facing the exam.
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At
http://www.math.wisc.edu/~wilson/Courses/Math340/340spr11/Schedule.htm
you can find the course schedule. The reading assignments should be read before
we reach that point in class. The schedule includes suggested homework
problems: They are for your own calibration, to see how well you understand the
material, and not to be handed in. Your TA may assign others, and may have you
turn in some of those as part of the discussion grade. As the saying goes,
“Mathematics is not a spectator sport.” You only learn it by doing it. If a day
does not have an assignment shown that does not mean we have no class!
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You
are not required to have a calculator for this course. A scientific calculator
might be helpful, if you are used to using it : Some of the assigned problems
require you to do a significant amount of arithmetic. On quizzes and exams you
will be allowed to use calculators, but the questions will be designed to be
fair to those not using calculators.
Similarly, you are not required to use any mathematical computer software. But
if you are going into a mathematics-using field, as is likely for a student in
340, you may want to learn to use such systems since they have become very much
the standard way to carry out mathematical calculations. Our classroom is not
setup to make the use of such technology convenient. I would be glad to talk
with you individually about Maple, the program I know best, or Matlab, which I
know to some extent. There are student versions of programs such as Maple,
Mathematica and Matlab available at reduced prices, and all three of these are
installed on some of the computer systems around campus in DoIT computer labs.
One thing that you probably know and I surely do: Most of the calculations we
will learn to do in this class can be done by computer software, and many by
fancy calculators. So why do we require you to learn about them? There are many
reasons… One is that many of you would complain even more if we just
required you to learn theorems and proofs! Another is that most of us
understand the theory better when we have something concrete to connect it to.
Certainly when I was in industry I was rapidly promoted in part because I
understood both how to do something and also what made it work, so that I could
see how it applied in new and different situations. But there is an important
point lurking here: If you only learn how to do calculations, you set
yourself up to compete against computers and calculators. That is always a bad
position: They don’t ask for vacation or sick time, and they might even be less
error-prone than you are. If you can’t do anything but what a piece of software
can do, your job prospects are not good.
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As
we progress, an answer to a typical problem will change from a number or
set of numbers to a proof that something is true, or finding a counterexample
to show it is not always true. I emphasize “answer” because that is what you
will be providing on homework or exams! While there will be calculational tools
developed in this class, theory is the most important part. There are other
courses that pay attention to how to use matrices to solve systems of equations
including efficient computation, as well as applications to computer graphics
and other subjects. But Math 340 for most students is the “jumping off point”
for all upper-level mathematics courses. In those courses a typical answer to a
problem is a proof, not a number. This course has to help you leap the gap
between the concreteness of calculus and lower level courses and the abstract.
Note in particular that we will start by working with matrices whose entries
are numbers, and vectors will be made of numbers. But before long vectors will
become whatever fits an abstract definition, and may not be lists of numbers at
all! I have sometimes described this course as resembling the cartoons where
the coyote pursues the roadrunner and runs 50 feet off of a cliff before
noticing that the ground has dropped away: Pay very close attention to this
shift and don’t be using columns of numbers as vectors when that is not
appropriate!
We start by talking about solving systems of equations: That is something you
probably learned to do in high school algebra, so why hit it again? Because we
will extract from it several things that are important in their own right. So
pay attention not just to finding the solutions but to how we find them now.
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The
text for this course is Elementary Linear Algebra by Kolman and Hill, 9th
ed. We will go through most of chapters 1 through 7. On the schedule
I have listed the sections we will cover, and when I expect to cover each: We
certainly will stray from this a little, faster or slower at different points,
since I view the class as made up of human beings rather than machines… But I
expect that by the end of the semester we will be approximately on schedule.
There are a few dates with no reading assignment listed: That means either that
I think the previous material needs extra time or that this is time for us to
get back on schedule. A blank date does NOT mean there is no class! I have
listed on the schedule some problems from the textbook for each section. These
are ones you should regard as a minimal set to test your mastery of what you
study. Your TA may (and may not) ask you to turn in some problems for grading,
possibly including some of these. The text has in the back answers for some of
the odd numbered problems so I have mainly chosen odd numbered ones for you to
test yourself on. Many exam problems will resemble problems from this list.
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I
will post general announcements, sample problems, etc. at the course web site, which is, listed at the
top of this document.. In addition I will send email messages to the class:
Make sure your email address is correctly entered in the UW database. The
university maintains the email list based on your email address on record with
the registrar. (I cannot add to or modify that automatically constructed list!)
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My
schedule, including office hours, is posted at my web site, http://www.math.wisc.edu/~wilson.
My office is 411 Van Vleck Hall, where the telephone is (608) 263-5944. My
email address is wilson@math.wisc.edu.
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I
officially retired a couple of years ago. I still enjoy teaching and enjoy the
material we will be covering in 340. But I have suffered several health
problems (one knee has been replaced twice and the doctor says it needs a third
time, one shoulder has been operated on four times and replaced twice, and my
back had the bottom section beefed up with titanium last summer…) so I may be
in some pain in class. I apologize in advance if I sit down during lecture, I
never used to do that! And I have for now only listed a limited set of office hours at my
website. I will see as we go along whether I can extend those, and I will try
when possible to see you at other times if you email me to make arrangements. (I cannot
promise to come in at just any time. For one thing, UW has not nearly enough
disabled parking places, and there are times when I know I won’t be able to
find a place.)