Schedule of Lectures -- This schedule has
the dates of all of the exams, and a rough schedule indicating which
lecture (from the syllabus) will be given on each class day.
Students are urged to read the appropriate section of the book BEFORE
the lecture, so that they will have a general idea of what problems
will be addressed and what approaches will be taken so that they can
make better use of class time.
Solutions to Exam 1
Solutions to Exam 2
Solutions to the Final Exam
Practice Problems on Complex / Hermitian
Stuff
The Remainder
Theorem and the Factor Theorem
-- These are fundamental facts about polynomial algebra, and they are
simply stated and easy to prove; but for some reason they are not
covered in most high school curricula any more. I strongly
encourage students to look at this brief description and ensure an
understanding of these theorems and their proofs.
Java Applets --
This is a site that was created by a former colleague of mine; several
of
the tools there could be useful to you.
Homework
Homework problems are assigned for every lecture, and students should
ideally complete each assignment on the day of the lecture.
Make sure you staple your homeworks! We cannot give credit to
students for work that was lost as a result of not being stapled.
Also, make sure to put at the top of the front page your name, the
lecture number(s) for those problems (indicated on the syllabus), and
the course information (Math 104, Clark Bray)
In order to give flexibility to students, the assignments for the
previous three lectures will be picked up in class every Friday at the
beginning
of class, and will be graded and returned as soon as possible.
No late homework will be accepted.
In calculating homework grades, the lowest of your homework scores will
be dropped. The purpose of this policy is to handle exceptional
circumstances such as a serious illness.
Please do not request to have late
homework accepted. Also, it is inadvisable to skip a homework
unless absolutely necessary, since only one homework will be dropped.
Working together in groups on homeworks is
strongly encouraged!
You will find that the people you are working with either (1)
understand something you don't, in which case they can explain it to
you; (2) understand something that you do understand, but from a
different point of view -- these additional perspectives can prove to
be very useful; or (3), don't understand something that you do
understand -- in which case you have the opportunity to explain it to
them... I think you will find that in the process of explaining
something, very often you will achieve a better understanding yourself.
Of course, it goes without saying that even though you may work in
groups, the homeworks you turn in must be your own work. You may
share ideas, perspectives, approaches to problems, but copying is not
allowed. Furthermore, keep in mind that the homeworks are
primarily a learning tool, and count for a fairly low percentage of
your grade. Do not deprive yourself of this invaluable learning
opportunity!
Grading and
Exams
Final grades for the class will be determined by the total number of
points earned in the class. These points are given based on
performance on the items below, with the following maximum possible
scores:
Homework average: 50 possible points
Tests:
300 possible points
(2 exams x 150 points each)
Final Exam:
200 possible points
------------------------------------------------------------------------------------------------
Total:
550 possible
points
The student should be prepared for the fact that the grading system for
these exams is NOT the same as the one most students became accustomed
to in high school. There are two main properties in particular of the
high school system that will not be used in this class :
1) In most high school grading systems, there are fixed, arbitrary
numbers that determine the cutoffs between different letter grades --
these cutoffs were invariant, and independent of the exam. The problem
with this that it forces the instructor to create exams that are always
the same difficulty; in other words, the instructor must make sure that
all exams will yield the same mean score. Furthermore, it requires that
the distribution of scores also be roughly constant. Achieving both of
these goals is not only difficult, but impossible to perform perfectly.
This system ties the instructor's hands severely, and is totally
unnecessary! Of course it is important that final letter grades for a
class follow a prescribed plan, so that those letter grades have some
meaning outside of the context of that class. Ensuring that is actually
easier if the instructor chooses the cutoff numbers after having seen
the distribution of student scores. The cutoffs can then be chosen
while incorporating important considerations such as the difficulty of
the exam, or any other points about the exam that may be relevant.
2) The class average on exams in most high schools was usually
expected to be somewhere in the mid-eighties. While this is reasonable
considering the nature of high school, it is not always appropriate for
a college setting.
In this class, certainly, there are expectations for the student
that are much more demanding than those of most high schools. We expect
that the student will achieve much more than the mere ability to
reproduce what he or she has seen in class. In particular, we expect
that the student will achieve an understanding of the ideas that are at
the foundation of the methods -- and thereby gain the ability to apply
those ideas to situations that he or she has not already been exposed
to.
Since the expectations of this class are more difficult than those
of high school, it stands to reason that the exams, designed to test
the students mastery of these more lofty goals, must involve more
difficult questions; and therefore, the exams must be more difficult.
Clearly this will result in class averages that are lower than what one
would expect if the exams were more like those of high school. It will
also tend to result in score distributions that are more broad, since
the students responses can be expected to be more varied.
The student should be fully aware of these points before taking an exam
in this class.
It is very dangerous to associate letter grades with performances on
individual exams, because it is very difficult to predict how the
distributions for those exams will interact when the total score
distribution is formed. Therefore, the class will usually be informed
only of the class median and mean for a given exam -- letter grades
will not be assigned. Rough cutoffs may be given to assist the student
in understanding his or her performance, but I emphasize that these
rough cutoffs have no relevance in determining final averages. The best
idea one can get about his or her performance is to compare his or her
score to the mean and the median scores.
Calculators
We will not be using calculators in any aspect of this course.
You may use a calculator on a homework problem if you feel that it will
help you understand the concepts, but you may not make any reference to
the use of a calculator on the homework you turn in.
Calculators will NOT be allowed on any of the exams. I
also generally discourage their use on the homeworks.
Getting help
There are several resources that students should be aware of; make sure
to read the
Sources
of Help for First-Year Students.
You can also come to my office hours, or just
swing by sometime to see if I'm available. If you need to make a
special appointment to see me, send me an email.
I'd also like to emphasize that classmates can be an excellent resource
as well. I refer you above to my comments on this in the homework
section.
Be sure to realize that you are encouraged to use these resources for
more than just help on the homework... Ask questions about
general ideas you are having trouble with specific parts of the
lectures that you did not understand... Of course you should also
seek help with homework if you find yourself stuck on a problem for an
extended period of time.
Honor Code
The Honor Code is taken very seriously on Duke campus, and you are all
reminded to make certain you are familiar with it.
In this course some collaboration is allowed and encouraged, but of
course your work must all be your own. Here are some specific
comments about the graded items in this class:
Homeworks -- You are encouraged to work in groups to exchange ideas and
help each other understand how to approach problems, but the student's
work must be his or her own. Copying and dictating are not
allowed.
Exams -- Students are not allowed to have any outside help
during exams.
Attendance
Attendance at all lectures is required . If you miss a
lecture, it is your responsibility to catch up on the
topics that you missed. You should keep in mind that in this course,
the material builds on itself; if you miss some of the material,
subsequent lectures will seem more difficult to you.
Absences from exams will be excused only for reasons such
as serious illness or appropriate official university activities.
In either case, a written notification from the dean is required.
In the case of illness, this must be done with the
Short-term
Illness Notification form. In the case that an absence from
an exam is excused, the grade will be determined based on your
performance on the final exam for the course, and relative to the
performance of the rest of the class on that exam.