I often wonder about Mathematics Education in China, particularly at the late high school and undergraduate level.
In the US, a typical undergraduate math degree will include lower division: 1-2 years of calculus (3 courses) different equations (1 course) linear albegra (1 course)
upper division 1 year of analysis (2 or three courses, real and complex) 1 year of algebra (2 courses) and a mix of: number theory, topology, more linear algebra, and so on.
I have heard from Chinese friends and seen on a few websites that Chinese students are often a few years ahead of our pace here in the US. For instance, they have often already started working on analysis and topology in late high school. It seems that they are doing US graduate level work by half way through their undergrad. What's more they are probably better at whatever subject they are learning too based on the sheer effectiveness of their education system.
I am wondering, for all that the romantic values of the US education are worth, why it seems that the Chinese system simply makes better, and frankly, more mathematically intelligent students. It seems that the best Chinese students read more, for longer hours, do more math problems etc. Whether or not this is by their own volition or because they are feeling pressure to do so (as is often case, so it's explained to me), the end result is the same regardless; They spend more time doing math, and they are better at it.
How can a student in the US honestly hope to learn enough math to be on an equal footing with a student who has worked 50% longer hours, and begun their mathematics education years earlier (if we're also not looking at particular cases of geniuses emerging at a young age in either country, but rather the average intelligent student)?
Please do share any knowledge, experience, or opinion you have related to these questions. I am a math student doing my undergraduate degree in the US, and I feel my education is not rigorous or thorough enough, despite being at a reputably challenging, well regarded institution. Furthermore, when I express my desire to work longer hours than other students, I am met with negative comments about how more work does not mean more knowledge. I think that's just plain wrong, so long as you're remaining healthy.
I have heard similar things about Russia, and even Japan and Korea. Please do share your thoughts.
Thank you for your input.
Edit and clarification: I agree with the sentiment that a broader education can help students deal with the real world, so to speak, better than a narrow one can in some respects. But first I'd like to suggest that we can't use the fact that the US was doing the best science in the last century to suggest this system is better. Many of the great discoveries and advancements I think of here in the last century are disqualified from this discussion by two factors. Firstly, the imperial history of the U.S. and its strategic footing during the World Wars allowed it to dominate in almost everything globally, from trade, to military power, to science. Secondly, many of the great advancements I think of in the past century were done by either exceptional geniuses who typically exhibited exceptional abilities at a young age, and furthermore many foreigners who came to the US for the reason above (I'm thinking Von Neumann, Einstein, etc). As the US loses its global dominance, I think that we will see less of this sentiment that the US education system really works exceptionally well in the ways that we imagine and discuss in this thread, and more recognition that other factors were at play. Furthermore, having first hand experience, it really does seem that my Chinese peers are better at math, their knowledge is not shallow in any respect. They work harder than most students here, and know the material better. They spend more time on homework and do more problems in their universities. It's not necessarily the breadth of our education that is responsible, but a combination of the breadth our lack of devotion to long hours and thorough understanding in exchange for serious labor.
Think, Chinese students will get perfect math GRE scores and be rejected from US math programs, while US students rarely if ever get such a score. Yet we still dismiss them as simply having memorized facts for the test. I think this is a big mistake, and will come back to bite the US, and its romantic liberal arts style education.