I have seen some answers on this site which say that a bachelor of science in mathematics in USA is a general degree and a student needs to study other subjects as well. It also seems to me that many students who did their undergraduate in USA do not have any research experience in mathematics.

I did my undergraduate in an Australian university and it took me 4 years to complete. Each year, I had to do 8 subjects which all of them were mathematics subjects except one subject in the first year which was a programming course. I also did summer research at the end of each first three years in summer and I had to write a research thesis in the honor year (fourth year).

This makes me wonder if those people who did their undergraduate in USA are ready for graduate school because it seems that they may not have done enough mathematics subjects?

Even though I did all mathematics subjects in my undergraduate, I feel that there is some gap in my mathematics education for graduate school.

How those people who did their undergraduate in USA feel about this? do they also see this gap and that they need to work hard?

What do I mean by ready for graduate school?

By being ready for graduate school, I mean that for instance a graduate student at university of Pennsylvania have seen all the materials in graduate preliminary exam in his undergraduate. Or if a graduate student takes any first year graduate courses, the pre-requisites for doing that course are satisfied and he does not need to learn assumed knowledge in a particular first year graduate course.

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    People who didn't do research as undergrads don't go onto grad school right away as a rule. Plenty of students have that research experience. I don't think anything else is predictive of success because a couple extra maths classes just means you're better at classes. Not maths. – user101106 Jan 17 '19 at 4:50
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    At least in my department, students are not expected to have done research in math already but to be prepared to do research. I did my undergrad in the US and took no graduate courses. I also did no summer research. Currently at a program with reputable faculty. There is some catching up to do, of course, depending on what things one needs to learn. I probably would have been a stronger candidate with more courses and just more knowledge, though. – user74089 Jan 17 '19 at 5:03
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    US math graduate students are overall reasonably ready for graduate school in US graduate programs. It's just a much different system in the US compared to Australia or Europe. US math grad programs typically involve a lot more coursework at the beginning, and then begin research later. – Morgan Rodgers Jan 17 '19 at 6:59
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    I'm struggling to imagine a definition of "ready for graduate school" that is not about success. – JeffE Jan 17 '19 at 10:49
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    I think that how you have defined "ready for grad school" is silly. You're ready for grad school if you can be successful in grad school and stamp collecting prerequisites is as relevant to that as being able to drain free throws. – user101106 Jan 17 '19 at 13:16

Actually, since they do make the transition regularly, the answer is yes. But that doesn't mean that they are immediately ready to take comprehensive exams or begin thesis work.

Note that most US undergrads go to US grad schools if they move on. Each country's educational system is different. The fact that a US math major takes only about 1/3 of her/his credits in mathematics doesn't affect anything, since US grad schools expect that.

The natural progression is to go from a BS to an MS and then to a PhD. Not all schools, however, require the master's degree for admission to the doctorate, but those that don't will have a system of courses and exams that assure that the student is ready for research when they start, whether or not an MS is part of the progression. Many schools that directly admit doctoral students will offer an MS as a painless "stepping stone" as part of the studies. Sometimes all you need to do is fill out a request form, but a short thesis or exam may also be required (as it was in my case).

The prelim/comp exams, however, aren't based, for the most part on the undergraduate material. For example, I didn't study measure theory or delve too deeply into topology until I was a grad student. My undergrad was heavy in analysis and secondarily in algebra. But the early graduate courses built on the undergrad experience and so I was ready by the time it was necessary. But comps didn't come until late in the third year of grad study and little research was needed until that time.

The system works as long as you stay in one country or move to a country with a similar system. Moving from an undergrad major (in any field) in the US to a grad program in UK might be a different story though, since the undergrad program in UK is much more specialized by field.

But at the end, the students wind up in about the same place. You get a comprehensive view of the breadth of mathematics and a very deep dive into a specialized part of it so that you can do research.

The US system isn't inferior, as the question seems to imply. It is just different.

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  • Your third paragraph understates the situation for mathematics in the US. Currently, the vast majority of US mathematics PhD students never get an MS, either before or during their PhD program. – Mark Meckes Jan 17 '19 at 15:56
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    @MarkMeckes, are you certain it is "vast majority"? I don't have statistics. But is it still offered as an option, at least? That is what I said, though my information is old. – Buffy Jan 17 '19 at 16:02
  • I don't have statistics either. This is based on every American math PhD program I have had much interaction with over the last 20ish years (which admittedly may be a biased sample). I tried looking for statistics, but the only statistics I could find for numbers of master's degrees lump together Mathematics and Statistics, and the MS in Statistics is (again, in my experience) a much more popular degree. – Mark Meckes Jan 17 '19 at 17:17

The question broadens beyond mathematics (and the answer remains the same):

Does an undergraduate degree sufficiently prepare students for graduate school?

TL;DR: No.

An undergraduate degree is not intended to -- nor does it -- prepare students for graduate school. Ultimately, students must deliver a thesis. That thesis will be unique and the skills required to deliver it will be rather specialised. So, many of the required skills will not be part of undergraduate degrees (nor should they be). Students must learn the necessary skills during graduate school.

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    Could you clarify your definition of "ready for graduate school"? It looks like to you it means: "Able to sit down and write a thesis without learning any new skills", which does not sound like a very reasonable definition to me. I would think that whatever your definition of "Ready for grad school" is, it should include anyone who goes on to complete it in a reasonable time frame. – Peter Jan 17 '19 at 10:20
  • @Peter I haven't used the phrase "ready for graduate school," I certainly wouldn't use it to mean "[a]ble to sit down and write a thesis," that's the end result of graduate school, not an entry requirement. I don't think "ready for graduate school" has any concrete meaning. If you can elaborate your comment, then I'll try to respond more precisely. – user2768 Jan 17 '19 at 10:42
  • @JeffE I suppose that depends where you draw the lines. I'll contend that many excellent undergraduates drop-out of graduate school, because they weren't ready for research. I don't consider that a problem. An undergraduate degree shouldn't prepare a student for research (there are other priorities). The early stages of graduate school should ready a student for research and any student that isn't sufficiently ready should consider dropping out. – user2768 Jan 17 '19 at 10:52
  • Please see my edited question – Georgia Jan 17 '19 at 11:14
  • @Georgia Further to your edit: Questions relating to the University of Pennsylvania are off-topic here. Regarding satisfying all the pre-requisites of any first year graduate course, I think that is an unrealistically high expectation. – user2768 Jan 17 '19 at 12:48

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