The thursday drop-in group will be an oracle.
As we are way behind the schedule, we will not have time to do the Galois theory in a decent way. So I have decided to take the sections 48-56 out of the curriculum.
The pensum is then: Fraleigh, John B.: A first course in abstract algebra, 2003. Addison-Wesley. ISBN: 0-321-15608-0, 7th edition.
Sections 0-6, 8-11, 13-16, 18-23, 26-27, 29-30, 31 (until 31.18), 36-38.
Next week we will repeat and do exercises. On monday 30. we repeat, and on tuesday 31. I'll be in the auditorium to answer questions, but I will not prepare any thing.
Om tuesday we only did exercises, so next tuesday we will only do theory to catch up. A have given some old exam-problem to the drop-in group. In one of them the term monic polynomial is used. This means that the coefficient of the term of highest degree is equal to one.
On monday we almost finished section 23, what is left is 23.11, 23.12 and the paragraph called "Uniqueness of factorization in F[x]" on page 217. Today we only did exercises. We will finish section 23 on tuesday after easter, and if time permits, start on section 26.
We are now out of face with the teaching plan. It so complicated to update it that I will not do that. I ll use the messages to keep you updated with the progress and the plans.
One thing more: There is of course no lecture on 25. April. That day ispart of the easter-vacation.
To day I did section 18, 19 and 20 until the paragraph called "Applications to ax etc." on page 187. To morrow we continue with that, and in addition I plan to do section 21 and 22 and may be start on 23.
Monday we finished section 37, and that was the last chapter in group theory. We start on section 18 – Rings and Fields – on Monday April 4. We are a little behind schedule, but not lagging seriously.
There are no lectures next week.
Misprint in the announced exercises: Ex 13.4 given for tomorrow should be 13.44
I also decided to take section 34 and 35 out of the curriculum. I am worried about the time, and I find it better to slow a little down and do thing (i.e., the Sylow theorems) properly, than to rush through things. I am sorry for a late decision. I does not affect the later theory seriously - but we will need the concept of solvable groups i.e. definition 35.18, which we'll do at a certain point.
To day I recapitulated section 16 and started on section 36 and finished Cauchy's theorem (36. 3). To morrow we continue with Sylows theorems, and we ll use the whole next week on those and their applications. The week after that, we hopefully will be on schedule again.
On monday and tuesday we finished section 16. I will recapitulate some of it next week (16.16).
I have decided to skip section 17 - so that section is now out of the curriculum.
It is not very central and not important for the rest of the course, and I am a little worried about the time.
So next week I will use some more time on section16, and then continue with section 34.
Mandatory Assignment: The problems for the mandatory assignment are now on the net. Remember the deadline: 17. March at 14.30.
On monday and tuesday I did section 13 and 14. Next week I plan to do section 15, 16 and 17. So in fact we are really on schedule.
Mandatory assignment: You will get the problem set here on the home page of the course on Friday 4. March. I will make both an english and a norwegian version. The deadline for the assignment is Thursday 17. March at 14.30.
On monday I did what was left of the proof of theorem 9.15 and I proved Cayleys theorem ( 8.16), and by hat we are through section 8 and 9. To day we did the whole section 10 and started on section 11. We came to page 108 ( except for theorem 11.5)
Next week we continue with section 11, we will do 11.5 and the rest of the section. Section 12 is not "pensum", so we will go on with section 13 an 14.
To day we showed that S_n is of order n!, we spoke about cyclic permutations and proved theorem 9.8
We have postponed Cayley's theorem.
To day I did the exercises and the "extra" exercise about the subgroups of the symmetry group of the square. I started on sec. 8 and defined the symmetric group.
Next week we continue with sec. 8 and sec.9.
Today - monday January 31 -- I did subgroups of cyclic groups. Corollary 6.7 in the case of infinite groups and theorem 6.14 and 6.16 in the case of finite groups. We also did the greatest common divisor, 6.8. And some examples.
To morro we will do the exercises, and if I get time finish part one. That means 7.1 to 7.6. Cayley graphs are not in the course.
Om Tuesday I finished partitions and equivalence relations. Defined Zn and spoke a little about congruences mod n. We did the group of symmetries of a square as an example. We defined a group and did some of the elementary properties. We have now basically finished section 4 of the book.
Next week Knut Berg will give the lectures. He will do section 5 and 6 and may be some of section 7 depending on the time. There are also exercises on tuesday.
On Thursday next week the drop-in-group starts. It takes place in Rom 534 Niels Henrik Abels hus.
To day I did some set theory - basics, maps, injectivity and surjectivity, invertible maps, partitions and equivalence relations- basically sec. 0 in the book.
To morrow I'll finish with equivalence relations and start on groups - a little from sec. 2, but mostly from sec 4. Roots of unity will be a basic example.
I have written a note about the symmetries of a square. It is ment as motivation for the introduction of groups. I will say a few words about it to day or to morrow. There is one Norwegian version, and one in English.
Welcome to MAT2200 - the lectures start on Monday January 17th.
I will start with recalling some of the set theory we shall need. Then I will give a motivating example of a group and proceed with the definition of groups and some of the their first properties. This covers sections 0-5 in Fraleigh.
I have written a small note about sets which might be useful for you.
Velkommen til MAT2200!