Algebra 3

These lecture notes correspond to the course Algebra 3 from the Bachelor en Sciences et Ingénierie, Filière mathématiques, of the University of Luxembourg. This course was taught in the Winter Term 2013 and it consists of 14 lectures of 90 minutes each. This lecture belongs to the third semester of the Bachelor, and it builds on the lectures Algebra 1 and Algebra 2, belonging to the first and second semester respectively.

The aim of this course is to introduce the students to the theory of algebraic extensions of fields, and culminates with the application of the theory to the solution (negative solution, in fact) of the three classical Greek problems concerning constructions with ruler and compass. This lecture is also a preliminary step towards Galois theory, which is taught in the fourth semester of the Bachelor.