[quote=Anonymous][quote=Anonymous]Can anyone explain why nearly all the Putnam top 100 scorers are from MIT? Why aren’t the top students more evenly distributed among Princeton, Harvard, Chicago, Caltech, etc?[/quote]

MIT specifically selects students who will be able to win Putnam awards every year. They don't look at students who are not in that category.
Caltech has been playing the admissions game for some time now, which is why you'll see that they don't accept students who have the competition-capability only. (I really have serious doubts about Caltech because they played to get their yield at a higher level. Read the prof. letter published in 2023).
Princeton, on the other hand, will accept a non-competition expert in place of a competition expert. (As a counselor, I have first-hand experience with this.)
UChicago, we all know their marketing gimmick. (Do they really need that if they are known as the super elite?)
Harvard, they'll discard the math kid if the parents are not a legacy. Known fact![/quote]

This is all myth. MIT has Putnam kids because MIT has the oldest Putnam training program and Putnam kids want to go to college together.

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Anonymous wrote:Take NyU off and add some ivies and uchicago

Really? Ever hear of Courant? NYU is very good at math.

That's at the graduate level, though. I don't see any evidence of their undergraduate program being particularly rigorous.

Who said this is just about undergrad? Why do you make the rules?

And how do you determine if an undergrad program is rigorous? One of the smartest mathematicians I have ever met went to a completely random school for undergrad, mainly for financial reasons. They were highly motivated and did the work to get into an elite PhD program and went from there.

So we should just conclude that every college has a good math program since there’s always going to be an incredibly intelligent student who can make it work? What a useless comment.

I'm saying that it is very hard to differentiate between these schools at such a granular level and most people who are capable of doing so are likely doing better things with their lives than posting here. And that most people doing so might be doing it based on one or two data points, so I am pre-emptively shooting all of that down by providing a contrarian data point.

There are a handful of kids in America for whom the nuanced differences between different math departments truly matter. These kids are off the charts. You know them when you meet them (and you probably haven't met them). Skippy or Sanjay or Hong taking Calculus at TJ or Stuy as a freshman or sophomore does not qualify him in this group.

On the contrary, that elite group is the best equipped to make a random school work for them by impressing professors to get research opportunities, skipping prerequisites, taking grad courses first year even if that's against department policy, etc.

Skippy, Sanjay, and Hong need a school with a strong official math track that will challenge them without also requiring them to fight their way through red tape at the same time. Not to mention the social benefits of having a cohort of students at the same level as you whom you can bounce ideas off of and, yes, even learn from. And they stand a good chance of running out of math at a LAC, considering they could be taking analysis junior year.

Junior year? Analysis is a first or second year course for students who take MVC in high school. It is the standard honors freshman math class for the top tier of incoming math talent/preparation. Over 50 students per year take analysis as their first math course at a top school. The only prerequisite for analysis is MVC or Calculus and familiarity with proofs. (Or, the rare student who is extremely comfortable with abstract proof math but hasn’t bothered to learn calculus)

read the next comment. The only prerequisite for analysis is calculus.

At a particular university? Our DC’s requires proof-based linear algebra

It's arbitrary. Mine took real analysis and then linear algebra.
Usually one of those is the first proofs course, (or a Pure Math 101 for students with no previous exposure to pure math). The order doesn't matter, but some school put everyone in the same order to cohort students together.

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Anonymous wrote:Can anyone explain why nearly all the Putnam top 100 scorers are from MIT? Why aren’t the top students more evenly distributed among Princeton, Harvard, Chicago, Caltech, etc?

MIT specifically selects students who will be able to win Putnam awards every year. They don't look at students who are not in that category.
Caltech has been playing the admissions game for some time now, which is why you'll see that they don't accept students who have the competition-capability only. (I really have serious doubts about Caltech because they played to get their yield at a higher level. Read the prof. letter published in 2023).
Princeton, on the other hand, will accept a non-competition expert in place of a competition expert. (As a counselor, I have first-hand experience with this.)
UChicago, we all know their marketing gimmick. (Do they really need that if they are known as the super elite?)
Harvard, they'll discard the math kid if the parents are not a legacy. Known fact!

What does the non-competition expert need at Princeton?

Advanced coursework. We know a student there currently and she took complex analysis before going to college and is still grinding through curriculum. It's for advanced students.

What about international students or students from areas where official enrollment isn't feasible?

