Intro to full course
What you will learn
Mathematical thinking and culture
Algebra, Geo, Number theory, combinatorics
Proofs and statements of elegant results
Idea of some open problems past and present
Description
The aim of this course is to promote the main course which is not contained here. The main course is a course on the beautiful topic of Galois theory and how it brings together many of the classical topics that one might be familiar with :Algebra Number Theory Geometry Combinatorics.
The main course is on Learnworlds but here we talk about the overview and summary of the course. The main Galois theory course is usually a course reserved for undergraduates in their 3rd year of university or graduate students but this is only because the formal pre requisites are slow to build and rather impractical.
The reality is that this wonderful course can be taught to even high school students. The fundamental topics involved are high school topics, polynomials and ruler compass constructions for example, they need not be formalised so much as to be inaccessible to young students.
That is what we attempt in the main course. They are the record of a 10 day intensive but intuitive program to teach talented young students the beauty of Galois theory. Galois himself was only a teenager when he made his main contributions and it is that youthful curious spirit of exploration that I want to cultivate in the main course.
Content