The Math Circle
This is the home page of The Math Circle, a program of courses founded in 1994, designed for students who enjoy math and want the added challenge of exciting topics that are normally outside the school curriculum. Its teachers are experienced, committed, and enthusiastic. Our classes encourage a free discussion of ideas; while the courses are mathematically rigorous, the atmosphere is friendly and relaxed.
Math Circle Summer Teacher Training Institute
We held our first Math Circle Summer Teacher Training Institute on the Campus of Notre Dame, in South Bend Indiana, from July 6th to 12th, 2008.
Demonstrations of our approach, practice sessions in running Math Circles, discussions of theory and practice, and conversations about selected math topics were hosted by Bob and Ellen Kaplan, Amanda Serenevy and Sam Lichtenstein.
The program was supported by generous grants from the Flom Foundation, the Herbert O. Wolfe Foundation, and MSRI, and was sponsored by the Northern Indiana Science, Mathematics, and Engineering Consortium.
Tuition was $750 for the week, room and board included.
Inquiries concerning future institutes can be made by e-mail to kaplan@math.harvard.edu.
Our
Philosophy
-
"What you
have been obliged to discover
by yourself leaves a path in your mind
which you can use again when the need
arises." --G. C. Lichtenberg
[learn more...]
Recent Courses
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Sunday
- Elliptic Curves (Notes: 1-2 3 4)
- Set Theory (Notes: 1-2 3 4 5-7)
- The Four Numbers Game (Notes: 1 2 3 4 5)
- Constructing the Real Numbers (Notes: 1 2 3 4)
- Group Theory, Topology, and Physics
- Quantum Mechanics
- Computational Complexity Theory
- Non-Euclidean Geometry
Weekday
- Are There Numbers Between Numbers?
- Probability
- The Pythagorean Theorem
- Continued Fractions
- Random Walks
- Graph Theory
Where are our courses located?
Our classes begin with a free discussion of ideas and play of invention around a developing problem; then - once insight blossoms - we link this insight formally to axioms, aiming for elegance and clarity. While the courses are mathematically rigorous, the atmosphere is friendly and relaxed. We want our students to feel free to express their ideas, to suggest their own approaches, and to make mistakes. We work in a spirit of friendship, cooperation, and enjoyment of one another.
schedule
Problems of the Week
- Is there a last prime?
- Are there more decimals than fractions?
- What proportion of the powers of two begin with a "7"?
- What is ii?
- Is n × (n-1)+ 41 a prime for every whole number n?
- Can you trisect any angle with straightedge and compass?
- What's a geometry like with no parallel lines?
- Can a polyhedron have an odd number of faces with an odd number of sides?
- A soccer ball is made of pentagons and hexagons, with three edges meeting at each vertex. Why MUST the number of pentagons used be twelve?
- Can you tile a square with squares all of different sizes?
- Which numbers are the sum of two squares?
- Which numbers whose digits are all equal are prime?
- more problems...