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Galois theory course PROMO
Rating: 4.5 out of 5(4 ratings)
492 students

Galois theory course PROMO

Intro to full course
Created byDr Michael Sun
Last updated 4/2023
English
English [Auto],

What you'll learn

  • Mathematical thinking and culture
  • Algebra, Geo, Number theory, combinatorics
  • Proofs and statements of elegant results
  • Idea of some open problems past and present

Course content

1 section • 5 lectures • 1h 31m total length

  • Introduction33:39

    Explore how Galois theory explains which polynomial equations are solvable by radicals, from quadratics to quintics, and how the fundamental theorem of algebra emerges from algebraic reasoning.

  • Introduction 238:26

    This lecture links geometry to algebra through straightedge and compass constructions, showing which regular polygons are constructible, including the Gauss landslide theorem and the 17-gon construction.

  • Introduction 36:08

    Explore Galois theory from number theory and algebraic number theory, linking finite counting, combinatorics, and Galois representations to Fermat's last theorem and the Langlands program.

  • Full course Black Friday PROMO4:47

    Promote this Galois theory course with a 10-day intensive holiday program that introduces fundamentals and main ideas for students without prior background, online during Black Friday.

  • Full course Black Friday PROMO (chinese)8:09

    Explore the full Galois theory course with a Black Friday promo, featuring enrollment details, coupon offers, and guidance on getting started.

Requirements

  • Better than basic logical thinking

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.



Who this course is for:

  • Talented students without the prerequisite formal studies for Galois theory

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