Oxford or Cambridge for Pure math major

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The person I know who attended Cambridge for maths was a USAJMO qualifier in HS, and had a several top 10 and recognition awards in less-popular but still prestigious national-level pure and applied, individual and and team, exam and project, math contest
award, and a research internship in HS.

That's about top 100 to 200 in USA in-grade-level performing HS math student.

It may be true that there are a good number of high performing math olympiad kids studying math at prestigious university math programs. However, competition math and the math you study in college are quite different. Competition math is not everyone's cup of tea and you don't need to have invested in becoming a math competition champ to be good at the kind of math one does in college or graduate school or as a career mathematician.

"Competition math" (aka advanced, more abstract, deeper math) is the closest thing to college/grad/mathematician work than anything else done in high school.

No, much of competition math is fun tricks and skills particular to the competition format. Taking actual math courses is the closest to college math work.

Please explain the "fun tricks" particular to USAMO: https://artofproblemsolving.com/wiki/index.php/2024_USAMO_Problems

Being able to solve these types of proof-based problems is a much better predictor of your ability to succeed in pure maths than how well you can plug and chug in a college multi/diffeq/lin alg course. That's why trinity college in Cambridge, the most selective Cambridge college for maths, maintains such a close relationship with the UK's top competition math students but not the accelerated students who take university math classes through the Open University.

Just because you post math you don't understand, doesn't mean there isn't a formulaic way of going about studying competition math. It's okay to be stupid, just don't be confident in that ignorance.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The person I know who attended Cambridge for maths was a USAJMO qualifier in HS, and had a several top 10 and recognition awards in less-popular but still prestigious national-level pure and applied, individual and and team, exam and project, math contest
award, and a research internship in HS.

That's about top 100 to 200 in USA in-grade-level performing HS math student.

It may be true that there are a good number of high performing math olympiad kids studying math at prestigious university math programs. However, competition math and the math you study in college are quite different. Competition math is not everyone's cup of tea and you don't need to have invested in becoming a math competition champ to be good at the kind of math one does in college or graduate school or as a career mathematician.

"Competition math" (aka advanced, more abstract, deeper math) is the closest thing to college/grad/mathematician work than anything else done in high school.

No, much of competition math is fun tricks and skills particular to the competition format. Taking actual math courses is the closest to college math work.

Please explain the "fun tricks" particular to USAMO: https://artofproblemsolving.com/wiki/index.php/2024_USAMO_Problems

Being able to solve these types of proof-based problems is a much better predictor of your ability to succeed in pure maths than how well you can plug and chug in a college multi/diffeq/lin alg course. That's why trinity college in Cambridge, the most selective Cambridge college for maths, maintains such a close relationship with the UK's top competition math students but not the accelerated students who take university math classes through the Open University.

Just because you post math you don't understand, doesn't mean there isn't a formulaic way of going about studying competition math. It's okay to be stupid, just don't be confident in that ignorance.

Exactly the response I expected.
"It's formulaic, but I can't explain how, just trust me, I know more than Trinity"

[Anonymous]

I can't remember the last time I looked at competition math, but these are exactly the kinds of problems you play with in college, especially the proof based ones. I don't understand how this is even being 'debated' here.

[Anonymous]

As someone who went to Cambridge (undergrad from the UK) I would say your kid sounds more than qualified. It’s a hard course but it sounds like he is very good at maths. The British kids getting in are not all geniuses, they are, like him, just very good at maths.

[Anonymous]

Anonymous wrote:I can't remember the last time I looked at competition math, but these are exactly the kinds of problems you play with in college, especially the proof based ones. I don't understand how this is even being 'debated' here.

Look at the Cambridge entrance exam training assignment #1, linked earlier.

It's exactly what you see in a math contest and never see in US mainstream classes, outside of special magnet classes.

https://maths.org/step/sites/maths.org.step/files/assignments/assignment1_0.pdf

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The person I know who attended Cambridge for maths was a USAJMO qualifier in HS, and had a several top 10 and recognition awards in less-popular but still prestigious national-level pure and applied, individual and and team, exam and project, math contest
award, and a research internship in HS.

That's about top 100 to 200 in USA in-grade-level performing HS math student.

It may be true that there are a good number of high performing math olympiad kids studying math at prestigious university math programs. However, competition math and the math you study in college are quite different. Competition math is not everyone's cup of tea and you don't need to have invested in becoming a math competition champ to be good at the kind of math one does in college or graduate school or as a career mathematician.

"Competition math" (aka advanced, more abstract, deeper math) is the closest thing to college/grad/mathematician work than anything else done in high school.

