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You can give your evaluation of this course by answering this "nettskjema".

The grades have been published.

The grades are decided by following central guidelines that apply for mathematics courses. Each grade also reflects the individual exam solution.

Problem 1:

1a: 1-2 points reduction for each of incomplete or incorrect: associativity, closure of operation, existence of inverse in G, non-abelianity of G, order of G.

1b: 1-2 points reduction for each of incomplete or incorrect: elements of order 3, existence of normal subgroup.

Problem 2:

2a: maximum number of points requires correct and complete proof that G is a union of its elements of order d.

2b: maximum number of points requires correct and complete proof based on estimating the number of elements of order d using the given hypothesis and applying part 2a to get the asserted equality for all divisors, then specialising to n.

Problem 3:

3a: maximum number of points requires explanation ...

A suggested solution to the exam problem is available here.

See "Notes" under Schedule.

The entry "Oppgaver" has been updated (thanks to the study administration for help). Note that under "Fasit" you can find suggested solutions.

A digital lecturer's round will be organised during exam. The meeting will be in Zoom and will start at 16:00 (1 hour after exam start). Link to the meeting will be available from Canvas. The meeting will be set up with a waiting room mode, and I will answer questions from one candidate at a time. Should there be a problem and you cannot access the Zoom-link, you can call me on my office phone number 228 55489. 

Det blir oppklaringsrunde (tr?sterunde) under eksamen. M?tet vil v?re i Zoom og starter kl 16:00 (1 time etter eksamensstart).  Lenke til m?tet vil v?re tilgjengelig fra Canvas. M?tet blir satt opp med venteromsfunksjon, slik at jeg svarer p? sp?rsm?l fra ¨¦n og ¨¦n kandidat av gangen.Hvis du f?r problemer med ? komme p? Zoom-m?tet kan du ringe meg p? mitt kontor, tlf. nr. 228 55489.

The lecture on Zoom will be without a break and we will finish at the latest at 11:45. This change facilitates attendance in the online event "Women in Mathematics" at the department.

In general, the following guidelines apply in courses at the Department of Mathematics: 
- The examination lasts 4 hours. In addition, you will have an extra 30 minutes to scan and upload your PDF. 
- All examination aids are allowed (e.g. books, online resources, scientific programming tools, etc.). 
- It...

Can be found here.

Exam sets from earlier years can be found by following the link under "Oppgaver" in the menu on the left on this webpage.

Here is a suggested solution.

As indicated in the time schedule for this course, we will go over some part of the Galois theory for arbitrary fields. I will upload some (handwritten) notes next week. The material will follow the presentation in Fraleigh's book, however it will not be necessary to get that book. The notes will collect all the relevant results from Fraleigh in order for us to compute some important, basic examples. The goal is to understand how certain splitting fields of polynomials over a given field are related to, and determined by, certain known groups such as finite cyclic groups or dihedral groups.

There is a small issue with the videos from week 11 that I must fix. In the meantime, I posted pdf-files of the lecture notes.

In the current situation of increased infection where the message is to "do our part" I will pause the physical presence in the auditorium. Hopefully this will only be for a short time. So the lectures on Monday 15 and Wednesday 17 March will be on Zoom at the scheduled time.  A recording will be available afterwards. The plenary session on Tuesday 16 March will also be on Zoom. Notes will be available afterwards.

It suffices to set up the bijection by explaining what it does to elements in G/K. For example, the coset of 1  in the factor group G/K is 1+K={1,10,19,28}. The coset of 1 in the factor group G/H is 1+H={1,19}. The bijection in the third isomorphism theorem pairs the coset (1+H)+K/H  in the factor group (G/H)/(K/H) to the coset 1+K in G/K. Concretely, K/H has the two cosets H and K\setminusH={9,27}, so (1+H)+K/H ={{1,19},{10,28}}={1+H, 10+H}. Thus the bijection pairs {{1,19},{10,28}} with {1,10,19,28}. Similarly for 0+K,2+K,..., 8+K in G/K. 

The lecture will be recorded live from Aud  5 and can be followed on Zoom. A small number of students (at most 20) can be in the auditorium.

I have set up a Zoom-link in Canvas with the intention to have a hybrid lecture today, if possible. There is no guarantee that it will work, as several technical solutions need to be syncronised. We'll try.

Based on the email responses so far we plan physical teaching next week. Those of you who have flexible schedule please come on Wednesday. Those who expressed preference for Monday may come then. The exercise class on Tuesday will also be with physical attendance. In case more than 20 students meet at any of these three sessions, it is first come principle that counts.

The lectures on Monday and Wednesday will be recorded in real time, and the videos will be available at the end of the lecture. For the exercise session, we will try to have a Zoom session integrated in the class, and at least pdf version of notes will be posted.

There are more than 20 students registered for this course. Before we can consider starting physical presence in the auditorium we need to regulate attendance. If you are willing to attend lectures in the auditorium, can you send me an e-mail indicating this, and also indicating your priority for day, Monday or Wednesday.

We continue with digital teaching next week, in the same format, that is video recordings for the lectures on Monday 1 March and Wednesday 3 March, and  Zoom-meeting on Tuesday 2 March. During the week we will clarify the practical aspects that need to be in place before we can have teaching on campus at Blindern, hopefully from March 8.

We need a student representative for this course. Interested? Send me an email.

There will be one mandatory assignment in this course. The assignment will be posted on February 25 and must be submitted at the latest 11 March. More information will come soon.

The department organises an online session where you can get help to questions you might have about the courses you take at the bachelor level. The link can be found here.

There are inevitably some mistakes in the videos. Sometimes I say the correct statement but write something wrong, other times it is the other way around. I try to list the mistakes when I find them. If you find something in the videos that appears to be a mistake, please send me an email about it.