In this one-week intensive seminar for mathematically charged and interested high-school students, we will, using the domain of Geometry, explore what it means to prove something. If you ever wondered how we _know_ that any triangle with three sides of equal length is congruent to any other, or that two parallel lines never cross (I mean, maybe we just haven't found where yet) or if you ever wondered what circle really was, then this course is for you. If you ever felt that sure, your Geometry teacher taught you that there are all these things that are true about triangles, and those other shapes with different rules, but how did you really know that your Geometry teacher wasn't lying to you all along, then this course is for you. If ever Mathematics had a rule, it is "don't believe the hype." Anyone can tell you that the centroid has magical properties, but why should you believe them? Because they are a teacher? Oh please. Build it yourself from the ground up. It's the only way to be sure. Also it's prettier that way.
Goals: Mathematics can be a truly awakening experience. Mathematics in the truest sense, not the way it is generally taught in school. The goal of these courses is open your eyes to this new and exciting world. Mathematics is coming up with conjectures (theories) and then proving them correct. It is an essentially creative process that uses intuition, logic, imagination, and determination. Thus another goal is to build these abstract thinking and logic skills. Practicing these core skills develops them and hopefully this carries over to other aspects of life. Math is the ultimate boot camp for the brain.
Who should apply? If you have been bored in math because it is too easy, then apply. If you love math and just want to do more of it, then apply. If you have the spunk to try and fill out the application, below, and more or less succeed, then apply. This course is for mathematically strong high-school students or just graduated high-school students.
Resources
Checklist for Application Process
Contact me via e-mail (conjecture@vzvz.org) or phone (510-735-7635).