Presenter Information
Topic Ideas
Here are some potential topic ideas from parents and past presenters:

1. Basic combinatorics (non trivial, but interesting problems, like dividing n identical balls into k groups)
   
2. Basics of boolean algebra (based on the example of sets). Is it possible to teach it at this level?
   
3. Zeros of polynomials: quadratic formula, formula for 3 degree (simple cases), examples, Galouis theorem.
   
4. Induction as a principal and may examples of its use (tower of Hanoi problem, etc)

​Presentation
One of the distinguishing features of a Math Cirlce is the variety of presenters. The students participating in a Math Circle will be exposed to not only a variety of mathematical ideas but also to a variety of mathematicians. Here are some key points to keep in mind when preparing a presentation for the Washington University Math Circle.

1. It is very difficult to get the right level of presentation. Many, if not most, math circle presentations I have seen have been too difficult at times. This has been due to a variety of things including the presenter going too quickly or expecting the students to understand too much too quickly. 
   The remedy to this is easy---just remembering that any mathematics you want to present can be presented in an an exploratory way where the students are the ones doing the work.
   
   
2. Every bit of mathematics that you may want to present can be given as a project for the students to work together on and then the students can come to the board and present what they discovered. This is the pattern of the best math circle presentations.


3. Active participation is critical. Please make sure you have activities for all levels (there will be a range of abilities in the group). Activities that they can do together are best and you will need to encourage this group participation. Your goal should be for them to be working on math for at least 90% of the time and you speaking at most 10% of the time.


4. Again, remember that the best preparation for a good math circle is the preparation of a set of activities for the students to work on. Have activities that the students can present to others by coming to the board.
   • Divide the students into groups to work on a problem.
   • Let students do computations together, draw pictures, etc.
   • Give the students plenty of time to work things out.
   • While the students are working, you can walk around the room and engage the students.


5. We are lucky to have undergraduate math circle mentors there to help out. They are very good at floating around helping to engage students during the time that the students are working. These mentors are also good at knowing if you need to adjust your presentation or if things are too easy or too difficult (just ask them). If you have anything special you want them to do, you can let them know.


6. Try to arrive a bit early (5 minutes) and have something for the students to work on as they come in. Talk to the students as they come in.


7. We are lucky to have undergraduate students helping with the circle. These undergraduate math majors are there to help interact with the math circle students when they are working (ask them questions, engaging the students, etc.) You should think about how you want to use these students.


8. Do not do proofs at anything but the most basic level (and even then it will take some real thought to get the level right).


9. The main point is not to demonstrate some fantastic mathematics. The main point is to get the kids engaged in mathematics by giving them problems to work on that they can actually do.


10. If you are willing to type up some notes (or share your handwritten notes), I would love to have them so that we can maintain an archive of such materials.