Why do US and foreign math programs differ in required coursework?

[goingmeta]

I was doing some searching and landed on a post by micromass where it was revealed that he/she had taken twenty-some math courses at the undergraduate level at a university in Belgium. I got the impression from that thread that it was not uncommon to have taken that many.

I'm currently an undergraduate who started mathematics late. At graduation, if all goes well, I will have taken around 10 proof based math courses (such as algebraic geometry, algebraic topology, and so forth). My American university, which is well known, requires 8. I don't think that number is uncommon (or unrepresentative) for many American universities and I feel it will be substantial work, for me, to even achieve that many. I recognize that there are some who will exceed that amount by a lot, but even in my program, I get feeling the they are in the minority.

At this point, I feel somewhat intimidated because I'm underprepared. Why is there this difference? What is the justification for having such a lower requirement? Are there trade-offs?

(Obviously I generalized in this post from my experience, feel free to correct me.)

 

[dx]

At my undergraduate university in England, I was required to take approximately 120 credits per year. Algebraic geometry for example is 18 credits, so that is about 6 or 7 courses at least per year.

When you say 8, do you mean per year or 8 courses in total for the undergraduate degree?

 

[goingmeta]

8 total for the undergraduate degree.

 

[dx]

I don't think its really a problem. Even with 8 courses you can cover all the core material needed to go to grad school.

If you are taking courses like algebraic topology and and algebraic geometry, I assume the other courses you took are something like the following:

analysis
abstract algebra (linear algebra, group theory etc..)
topology
differential equations
complex analysis

If you've done all these then you are well prepared for grad school.

 

[goingmeta]

Something else I was wondering about: do schools in Europe also force their students to go through with a computational calculus sequence as they do here in the US?

 

[dx]

By 'computational' I guess you mean one that teaches you how to calculate various integrals and derivatives as opposed to the rigorous real analysis?

At my university in the UK we did not have such a course. People starting the degree were assumed to already be familiar with calculus at that level from high school, and were ready to take real analysis and differential equations.