Oxford or Cambridge for Pure math major

[Anonymous]

Anonymous wrote: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.

At which uni did she take them? Most families only have access to CC.

[Anonymous]

math tutor would be the easiest way

[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.

Math 55 was replaced over 10 years ago by "Math 55" which is just Math 112, 123, 121, and 122 (real analysis , complex analysis, theoretical linear algebra, and group theory algebra), cohorted with only first years and granted only half credit so that that students are encouraged to take more math classes later on.

But Harvard is still tippy top tier university for math. There certainly is no institution "much more prestigious" than Harvard math department.

Some examples

https://www.usnews.com/education/best-global-universities/mathematics


https://www.niche.com/colleges/search/best-colleges-for-math/

[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.

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)

Speed is what separates the mid-high performers (top 1000 per grade) from the top performers (top 100 per grade) on pre-Olympiad AMC, AIME, ARML, etc. (Most of the fast students can probably also do harder problems, but that's not on the tests.)

Of course the average students can't do any of it beyond the warmup problems.

[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.

I'd bet that half the students with a 750+ SAT (~80K students) could not ace that paper, and that's the easiest one of the curriculum.

[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.

Math 55 was replaced over 10 years ago by "Math 55" which is just Math 112, 123, 121, and 122 (real analysis , complex analysis, theoretical linear algebra, and group theory algebra), cohorted with only first years and granted only half credit so that that students are encouraged to take more math classes later on.

But Harvard is still tippy top tier university for math. There certainly is no institution "much more prestigious" than Harvard math department.

Some examples

https://www.usnews.com/education/best-global-universities/mathematics


https://www.niche.com/colleges/search/best-colleges-for-math/

I’m sorry what? Uchicago, MIT and Princeton are better at Harvard at Mathematics

[Anonymous]

Anonymous wrote:

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.

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)

Speed is what separates the mid-high performers (top 1000 per grade) from the top performers (top 100 per grade) on pre-Olympiad AMC, AIME, ARML, etc. (Most of the fast students can probably also do harder problems, but that's not on the tests.)

Of course the average students can't do any of it beyond the warmup problems.

I don't believe speed is the distinguishing factor of those who qualify for the next stage (AIME/USAMO). It might be for the top scorers in the lower stages, but that's not as impressive as reaching a higher level. Making MOP is more impressive than getting a top 50 AMC/AIME scores, for example.

It's true that the best students are faster than average, but they're faster because they're stronger competitors - they're not stronger competitors because they're faster.

[Anonymous]

Anonymous wrote:

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.

Math 55 was replaced over 10 years ago by "Math 55" which is just Math 112, 123, 121, and 122 (real analysis , complex analysis, theoretical linear algebra, and group theory algebra), cohorted with only first years and granted only half credit so that that students are encouraged to take more math classes later on.

But Harvard is still tippy top tier university for math. There certainly is no institution "much more prestigious" than Harvard math department.

Some examples

https://www.usnews.com/education/best-global-universities/mathematics


https://www.niche.com/colleges/search/best-colleges-for-math/

I’m sorry what? Uchicago, MIT and Princeton are better at Harvard at Mathematics

DP, I think honors analysis at UChicago and math 216/218 at Princeton are more rigorous/challenging than math 55, but it's not a dealbreaker or anything. What matters is that they allow students to place into classes that fit them, even skipping those intro classes for truly exceptional students. Cambridge, on the other hand, does not allow this.

[Anonymous]

Anonymous wrote:

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

Understood. Still this is the opposite of competition math in flavor. It's just calmly demonstrating useful skill, and it is walking the student in the right direction. The full test is not different in intent.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

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

Understood. Still this is the opposite of competition math in flavor. It's just calmly demonstrating useful skill, and it is walking the student in the right direction. The full test is not different in intent.

I think there's quite a bit of overlap. An American student, for example, might never have had to write a proof outside of geometry (even those dual enrolled at CC), whereas any American student preparing for USAMO will be learning proofs in depth.

[Anonymous]

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.

I am the PP you responded to here and have not posted since then. One of my majors was in math and yes I did math contests before college. I never knocked math competitions as shallow. But I also had friends more gifted than me who went into the field, are very successful, and who had never entered a math competition in their lives. I probably could have beat them at high school math competition questions because I had more familiarity from practice and better speed. Sure, math competitions are a great way to get young people into math, and my own kid has done them. But I hope we can agree it’s stupid to measure math potential only by this method. This is like saying you’re only a good musician if you have won music competitions. People do have ears and other ways to recognize talent.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

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.

Math 55 was replaced over 10 years ago by "Math 55" which is just Math 112, 123, 121, and 122 (real analysis , complex analysis, theoretical linear algebra, and group theory algebra), cohorted with only first years and granted only half credit so that that students are encouraged to take more math classes later on.

But Harvard is still tippy top tier university for math. There certainly is no institution "much more prestigious" than Harvard math department.

Some examples

https://www.usnews.com/education/best-global-universities/mathematics


https://www.niche.com/colleges/search/best-colleges-for-math/

I’m sorry what? Uchicago, MIT and Princeton are better at Harvard at Mathematics

DP, I think honors analysis at UChicago and math 216/218 at Princeton are more rigorous/challenging than math 55, but it's not a dealbreaker or anything. What matters is that they allow students to place into classes that fit them, even skipping those intro classes for truly exceptional students. Cambridge, on the other hand, does not allow this.

How do you know this? Do you have access to all the psets and exams?

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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

Understood. Still this is the opposite of competition math in flavor. It's just calmly demonstrating useful skill, and it is walking the student in the right direction. The full test is not different in intent.

I think there's quite a bit of overlap. An American student, for example, might never have had to write a proof outside of geometry (even those dual enrolled at CC), whereas any American student preparing for USAMO will be learning proofs in depth.

But a kid who loves math would be self learning math and getting to proof based math outside of school. Just like competition kids invest time outside of school.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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

Understood. Still this is the opposite of competition math in flavor. It's just calmly demonstrating useful skill, and it is walking the student in the right direction. The full test is not different in intent.

I think there's quite a bit of overlap. An American student, for example, might never have had to write a proof outside of geometry (even those dual enrolled at CC), whereas any American student preparing for USAMO will be learning proofs in depth.

Are you laying that proof thing a bit thick? No proofs after Geometry and even in Calculus? Almost all youtube videos regurgitate proofs as a sole means of explanation. Proofs look to be good on surface and sound intellectual - an intuitive understanding is what even HYPSM math/physics graduates don't achieve. The Oxford/Cambridge tutorials are meant to achieve this level of intuition that proofs alone do not generate.

[Anonymous]

Anonymous wrote: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.

OP Here: can you share more how your DD's experience at Harvard is? Is she pure or applied math? was it easy getting into grad classes? Did she take classes at MIT? how was other math students at Harvard?

lastly, any advice for my DS who's also gunning for Harvard math? ty!