Mathematicians opinion on university modules

[synkk]

Hi,

I'm wondering if anyone could suggest which out of the two below universities would give me the "better" mathematics major. By better I mean the most rigorous, the hardest and the one which will prepare me most for a phd.

1. http://www.ucl.ac.uk/maths/courses/undergraduates/

I won't be taking any of the joint students course as I've been admitted to the straight mathematics course only.

2. http://www.kcl.ac.uk/nms/depts/mathematics/study/current/handbook/progs/modules/index.aspx

Level 4 is year 1, 5 year 2 and so on

There is descriptions of all the modules but I have no idea what they're talking about as I haven't done any of the modules yet (obviously), so I'm hoping someone with more experience could advise me on which university to choose. I live nearby to both universities and I'm more inclined to the first one atm (UCL), due to it's reputation and they've offered me a scholarship.

Thanks,

 

[chiro]

Hey synkk.

I'm more inclined to agree with you about UCL based on some of the course outlines I read.

If you can get into the honours course at UCL I think that will keep you busy for a while (and facilitate you in becoming a good mathematician/statistician in both theory and practice).

 

[synkk]

Hey synkk.

I'm more inclined to agree with you about UCL based on some of the course outlines I read.

If you can get into the honours course at UCL I think that will keep you busy for a while (and facilitate you in becoming a good mathematician/statistician in both theory and practice).

Hi, thanks for replying. Could you be a bit more specific why you'd choose UCL over KCL? I don't really understand why universities have such a different structure. For example, UCL don't seem to offer geometry in the first year, while KCL do, and UCL make it core to take a lot of analysis in the first and second year, while KCL only take analysis in the second year, and take real analysis in the first year (while UCL do it in the second year).

Thanks again.

 

[n10Newton]

KCL or UCL, I am not from UK, so I don't know who is reputed in UK. but take my experience in my country there is two University for Maths known for best, one focus on Algebra and Another on Analysis, this is not shown by there University Syllabus/modules, there/professors main focus observed by Students.

So, Fact upon writing this the Syllabus/Modules don't represent the University's Quality. If you compare Modules of Harvard Maths to your KCL or UCL there is not a big difference, so before applying visit University/contact their students, know about Professors and decide which one suits you better.

 

[Mépris]

Greater flexibility at Harvard, and US colleges in general. Depending on one's preparation (or rate of learning, for instance), one could go as far as graduating from there after having taken all the courses necessary to take the PhD qualifiers.

UK universities have a more clear-cut path.

 

[synkk]

KCL or UCL, I am not from UK, so I don't know who is reputed in UK. but take my experience in my country there is two University for Maths known for best, one focus on Algebra and Another on Analysis, this is not shown by there University Syllabus/modules, there/professors main focus observed by Students.

So, Fact upon writing this the Syllabus/Modules don't represent the University's Quality. If you compare Modules of Harvard Maths to your KCL or UCL there is not a big difference, so before applying visit University/contact their students, know about Professors and decide which one suits you better.

Thanks, I've visited UCL already and spoken to the professors actually. It's a rather small department (but so is KCL), and they told us that their course is very rigorous and kept fixating that'd we would have to be on the top of our game at all times. I kind of liked that, I don't want to go to a place where I'm not challenged. I also did do some research on the professors there, but I don't know exactly what I'm looking for as: 1. I don't even know what branch of mathematics interests me yet and 2. I don't know even if I'm good enough for maths research so it's hard to make a choice based on who teaches there.

As said before, both universities are close to my home and they are both University of London so they do share some facilities, like the libraries and you can also take modules in the 4th year from the other university, but the first 3 years you can't. I'll visit KCL soon and try to make some sort of decision but I hope I get other opinions on the matter.

 

[n10Newton]

1. I don't even know what branch of mathematics interests me yet
Just go through Educational Stream, after 4 years of Maths Education ask yourself and take that brach for Graduate School. here in 4 years you have need to know all, to give all branches the same love is essential.

 

[micromass]

Let me take four arbitrary (advanced) courses in pure mathand see how the two universities compare:

1) Measure theory
The UCL course on measure theory is pretty disappointing. It covers the very basics, but not much more. If I compare with my course on measure theory, then we really covered double of the material of the UCL course.

The KCL course doesn't even do measure theory. Not even in a real analysis course. Big red flag!

2) Abstract algebra
UCL seems to be very ok. It covers all the important things (but not much more). I did expect some more of its commutative algebra course. Things like tensor products never seem to be covered in detail, which is a pretty big omission.

