I was wondering whether the notes online are the complete set? I have noticed that towards the end there are certain chapters which do not have any notes e.g. Lecture 24, 25, 26. Is the content of those topics essential and if yes, then will there be material provided to cover those areas? ——————————————————– Yes. [...]
Dear Prof. Kim, I’ve noticed that the material in the online notes is a bit different from the lecture notes. Would it be reasonable to use the online notes as the main revision material and lecture notes as a supplement (say, for additional examples) while preparing for the exam or should we go thoroughly through [...]
March 23, 2011 – 11:08 am
There will be revisions sessions for Math 3704 and Math M211 as follows: 3704 Wednesday, 20 April, 10:00-12:00 in Math 706 M211 Wednesday, 20 April, 14:00-16:00 in Math 706. Because of the many holidays towards the end of the month, it was hard to find any other days possible. I hope many of you can [...]
February 10, 2011 – 3:45 pm
There was a question about a classic exercise: Let be a cubic irreducible polynomial, which we take to be monic, and let be the roots. Let and . Clearly, , but the exercise is about the degree of . Fact: is 1 or 2. Proof: We have , so that we can divide by in [...]
February 1, 2011 – 10:50 am
I am asking a question about Sheet 2 Problem 9 (solutions are provided for up to 8). Why and are conjugates of ? I’ve managed to find minimal polynomial using DeMoivre’s Theorem and I’ve shown that , satisfy it (). But the question asks to do the opposite: show that they are conjugates and hence [...]
January 23, 2011 – 11:44 pm
There is one thing that you haven’t discussed in detail in the lectures is the computation of the inverse of any given nonzero element alpha in an algebraic number field. In question 2 of Exercise Sheet 2, where the number field is isomorphic to I managed to work out that the inverse of the element [...]
Hi, I have a couple of questions concerning algebraic number theory. Why does contains imply divides ? Firstly assuming contains how do we know there exists a fractional ideal such that and then how do we get that is actually an integral ideal? Another problem I am having is in proving: if is ideal and [...]
February 23, 2010 – 11:57 pm
Dear Prof Kim I can show that . But not 8. Why is that? Can you explain why and give me instruction to prove it please? Thanks very much. ———————————– Reply: It’s important at this point to understand precisely what goes into the tower theorem. For the first case, we have But the important point [...]
