MA3202 Galoisteori – våren 2020

Eksamen med løsningsforslag våren 2019

NB! First lecture will be Monday January 06th 2020 at 10:15-12:00,Room R73
This lecture will give a historical survey of Galois theory
with its background in solving polynomial equations by radicals.

Fredag 6. mars vil vi se på oppgavene i øving 3.

Mondag 9th of Mars we did the rest of Exercuise 3 and started on exercise 4.

Friday 13th of Mars we will go through the rest of exercise 4 and start on exercise 5.

NTNU closed on Thursday the 12th. So if you have any questions about the problems in exercise 4 or 5 or any of the other exam problems given, send me an email, and I will try to give some hints, so you can solve the problem, or in the end give you a complete solution.

You can also contact me by phone: 48293975. Good luck! I am still waiting for questions regarding previous exercises and exams.

NB: There will be a take home exam this year, with grading:Pass/No Pass. Det blir hjemmeksamen i år med karakter Bestått/Ikke bestått.

Sverre O. Smalø
Rom 850, Sentralbygg II.
Telefon 48293975.
E-post: sverre [dot] smalo [at] ntnu [dot] no

Mandag 10.15-12.00, Rom R73
Fredag 10.15-12.00, Rom K26
Eksamen: 06.05.2020 kl. 9.00

P.B. Bhattacharya, S.K. Jain and S.R. Nagpaul
Basic Abstract Algebra
Cambridge University Press Second Edition ISBN: 0-521-46629-6

Kapitlene 11, 15, 16, 17, 18.

1. Évariste Galois (1811–1832) – Life History (Wikipedia)
2. Galois' Testamentary Letter of 29 May 1832

Chapter 11.1: 1, 2, 3, 8
Chapter 11.3: 2, 4, 8
Problem posed by Fermat:
Prove that the Diophantine equation y²+2=x³ has only the integer solutions y=±5, x=3. [Hint: Use that Z[√(-2)] is a Euclidean domain with norm N(a+b√(-2))=a²+2b²

Fredag 24 januar kl. 10:15-12:00

Chapter 15.1: 2, 4, 6(b)
Chapter 15.2: 2, 4
Chapter 15.3: 2, 4, 6, 10
Problem 4 (Continuation Exam August 2013)

Fredag 14. februar kl. 10:15-12:00

Continuation Exam August 2013: Problems 3,5
Exam, May 2013: Problems 1,2,3,6,7

Fredag 6. mars kl. 10:15-12:00

Continuation Exam August 2013: Problem 2
Exam May 2013: Problem 5
Exam May 2012: Problem 5
Exam May 2011: Problem 2
Exam May 2010: Problems 1,5
Exam May 2009: Problem 2
Exam June 2006: Problem 3

Fredag 27 mars, kl. 10:15-12:00

• Exam 2013: Problem 4
• Exam 2012: Problems 1,4
• Exam 2011: Problems 1,3,4,5
• Exam 2010: Problems 3,4,6
• Exam 2009: Problem 5
• Exam 2006: Problems 1,5
• Exam 2004: Problem 5

Fredag 17. april, kl.10:15-12:00

2004, 2006, 2009–2013, 2014, 2017