KCL seems a bit light on algebra. They do some good stuff, but UCL seems more advanced in many ways.

3) Topology
I don't see a point-set topology course in UCL. I find this weird because they do have an algebraic topology course. I might have missed it, but the lack of a topology course is a pretty big omission.

The KCL topology course is pretty good. Their syllabus seems to be covering a lot of stuff. I find it strange that they cover that much and I wonder if they really go deep into the topics.

4) Differential Geometry
The UCL course seems very ok. They cover quite some nice things. It's what I expect of undergrad differential geometry.

The KCL course is also good, but they cover less than the UCL course.

Overall, I am more impresed by UCL than by KCL. Especially in analysis, I think that UCL is much superior. I only question the lack of a general topology course in UCL.

 

[synkk]

Let me take four arbitrary (advanced) courses in pure mathand see how the two universities compare:

1) Measure theory
The UCL course on measure theory is pretty disappointing. It covers the very basics, but not much more. If I compare with my course on measure theory, then we really covered double of the material of the UCL course.

The KCL course doesn't even do measure theory. Not even in a real analysis course. Big red flag!

2) Abstract algebra
UCL seems to be very ok. It covers all the important things (but not much more). I did expect some more of its commutative algebra course. Things like tensor products never seem to be covered in detail, which is a pretty big omission.

KCL seems a bit light on algebra. They do some good stuff, but UCL seems more advanced in many ways.

3) Topology
I don't see a point-set topology course in UCL. I find this weird because they do have an algebraic topology course. I might have missed it, but the lack of a topology course is a pretty big omission.

The KCL topology course is pretty good. Their syllabus seems to be covering a lot of stuff. I find it strange that they cover that much and I wonder if they really go deep into the topics.

4) Differential Geometry
The UCL course seems very ok. They cover quite some nice things. It's what I expect of undergrad differential geometry.

The KCL course is also good, but they cover less than the UCL course.

Overall, I am more impresed by UCL than by KCL. Especially in analysis, I think that UCL is much superior. I only question the lack of a general topology course in UCL.

Damn you really make these two universities seem like garbage!

If I don't get into Cambridge (and probably won't due to the interview) I guess I'll go with UCL.

Thanks, and if anyone else has anything to add then please do so.

 

[micromass]

Damn you really make these two universities seem like garbage!

They're not garbage. There are much worse universities out there. I'm sure that you can really get a quality education at both institutions. If you complete your education there, then you can call yourself quite knowledgeable of mathematics. So don't worry

But it is very important to not only rely on the course itself. You rely got to self-study and go actually beyond what the course teaches you. The best mathematicians I've seen were people who read about math outside their courses. In a way, you should see the courses at university as the basics. You will want to read for yourself to go beyond the basics.

 

[mathwonk]

I suggest examining who the faculty are at these universities to better determine what is available there. E.g. former staff members and/or students include Augustus de Morgan, J.J. Sylvester, Alan Baker, and Tim Gowers, the last two Fields medalists.

Read this page before you write them off as clearly some students there have found some success:

http://www.ucl.ac.uk/maths/the-department

 

[synkk]

I suggest examining who the faculty are at these universities to better determine what is available there. E.g. former staff members and/or students include Augustus de Morgan, J.J. Sylvester, Alan Baker, and Tim Gowers, the last two Fields medalists.

Read this page before you go off rudely and foolishly calling them names:

http://www.ucl.ac.uk/maths/the-department

I have indeed already read that page, however the field medalists did not receive their undergraduate education there, which is why I never really took it into consideration. One famous mathematician that I found that did do his undergraduate was Roger Penrose. EDIT: Alan Baker also did, a while ago.

I do apologise if my post at all seemed like I was calling any of universities garbage as it really was not intended. As micromass kindly analysed the course structure for both universities he pointed out a lot of flaws, which is what I was really looking for anyway, so my garbage term was not intended to be the way you perceived it.

Thanks again.

 

[micromass]

I have indeed already read that page, however the field medalists did not receive their undergraduate education there, which is why I never really took it into consideration. One famous mathematician that I found that did do his undergraduate was Roger Penrose. EDIT: Alan Baker also did, a while ago.

I do apologise if my post at all seemed like I was calling any of universities garbage as it really was not intended. As micromass kindly analysed the course structure for both universities he pointed out a lot of flaws, which is what I was really looking for anyway, so my garbage term was not intended to be the way you perceived it.

Thanks again.

Note that when I made my analysis I have only taken one criterium into consideration. That criterium was the amount of material covered. This is far from the only criterium to consider, and it is not even the most important one.

