Oxford or Cambridge for Pure math major

[Anonymous]

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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?

I've looked at syllabi and exams for honors analysis at UChicago and heresay for 216/218

[Anonymous]

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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.

I'm talking about making proofs, not understanding them.

[Anonymous]

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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.

While real analysis proof skills might carry over to the highschool material tested by STEP, math competitions are also focused on highschool material, so there's less of a leap there.