Instructor:
Patricia Cahn
Email: first dot last at dartmouth dot edu
My office is 243 Kemeny Hall. Tentative office hours: M 3:30-5, T 2-4, Th 1-2, and by appointment.
Class Meetings:
We
meet Monday, Wednesday and Friday from 12:30-1:35 in Kemeny Hall room
105. The x-hours are Tuesdays from 1:00-1:50, and will be used for
optional homework discussion sessions. We will use at least one
x-hour to make up a regular class.
Course Description:
From the ORC: This course will
provide an introduction to fundamental algebraic structures, and may
include significant applications. The majority of the course will
consist of an introduction to the basic algebraic structures of groups
and rings. Additional work will consist either of the development of
further algebraic structures or applications of the previously
developed theory to areas such as coding theory or crystallography. As
a result of the variable syllabus, this course may not serve as an
adequate prerequisite for Mathematics 81. Students who contemplate
taking Mathematics 81 should consider taking Mathematics 71 instead of
this course.
(So, if you plan to take Math 81 you should consider taking Math 71 instead, or come talk to me, or both.)
Course Goals:
1. Gain a solid understanding of basic concepts in group and ring theory.
2. Write proofs that are clear, well-written, and mathematically correct.
3. Practice communicating mathematics with classmates.
Teaching Methods:
In our usual (non-x-hour)
class meetings, I will spend some time introducing a new topic at the board.
The hope is to then spend as much time as possible working on problems
in small groups. This gives me a better idea of what you
understand, and it also allows you to practice doing problems while I'm
around before attempting the homework. Most importantly, I
strongly believe that you will learn the material better by actively
working through problems than by passively listening to a lecture.
During the x-hours, we'll have optional but highly recommended homework
discussion sessions. This will be (mostly unstructured) time for you to work on
the homework with each other, and also to ask me questions. I may
also ask for volunteers to present problems on the board.
Prerequisites:
Math 22: Linear Algebra with Applications or Math 24: Linear Algebra
Text and Resources:
Contemporary Abstract Algebra by Joseph A. Gallian, Seventh Edition. Available at Wheelock Books.
Expectations:
The course is going to move quickly, so it is important to be prepared
for class. This means you've tried your best to do the
homework problems and reading from the previous class. As a
student, I've found it helps to spend a few minutes looking over my
notes before class to get my brain in gear.
If you have questions, ask them! Either in class, office hours or the homework discussion sessions.
You can also email me. I will respond to emails the day I receive
them as long as I receive them by 10:00 pm. Keep in mind that I
can give you more detailed and personalized help in office hours (which
means you should start the homework early
enough so that you can come to office hours).
If some aspect of the class isn't working well for you, please let me know.
If several students have the same concern, I will try my best to fix it.
Homework and Exams:
Your grade will be based on homework (2 kinds), quizzes, and take-home exams.
The regular homework is designed to give you practice with the most
important concepts. It will be due on Wednesdays and graded by a
grader. Even though it will only be collected once a week, you
should at least attempt the problems as they are assigned, after each
lecture. This will prevent you from falling behind.
Certain problems will be starred (e.g. Chapter 6, problem 4*).
These problems will require you to write a proof. There
will be less than or equal to one of
these problems each week, and it will be due the same day as the rest
of your homework. I will grade these problems myself, on a
credit/no credit basis (but with comments so that you know where the
problems are). If you receive a score of no credit, you can
resubmit the problem once a week along with the current week's
homework assignment until you receive
credit (i.e., you have at most one week to rewrite your problem
between each resubmission). The primary point of this is to make
sure
that everyone learns to
write good proofs. The secondary point of this is to encourage
you to solve problems which might require more than one week of
thinking (but not all of these problems will be hard).
There will be 4 quizzes. The point of these is to make sure you
have certain definitions and computational skills at your fingertips,
so that you don't fall behind, and so that you will be better prepared to think about challenging homework
problems. The quizzes are not designed to stump you. If you
understand your class notes and the more basic homework problems you
will do fine.
There will be two take-home exams (one midterm and one final). I will talk more about these in class.
Grading:
Because everyone has bad
days/weeks, I will drop the lowest homework score and one no-credit
starred problem. As a result, no late homework will be accepted
under any circumstances,
including late starred problems (so once you miss a resubmission
deadline, you cannot receive credit). If you start your homework
early, you will always have something to submit.
If you miss a quiz for a good
reason (illness, family emergency, etc.) you will be allowed to make it
up, but it is your responsibility to contact me about this.
Otherwise missed quizzes receive a score of 0.
Homework: 10 points each (times 7 homeworks = 70 points total)
Starred problems: 5 points each (probably times 6 problems = 30 points total)
Quizzes: 10 points each (times 4 quizzes = 40 points total)
Midterm: 100 points
Final: 150 points
If your final score lies on the border between two grades, I will use
participation to decide which grade to assign. Participation
means coming to class, working productively in groups, and coming to
office hours and help sessions when you need them.
Honor Code:
On the homework:
I strongly encourage you to work on the homework problems in groups.
(Keep in mind that you will get the most out of the homework
assignments if you are an active member of the group. So come
with ideas, even if you don't think they will work, and come with
questions.) You must write up your homework assignment
independently--no copying is permitted. In particular, your
homework assignment must represent your own understanding of how to do
the problems, and must be written in your own words.
On the starred problems:
Same as above.
Students who have received credit
are encouraged to help students who have not
received credit understand how to do the problems (but again, no copying).
On the quizzes and exams:
Students may not receive assistance of any kind from any source
(living, published, electronic, etc.), except the professor.
Student Needs:
Students with disabilities enrolled in this course and
who may need disability-related classroom accommodations are encouraged
to make an appointment to see me before the end of the second week of
the term. All discussions will remain confidential, although the
Student Accessibility Services office may be consulted to discuss
appropriate implementation of any accommodation requested.
Whether or not you have a disability, the Academic Skills Center
is an excellent place to visit. Take some time to look at their videos
and other resources. Would you benefit from some of the planning tools?
Do you think you could improve your note-taking skills? Is stress
eating your life? You're the only one who knows what might benefit you,
and it doesn't hurt to look.
I realize that some students may wish to take part in religious
observances that fall during this academic term. Should you have a
religious observance that conflicts with your participation in the
course, please come speak with me before the end of the second week of
the term to discuss appropriate accommodations.