Monthly Archives: January 2008

Set Theory

Hey Prof Kim.

I was wondering if you know any good books in Set Theory? Well,I have been looking for one but i can’t really tell if they are any

Thank You
A. Locatelli


It is somewhat important to be aware that you’ll find at least two different kinds of books on set theory that can confuse beginners with their superficially similar appearances. The kind that involves set theory at the research level, you might be interested in at some point, but I suspect it’s not quite what you’re looking for at the moment. Many such books can be studied in principle with no prerequisites, but actually assume a good deal of mathematical sophistication on the part of the reader. On the other hand, the kind that’s more important for the beginning undergraduate is a solid book that just teaches you the language of mathematics rigorously, while giving you at least a flavor of the deeper issues. For this, the book I myself studied from as a student was

Introduction to Set Theory by K. Hrbacek and T. Jech

It’s available in the UCL library. I remember feeling quite satisfied with their presentation.

As with other books in mathematics, it’s rather important to do all the exercises. If you have specific questions as you work through them, don’t hesitate to let me know.



Southwest Center for Arithmetic Geometry

It’s something of a constant concern of mine to put students of every level in touch with mathematical culture. So I thought I’d call your attention to the Southwest Center for Arithmetic Geometry where I did most of my public service work from 1998 to 2005. If you browse through, you’ll find ten years’ worth of surveys, projects, videos, etc. covering virtually all aspects of arithmetic geometry. They host an annual

Arizona Winter School on Arithmetic Geometry

for post-graduate students. Students doing an MSc or above at UCL could benefit from attending sometime. It’s a really great educational event and a chance to interact with first-rate mathematicians as well as students from all over the world.


2201 coursework and past exams

Hi Professor Kim,

I hope you had an enjoyable Christmas and New Year.

I have recently been attempting to look at some past papers for the Further Linear Algebra course though it would be really useful to have the solutions. Do you know if they will be made available in the department office soon?

Also, we were told during the last problem class that the last few homeworks would be marked ready this term. Do you know where these can be collected from?

Many thanks,



Thank you very much. As it happens, I got rather sick over the break and consequently didn’t catch up on nearly as many things as I would have liked to!

The marked homework can be collected from the departmental office starting tomorrow.

Regarding the past exams, the general policy is that the past examiners decide whether or not to release the solutions. If they’re not available, I can’t really ask to have them. From a pedagogical point of view, I myself would rather not have the solutions made public because that tends to encourage a very passive approach to studying the material. Of course, when you are working through them, feel very free to ask specific questions!


2201 Sheet 6

The solutions to problem sheet 6, which had been missing, are now available on the course web page. I’m grateful to Adriana Pomella for calling my attention to this omission.


Some personal letters

Over the years, I’ve received a number of general inquiries from students about the life of a mathematician. Obviously, just from sitting in lectures and so forth, it is rather hard to get a real sense of what daily life might be like engaged most of the time in intellectual inquiry. Most importantly, in these diverting times, it’s impossible to entirely avoid the question of why?

During one of the last tutorials of the previous term, Jamal Muse asked me if I enjoyed doing mathematics, and even for this it wasn’t possible to come up with an entirely straightforward answer. Recursively, even the question of why the answer can’t be straightforward, I feel rather uncertain about. Meanwhile, I do take seriously a certain obligation on my part to give an honest answer to such questions,  since they relate to fairly serious decisions that can really affect the rest of a student’s life.

So I’ve finally decided to present an indirect reply. It is rather long, consisting of a series of twenty letters I wrote to my son a few years ago while traveling over the summer on research visits. Much of it is personal, and quite likely boring. I would myself normally frown upon such public exhibition of private letters. However, since I did at the time think exactly about the issue of conveying to my children some feeling for the time I spent away from them, it occurred to me that the letters may serve this other purpose as well.

To impart the semblance of an informal book, I’ve put in a title page and created separate links for the letters according to the dates. If you do end up browsing here and there, try to gloss over the very emotional passages. I’ve left them in to avoid the effort of editing. In any case, let me know if the letters are at all useful to you. Indeed, if they end up of any more than passing interest I may put in a more serious effort at some point to continue the story with a broader readership explicitly in mind.


title page
15 May, 2005
16 May, 2005
17 May, 2005
18 May, 2005
19 May, 2005
20 May, 2005
22 May, 2005
23 May, 2005
25 May, 2005
26 May, 2005
29 May, 2005
31 May, 2005
6 June, 2005
12 June, 2005
15 June, 2005
18 June, 2005
19 June, 2005
21 June, 2005
25 June, 2005
29 June, 2005

Remark on 2201 summary

Some of the questions provided in your course summary are not in the internet lecture notes, and as you said it was not necessary to take notes in your lectures so how do we do these questions then?


I’ve modified the summary slightly and put a few stars on questions that go a bit beyond the scope of the lecture notes. You should find the supplementary notes helpful for these. The remaining questions are all within the scope of the notes, in that you can figure out the answers on the basis of the material there. While quite a few problems are straightforward, there are also a few that require more thought than might have been the norm on the standard course material. These are what I had in mind when I wrote that the problems are not necessarily indicative of the exams. Still, I encourage you to try them out and then ask specific questions.


Prerequisites for 2201 exam?

hi, do the lecture notes provided by Richard Hill have everything we need to know for the exam? Or do we need to look at your notes as well?


Here is as accurate an answer as I can manage. The notes should be sufficient, provided you really understand what’s in it. What will probably not be enough is if you take what’s in the notes as scripture, and try to essentially memorize portions. This is an approach I would like to strongly discourage. In order to acquire the necessary understanding, you should read the supplementary material, and work out the questions in the course summary. Do this several times until you feel really comfortable with the associated notions, and can give reasonable answers in your own words.


Summary of linear algebra: update

There is now an expanded version of the practical summary for Math 2201. The main difference is that a list of questions of various flavors has been added. I have received several requests to make a practice examination available. This is something I am unwilling to do because my past experience is that practice exams encourage a very passive approach to studying. So the list is something of a substitute. However, they should not be taken as directly indicative of exam problems. As I’ve repeated many times, the exam will be very similar in pattern to previous ones. Regarding my list, the intention is to encourage reflection, and a view of the connections between the topics you’ve studied. Of course, if you feel entirely comfortable with the material surrounding these questions and can work them out efficiently, you should have no difficulty with the exam. Feel free to ask for elaboration, after you have given them sufficient thought .

The summary is likely to be amended in the coming months, so be sure to check back every now and then.