There are other things you can ask yourself. For example: how difficult are the exams and problem sets?? For example, it may be that the lectures covers a lot of ground, but that the problems are all computational. This is not good. It may also be that you didn't do very much in lecture, but you did it all very rigorously and deep. And it may be that the problem sets are quite difficult and are designed to make you think deeply and make you look up material in books. This is something to consider.

And what about the quality of the office hours or the lectures? The amount of material covered doesn't say anything about this. If your teacher is a field medalist (and if he is really motivated to teach), then you can expect a very good experience.

What about your fellow students? Are they motivated for mathematics? This can make a lot of difference as well.

My analysis is only on aspect. You really need to look further than that. Go talk to some professors at the university. Or to some students. Look into some exams and problem sets. This can give you a lot of information as well.

 

[synkk]

Note that when I made my analysis I have only taken one criterium into consideration. That criterium was the amount of material covered. This is far from the only criterium to consider, and it is not even the most important one.

There are other things you can ask yourself. For example: how difficult are the exams and problem sets?? For example, it may be that the lectures covers a lot of ground, but that the problems are all computational. This is not good. It may also be that you didn't do very much in lecture, but you did it all very rigorously and deep. And it may be that the problem sets are quite difficult and are designed to make you think deeply and make you look up material in books. This is something to consider.

And what about the quality of the office hours or the lectures? The amount of material covered doesn't say anything about this. If your teacher is a field medalist (and if he is really motivated to teach), then you can expect a very good experience.

What about your fellow students? Are they motivated for mathematics? This can make a lot of difference as well.

My analysis is only on aspect. You really need to look further than that. Go talk to some professors at the university. Or to some students. Look into some exams and problem sets. This can give you a lot of information as well.

Thanks, you've given me a lot of things to research on. I've already visited UCL and spoken to the professors but they have another visit day coming up so I'll go again, and I'll do the same for King's.

As for the problem sets - I've already actually done this, I printed out 4 problem sets from 4 different topics from both universities, and showed them to my current teachers (high school), however they've told me that they have forgotten most of the material, and asked me to look somewhere else. Do you mind if I show you some of the problems sets (I'll PM them).

Thanks again to every who responded.

 

[micromass]

Thanks, you've given me a lot of things to research on. I've already visited UCL and spoken to the professors but they have another visit day coming up so I'll go again, and I'll do the same for King's.

As for the problem sets - I've already actually done this, I printed out 4 problem sets from 4 different topics from both universities, and showed them to my current teachers (high school), however they've told me that they have forgotten most of the material, and asked me to look somewhere else. Do you mind if I show you some of the problems sets (I'll PM them).

Thanks again to every who responded.

Sure, you can PM them.

 

[Vargo]

I could be wrong as I certainly know nothing about the UK university system. But how seriously can you take general course syllabi? Don't professors choose their own textbooks and make it up as they go along?

 

[pasmith]

I could be wrong as I certainly know nothing about the UK university system. But how seriously can you take general course syllabi? Don't professors choose their own textbooks and make it up as they go along?

Internal University regulations and the http://www.qaa.ac.uk/Publications/InformationAndGuidance/Pages/Code-of-practice-section-7.aspx impose strict rules on the process of designing and approving courses, and unapproved deviation from an approved course is not tolerated. What appears on the formal syllabus is what will be taught and what can be examined (save topics expressly marked as non-examinable).

Also set textbooks are virtually unknown in UK practice; lecturers write their own problems sheets and students are expected to use the library if their lecture notes are not sufficient.

 

[synkk]

Internal University regulations and the http://www.qaa.ac.uk/Publications/InformationAndGuidance/Pages/Code-of-practice-section-7.aspx impose strict rules on the process of designing and approving courses, and unapproved deviation from an approved course is not tolerated. What appears on the formal syllabus is what will be taught and what can be examined (save topics expressly marked as non-examinable).

Also set textbooks are virtually unknown in UK practice; lecturers write their own problems sheets and students are expected to use the library if their lecture notes are not sufficient.

As you seem to be experienced with the UK education system - Which university do you think would give a better education?

 

[pasmith]

As you seem to be experienced with the UK education system - Which university do you think would give a better education?

My experience consists of having studied mathematics at Cambridge, and I don't know enough about either UCL or KCL to comment. But the Guardian ranks UCL ahead of KCL in mathematics, as does the Complete University Guide.

That aside, if UCL have offered you a scholarship then I would be tempted to take advantage of that.

I would be willing to look at specimen problem sheets.