Governor's School for the Sciences -- Summer 2007
Math 300 -- Introduction to Abstract Mathematics
MTWRF 1:30-4:30 in Ayres 104
Professor: Dr. Chuck Collins
Contact Info:
Office: Ayres 312B, 974-4269
Email:
Assistants:
Keith Langston klangst2@utk.edu
Hutch Brock mbrock7@utk.edu
Course Goals: By the end of this
course you should be able to
- Read, understand, create and
write mathematical proofs
- Understand and work with some interesting mathematics
in such areas as logic, set theory, relations,
functions, graph theory, number theory, and analysis
- Discuss some of the nature, philosophy and history of
mathematics
- Say you worked hard but had fun
Course Resources:
- Textbook: How to Prove it: A Structured Approach, 2nd ed.,
by Daniel J. Velleman, Cambridge Univ. Press, 2006.
- Handouts: Each day you'll get a copy of the Math Mole,
a newsletter with some (hopefully) interesting content. Other material
will be distributed as needed.
- Web Resources: I try to keep an up-to-date webpage
containing
a class schedule, copies of handouts and other resources
associated with the class.
Class Work:
- Exercises: (40\%) Assigned daily.
These problems will be done in class or
as homework, due in class or by the next class period.
Some will be written up to turn in, some you'll do
on the board and some you'll evaluate as a group. A big part of
the learning in this class will come from self and peer
assessment of your work. There will be clear guidelines
given as to what is expected. There will be opportunities
for extra credit exercises and also chances to resubmit
corrected work.
- Portfolio: (20\%) Select proofs (at least 20)
will be put in a notebook as a
collection of your work. They will be reviewed at various
times during the term,
and given a final evaluation at the end.
- Quizzes: (30\%) We'll have 2 1-hour exams,
plus we'll have short
quizzes almost every day.
- Class Participation: (10\%) Just about every class will have some
activity to participate in, plus you should always be part of whatever
discussion or work is going on. Also, there will be some assignments
like providing material for the Math Mole newsletter
and rewards for participating or winning class contests.
Grades: The grading scale is 90% for an A,
85% for a B+, 80% for a B, etc. Earning at least the minimum
percentage will guarantee you the given grade. I may choose to lower the
cutoffs, but don't depend on it.
This is summer and an elective course, and I don't want the
grades to be a punishment
for you (or for me), so I will give you plenty of chances to maximize
your grade through selective re-dos and extra credit. It will be up
to you to take advantage of these opportunities.
Class Policies and Expectations
- Classroom Behavior: Besides the rules of GSS and
the common rules of good behavior, I expect you to come to class
prepared to do your best work, to encourage others to do their best
work, and to fully participate in the class.
- Out-of-Class Expectations: You should schedule regular
times daily to work on this material. You should keep up with the daily
work, and take time to
review and really learn the material. You should seek help if you need
it and give help if asked.
- In Case of Trouble: This course should be challenging
and that means at some time(s) you will be confused. If you are confused
in class, ask me, Keith or Hutch to clarify. If you are still confused after
asking, ask again. If you are confused outside of class, you can read
the book, especially if there are worked examples or written out
explanations, you can look over your class notes and exercises, and
you can talk to other students. Make sure you write down the clarification.
Do not let things go as in the end you are responsible for learning
as much of the material as possible.
- Group Work/Cheating:
I expect the final version of any work that you submit with only
your name on it to be your own work.
I also encourage you to talk with other students in the class.
You may ask other students questions about topics from
class, and you can discuss the problems in general. However, once
you start writing out a solution you must do it without any help
(i.e. no copying). If I suspect any offense, you'll get a warning
the first time. If it continues, both parties will get 0s on the
suspected work. More serious offenses will be dealt with on a case
by case basis in consultation with Dr. Kovac.
- Late Work/Makeups: Late work will not be
accepted (it can count as a re-do if the assignment allows).
This is to encourage you to schedule your time well and keep up
with the material. If you are sick or otherwise displaced, makeup
work can be arranged.