No, much of competition math is fun tricks and skills particular to the competition format. Taking actual math courses is the closest to college math work.

Please explain the "fun tricks" particular to USAMO: https://artofproblemsolving.com/wiki/index.php/2024_USAMO_Problems

Being able to solve these types of proof-based problems is a much better predictor of your ability to succeed in pure maths than how well you can plug and chug in a college multi/diffeq/lin alg course. That's why trinity college in Cambridge, the most selective Cambridge college for maths, maintains such a close relationship with the UK's top competition math students but not the accelerated students who take university math classes through the Open University.

Just because you post math you don't understand, doesn't mean there isn't a formulaic way of going about studying competition math. It's okay to be stupid, just don't be confident in that ignorance.

If only you could take your own advice...

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The person I know who attended Cambridge for maths was a USAJMO qualifier in HS, and had a several top 10 and recognition awards in less-popular but still prestigious national-level pure and applied, individual and and team, exam and project, math contest
award, and a research internship in HS.

That's about top 100 to 200 in USA in-grade-level performing HS math student.

It may be true that there are a good number of high performing math olympiad kids studying math at prestigious university math programs. However, competition math and the math you study in college are quite different. Competition math is not everyone's cup of tea and you don't need to have invested in becoming a math competition champ to be good at the kind of math one does in college or graduate school or as a career mathematician.

"Competition math" (aka advanced, more abstract, deeper math) is the closest thing to college/grad/mathematician work than anything else done in high school.

No, much of competition math is fun tricks and skills particular to the competition format. Taking actual math courses is the closest to college math work.

OK, so I see the problem is that you don't understand the difference between "competition math” and ”math competitions”. The " fun tricks and skills" are how the winners get crazy fast at the contests to get perfect scores. Yes, that is not helpful for higher level math. But that's the A1 sauce on the steak.

The meat of it is learning a ton of math, applying it in novel situation without being told which formula to use, learning how to prove results so you can answer questions like " how many solutions does this constraint have?", constantly sitting for tests that each cover 4 years of math in random, order, not just last week's lesson, and being happy solving problems that each take 5 to 100 minutes to solve.

People who wave off "competition math" are people who failed to even start learning it, looking for a excuse. Or people are legitimately in their own little world doing deep math study, not just Multivariable calculus. Is there what you are talking about?
Someone like Jacob Lurie, who won Westinghouse with a pure math paper in high school. Who, by the way also got a perfect score in the IMO?

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:The person I know who attended Cambridge for maths was a USAJMO qualifier in HS, and had a several top 10 and recognition awards in less-popular but still prestigious national-level pure and applied, individual and and team, exam and project, math contest
award, and a research internship in HS.

That's about top 100 to 200 in USA in-grade-level performing HS math student.

It may be true that there are a good number of high performing math olympiad kids studying math at prestigious university math programs. However, competition math and the math you study in college are quite different. Competition math is not everyone's cup of tea and you don't need to have invested in becoming a math competition champ to be good at the kind of math one does in college or graduate school or as a career mathematician.

"Competition math" (aka advanced, more abstract, deeper math) is the closest thing to college/grad/mathematician work than anything else done in high school.

No, much of competition math is fun tricks and skills particular to the competition format. Taking actual math courses is the closest to college math work.

OK, so I see the problem is that you don't understand the difference between "competition math” and ”math competitions”. The " fun tricks and skills" are how the winners get crazy fast at the contests to get perfect scores. Yes, that is not helpful for higher level math. But that's the A1 sauce on the steak.

The meat of it is learning a ton of math, applying it in novel situation without being told which formula to use, learning how to prove results so you can answer questions like " how many solutions does this constraint have?", constantly sitting for tests that each cover 4 years of math in random, order, not just last week's lesson, and being happy solving problems that each take 5 to 100 minutes to solve.

People who wave off "competition math" are people who failed to even start learning it, looking for a excuse. Or people are legitimately in their own little world doing deep math study, not just Multivariable calculus. Is there what you are talking about?
Someone like Jacob Lurie, who won Westinghouse with a pure math paper in high school. Who, by the way also got a perfect score in the IMO?

"competition math" is what's tested in "math competitions". They're pretty much interchangeable. Speed is mostly irrelevant (with some middle school competitions being exceptions) - for almost all highschool students, double time would not significantly increase their competition scores. But you're dead on regarding everything else.

