# MA3202 Galoisteori – våren 2021

**Eksamen med løsningsforslag våren 2019**

The NTNU-campus, Trondheim, is closed down at least until February 17th, so we have to go back to digital teaching next week. I will try to activate the use of the same link on Zoom as the one which was used before February 1st.

I can be reached by Zoom, by skype, by email or by phone if anybody has some problem or exercises they would like to discuss with me.

Problem session 3 is moved to 16th of February.

Problem session 2 is moved to February 9th.

We are now finished with the Fundamental Theorem of Galois theory.

It seems like we can start regular teaching again. We will meet on Monday 1st of February at 14.15 in room F2.

On Tuesday the 2nd of February the lecture will be given in H1 at 10.15.

NB! First lecture will be Monday January 11th 2021 at 14:15-16:00,Room F2

This lecture will be given online and will contain a historical survey of Galois theory

with its background in solving polynomial equations by radicals.

You can contact me by phone: 48293975 or 73591750 or by email: sverre.smalo@ntnu.no

## Foreleser

Sverre O. Smalø

Rom 850, Sentralbygg II.

Telefon 48293975.

E-post: sverre [dot] smalo [at] ntnu [dot] no

## Forelesninger

Mandag 14.15-16.00, Rom F2

Tuesday 10.15-12.00, Rom H1

Exam: Written and the time is not fixed yet

## Lærebok

P.B. Bhattacharya, S.K. Jain and S.R. Nagpaul

*Basic Abstract Algebra*

Cambridge University Press
Second Edition
ISBN: 0-521-46629-6

## Pensum

Kapitlene 11, 15, 16, 17, 18.

## Important Documents

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

## Øvinger

### Øving 1

Chapter 11.1: 1, 2, 3, 8

Chapter 11.3: 2, 4, 8

*Problem posed by Fermat*:

Prove that the Diophantine equation y^{2}+2=x^{3} has only the integer solutions y=±5, x=3. [Hint: Use that Z[√(-2)] is a Euclidean domain with norm N(a+b√(-2))=a^{2}+2b^{2}

Tuesday 26th Januar kl. 10:15-12:00

### Øving 2

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)

Tuesday 9. February kl. 10:15-12:00

### Øving 3

Continuation Exam August 2013: Problems 3,5

Exam, May 2013: Problems 1,2,3,6,7

Tuesday 16. mars kl. 10:15-12:00

### Øving 4

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

Tuesday 30 mars, kl. 10:15-12:00

### Øving 5

- 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

Tuesday 20. april, kl.10:15-12:00