Governor's School for the Sciences -- Summer 2007

Math 300 -- Introduction to Abstract Mathematics
MTWRF 1:30-4:30 in Ayres 104

Assistants:
Keith Langston klangst2@utk.edu
Hutch Brock mbrock7@utk.edu

Course Goals: By the end of this course you should be able to

1. Read, understand, create and write mathematical proofs
2. Understand and work with some interesting mathematics in such areas as logic, set theory, relations, functions, graph theory, number theory, and analysis
3. Discuss some of the nature, philosophy and history of mathematics
4. Say you worked hard but had fun

• 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.

• 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.

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.