A talented student who spends their time on competition math is much better prepared for STEP than an equally talented student who spends their time on freshman/sophomore math (calc 3, diff eq, linear algebra)

[Anonymous]

Anonymous wrote:

Anonymous wrote:I can't remember the last time I looked at competition math, but these are exactly the kinds of problems you play with in college, especially the proof based ones. I don't understand how this is even being 'debated' here.

Look at the Cambridge entrance exam training assignment #1, linked earlier.

It's exactly what you see in a math contest and never see in US mainstream classes, outside of special magnet classes.

https://maths.org/step/sites/maths.org.step/files/assignments/assignment1_0.pdf

NP. Those are just the sorts of things someone who understands HS math should be able to do. There's nothing tricky or out of the ordinary there. They are exercises that treat the student with more respect than an SAT question, but I don't know what you're on about. Competition math is fine for those who enjoy it, but it is a backwater.

[Anonymous]

It sounds like DCUM just have poor quality math courses. Proof based linear algebra, set theory, and combinatorics is what our DD took before going to Harvard for math- fit right into math 55 and did grad math courses from there.

Sure if you’re taking math for engineers, you have poor curriculum and training.

[Anonymous]

Cambridge for math. After you decide on the University you have to pick a college. Trinity tends to be the hardest to get into. That's where the Olympiad kids are. St. Johns is second but the year we applied it was harder to get into. If you don't get into your top choice you'll be pooled and could be picked up by another college. You should definitely visit. Ours was going to apply to Oxford and picked Cambridge. DD got in but chose Harvard. 10% of her 55 class were also accepted to Cambridge.

[Anonymous]

Anonymous wrote:Cambridge for math. After you decide on the University you have to pick a college. Trinity tends to be the hardest to get into. That's where the Olympiad kids are. St. Johns is second but the year we applied it was harder to get into. If you don't get into your top choice you'll be pooled and could be picked up by another college. You should definitely visit. Ours was going to apply to Oxford and picked Cambridge. DD got in but chose Harvard. 10% of her 55 class were also accepted to Cambridge.

Why choose Harvard? It is much less renown for mathematics education. Sure there's 55, but there's much more prestigious institutions that it sounds like your DD got into.

[Anonymous]

Anonymous wrote:

Anonymous wrote:Cambridge for math. After you decide on the University you have to pick a college. Trinity tends to be the hardest to get into. That's where the Olympiad kids are. St. Johns is second but the year we applied it was harder to get into. If you don't get into your top choice you'll be pooled and could be picked up by another college. You should definitely visit. Ours was going to apply to Oxford and picked Cambridge. DD got in but chose Harvard. 10% of her 55 class were also accepted to Cambridge.

Why choose Harvard? It is much less renown for mathematics education. Sure there's 55, but there's much more prestigious institutions that it sounds like your DD got into.

We want her close to home for school and work. Why rush through college in 3 years. She has the option to get a Masters by graduation but I told her to take non math classes and go to Cambridge if she wants a Masters. College isn’t just about the academics. The social component is very important.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Cambridge for math. After you decide on the University you have to pick a college. Trinity tends to be the hardest to get into. That's where the Olympiad kids are. St. Johns is second but the year we applied it was harder to get into. If you don't get into your top choice you'll be pooled and could be picked up by another college. You should definitely visit. Ours was going to apply to Oxford and picked Cambridge. DD got in but chose Harvard. 10% of her 55 class were also accepted to Cambridge.

Why choose Harvard? It is much less renown for mathematics education. Sure there's 55, but there's much more prestigious institutions that it sounds like your DD got into.

We want her close to home for school and work. Why rush through college in 3 years. She has the option to get a Masters by graduation but I told her to take non math classes and go to Cambridge if she wants a Masters. College isn’t just about the academics. The social component is very important.

Okay...why not Uchicago or Princeton?

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:I can't remember the last time I looked at competition math, but these are exactly the kinds of problems you play with in college, especially the proof based ones. I don't understand how this is even being 'debated' here.

Look at the Cambridge entrance exam training assignment #1, linked earlier.

It's exactly what you see in a math contest and never see in US mainstream classes, outside of special magnet classes.

https://maths.org/step/sites/maths.org.step/files/assignments/assignment1_0.pdf

NP. Those are just the sorts of things someone who understands HS math should be able to do. There's nothing tricky or out of the ordinary there. They are exercises that treat the student with more respect than an SAT question, but I don't know what you're on about. Competition math is fine for those who enjoy it, but it is a backwater.

This isn't the entrance test, it's the first of many assignments designed to progress students from school math to the level of the entrance test.

This is a past entrance test: https://nextstepmaths.com/downloads/step-papers/step2-2024-paper.pdf