Galois’ Dream: Group Theory and Differential Equations

Pre-Mathematics.- 0th Week No prerequisites.- 1st Week Sets and Maps.- 2nd Week Equivalence Classes.- 3rd Week The Story of Free Groups.- Heave Ho! (Pull it Tight).- 4th Week Fundamental Groups of Surfaces.- 5th Week Fundamental Groups.- 6th Week Examples of Fundamental Groups.- 7th Week Examples of Fundamental Groups, continued.- Men Who Don’t Realize That Their Wives Have Been Interchanged.- 8th Week Coverings.- 9th Week Covering Surfaces and Fundamental Groups.- 10th Week Covering Surfaces and Fundamental Groups, continued.- 11th Week The Group of Covering Transformations.- Everyone Has a Tail.- 12th Week The Universal Covering Space.- 13th Week The Correspondence Between Coverings of (D; O) and Subgroups of ?1 (D; O).- Seeing Galois Theory.- 14th Week Continuous Functions on Covering Surfaces.- 15th Week Function Theory on Covering Surfaces.- Solvable or Not?.- 16th Week Differential Equations.- 17th Week Elementary Methods of Solving Differential Equations.- 18th Week Regular Singularities.- 19th Week Differential Equations of Fuchsian Type.- References.- Notation.