Answers to the Final Exam
The final is on March 14 at 8:30 a.m.
Important dates:
There will be quizzes on some Fridays. These
will not count towards the final grade; they are for you to
judge your own progress. The midterm is on Friday, February 2
and the final is 8:30-10:20 a.m. on Wednesday, March ??.
(check this
date!).
You must use a blue book for exams.
Office Hours:
Monday 2:40-4:30 in Padelford C-418,
and by appointment.
Midterm answers
Winter 2007
Final
Winter 2007
Three fact sheets on group theory written by Prof. Ralph
Greenberg:
Homomorphisms ,
Basic Theorems ,
Cosets .
The textbook is Abstract Algebra, by I.N. Herstein, Third
edition, published by John Wiley.
My plan is to cover Chapters 4 and 5.
There are many books in the library that provide an introduction to
ring theory. I advise you to consult those books. They have a lot
to offer---different perspectives, different examples, different
emphases.
I wrote some
notes for a 403 class a taught a few years ago. They might be
of some use.
Homework:
Each week I will give you a list of a dozen or so Homework
problems. Of those, four or five or six will be
graded; each question is worth 5 points. You also get 10 points just
for doing all the problems.
Homework is due at the start of class each Wednesday.
Except in extraordinary circumstances, late homework will
not be accepted. If you miss the homework deadline, that homework
will be one of those which does not contribute to your best six.
The grader for the course is Dustin Moody. His office is PDL
C-430 and his office hours are 2:00--3:00 pm Wednesday.
His email is dbm25-at-(curse-the-bots)-math.washington.edu.
How to succeed.
You want a good grade and I want to give you a good grade.
I will do that if you demonstrate a reasonable degree of mastery
of the material in this course.
Conversely, lack of mastery will result in a poor grade.
The tests I give will make it apparent how much mastery you have of
the material in this course.
I post some old tests and practice problems on this website so
you will know the sorts
of questions that will be asked. I want you to know what I want you
to know.
Learning math requires more than reading books, or re-reading
the notes you take in class; that is necessary of course, but not
sufficient. You learn math by solving problems, doing exercises,
both those I assign, and others that you find in other books.
You will not master the material in this
course if you do only the homework problems that I assign. This
is a truth, a fact. Solving problems is the only way to
learn mathematics. So, do hundreds during the ten weeks of this
course. Yes, hundreds. I know your time is precious and
that there are many demands on it. But that does not change
the fact that to master 3 hours of lecture material
you probably need to do at least twenty problems; not
twenty variations on the same problem, but twenty different
problems.
You also need to be absolutely honest with yourself,
uncovering your own weaknesses and seeking help when you need to.
There is no shame in struggling or making mistaakes. I failed my first
course on abstract algebra because I was afraid to say "I don't understand"
and ask for help---I took a
group theory course my first year at university and was 3 or 4
years younger than everyone else in the class, all of whom had
already spent at least one year at university, and I just assumed
they all knew much more than me and that they would think I was
very
thick if I asked a question!
Now I know better---I was probably as smart as anyone in the class,
just more afraid than others to admit I was lost. I hope
you are better than me at asking for help. I am happy to give it.
It might be helpful for you to study with others. Check each others
solutions to problems, talk about the theorems and results.
I can not over emphasize the need for you to uncover your
own weaknesses and misunderstandings. Our powers of self-delusion
are enormous and those self-delusions run in one direction: we
believe we are smarter and more capable than we are.
Those who fail this course do so primarily
because they think they know more than they do, not because they
are intellectually deficient. Mistakes are part and parcel of
learning mathematics. The more mistakes you make during
the quarter, the fewer you will make on tests, provided you
either discover them yourself or allow me to find them for you,
and having uncovered them you must then address them.
(I will get great satisfaction from helping you uncover your
misunderstandings and pointing you in the right direction.)
Think of this as a test of character that may serve you well in
other parts of your life.
Message Board
403 Practice Questions
This contains some questions that I consider fair game for quizzes,
midterms, and the final. If you can answer all these you are
getting to grips with the material.
402 Practice Questions
If your group theory is rusty you might find it useful to look at
these group theory questions. There is quite a carry over from
Group Theory to Ring Theory so if your group theory is weak you
will find it harder to succeed in this course.
Ring Theory:
The topic for the course is Ring Theory. For almost all of you
this will be your second course in abstract algebra. I will assume
you have done some group theory. We will be using some of that
material in this course. At a minimum you need to
understand cosets, quotients,
homomorphisms, and the isomorphism theorems.
Old Homework, 2006.
Grades.
Your grade will be based on the homework, the midterm, and the
final. Your best six homework scores will contribute 25%, the midterm
will contribute 25%, and the final will contribute 50%.