Algebra 2: Field Theory and Galois Theory

Professor Karen E. Smith
362 MaD

Lectures Fall Semester 2016
MW 12:15 pm--2 pm in MaD 381

Demot (Timo Schultz): W 16:15-18pm

This is an undergraduate course (perus kurssi) on field theory, including elementary Galois theory. Details here: Kurssin Tiedote.

Daily Update: A brief summary of what was discussed in Class, updated after each lecture. Lists the definitions needed for Quizzes.

Harjoitukset 1 Syyskuun 14. menessa
Harjoitukset 2 Syyskuun 21. menessa
Harjoitukset 3 Syyskuun 28. menessa
Harjoitukset 4 Lokakuun 5. menessa
Harjoitukset 5 Lokakuun 12. menessa
Harjoitukset 6 Lokakuun 19. menessa
Harjoitukset 7 Lokakuun 26. menessa
No Homework due Nov 2, instead Exam for Algebra 2a (covers through Problem Set 6).
Harjoitukset 8 Marraskuun 9. menessa
Harjoitukset 9 Marraskuun 16. menessa
Harjoitukset 10 Marraskuun 23. menessa
Harjoitukset 11 Marraskuun 30. menessa

Quizzes: Quiz 1, Quiz 2, Quiz 3, Quiz 4, Quiz 5 Quiz 6 Quiz 7 Quiz 8 Quiz 9 Quiz 10 Quiz 11

Exams: The exam for Algebra 2a is on November 2 (also 16.11). The Algebra 2b exam is December 14. (ehka myohemminkin). Material covered on the exam for Algebra 1a will include the lectures through October 24, and problem sets 1-6.


My course is closest to Ian Stewart's Galois Theory Book . I actually prefer the second edition to the third and my lectures will be more similar to the second (slightly more abstract). However, the third edition is fine too; it has more history and may be more concrete (if slightly less elegant).

The same material can be found in Finnish on Lauri Kahanpaa's website: Mahdollisuuksia ja Mahdottomuuksia

A proof that pi is transcendental (also in Kahanpaa's notes, in Finnish).

Any good undergraduate book on abstract algebra might be a good companion. One recommended by students is Hungerfords's Abstract Algebra . A more comprehesive and sophisticated, but still starting from the beginning, is Dummit and Foote's Abstract Algebra. These books contain definitions, basic results and examples of groups, rings, fields, vector spaces and other pre-and-post-requisite material.

Just for fun: The trisectors