These days the top math kids are teaching themselves from YouTube videos or MIT online courses and the like. They don’t need Calc offered at their high school. They do it on their own because they love it.

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Anonymous wrote:Can anyone explain why nearly all the Putnam top 100 scorers are from MIT? Why aren’t the top students more evenly distributed among Princeton, Harvard, Chicago, Caltech, etc?

MIT specifically selects students who will be able to win Putnam awards every year. They don't look at students who are not in that category.
Caltech has been playing the admissions game for some time now, which is why you'll see that they don't accept students who have the competition-capability only. (I really have serious doubts about Caltech because they played to get their yield at a higher level. Read the prof. letter published in 2023).
Princeton, on the other hand, will accept a non-competition expert in place of a competition expert. (As a counselor, I have first-hand experience with this.)
UChicago, we all know their marketing gimmick. (Do they really need that if they are known as the super elite?)
Harvard, they'll discard the math kid if the parents are not a legacy. Known fact!

What does UChicago want from RD math / physics applicants?

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Anonymous wrote:Can anyone explain why nearly all the Putnam top 100 scorers are from MIT? Why aren’t the top students more evenly distributed among Princeton, Harvard, Chicago, Caltech, etc?

MIT specifically selects students who will be able to win Putnam awards every year. They don't look at students who are not in that category.
Caltech has been playing the admissions game for some time now, which is why you'll see that they don't accept students who have the competition-capability only. (I really have serious doubts about Caltech because they played to get their yield at a higher level. Read the prof. letter published in 2023).
Princeton, on the other hand, will accept a non-competition expert in place of a competition expert. (As a counselor, I have first-hand experience with this.)
UChicago, we all know their marketing gimmick. (Do they really need that if they are known as the super elite?)
Harvard, they'll discard the math kid if the parents are not a legacy. Known fact!

What does the non-competition expert need at Princeton?

Advanced coursework. We know a student there currently and she took complex analysis before going to college and is still grinding through curriculum. It's for advanced students.

What about international students or students from areas where official enrollment isn't feasible?

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Can anyone explain why nearly all the Putnam top 100 scorers are from MIT? Why aren’t the top students more evenly distributed among Princeton, Harvard, Chicago, Caltech, etc?

MIT specifically selects students who will be able to win Putnam awards every year. They don't look at students who are not in that category.
Caltech has been playing the admissions game for some time now, which is why you'll see that they don't accept students who have the competition-capability only. (I really have serious doubts about Caltech because they played to get their yield at a higher level. Read the prof. letter published in 2023).
Princeton, on the other hand, will accept a non-competition expert in place of a competition expert. (As a counselor, I have first-hand experience with this.)
UChicago, we all know their marketing gimmick. (Do they really need that if they are known as the super elite?)
Harvard, they'll discard the math kid if the parents are not a legacy. Known fact!

What does the non-competition expert need at Princeton?

Advanced coursework. We know a student there currently and she took complex analysis before going to college and is still grinding through curriculum. It's for advanced students.

Anonymous wrote:

Anonymous wrote:Can anyone explain why nearly all the Putnam top 100 scorers are from MIT? Why aren’t the top students more evenly distributed among Princeton, Harvard, Chicago, Caltech, etc?

MIT specifically selects students who will be able to win Putnam awards every year. They don't look at students who are not in that category.
Caltech has been playing the admissions game for some time now, which is why you'll see that they don't accept students who have the competition-capability only. (I really have serious doubts about Caltech because they played to get their yield at a higher level. Read the prof. letter published in 2023).
Princeton, on the other hand, will accept a non-competition expert in place of a competition expert. (As a counselor, I have first-hand experience with this.)
UChicago, we all know their marketing gimmick. (Do they really need that if they are known as the super elite?)
Harvard, they'll discard the math kid if the parents are not a legacy. Known fact!

What does the non-competition expert need at Princeton?

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Anonymous wrote:Take NyU off and add some ivies and uchicago

Really? Ever hear of Courant? NYU is very good at math.

That's at the graduate level, though. I don't see any evidence of their undergraduate program being particularly rigorous.

Who said this is just about undergrad? Why do you make the rules?

And how do you determine if an undergrad program is rigorous? One of the smartest mathematicians I have ever met went to a completely random school for undergrad, mainly for financial reasons. They were highly motivated and did the work to get into an elite PhD program and went from there.

So we should just conclude that every college has a good math program since there’s always going to be an incredibly intelligent student who can make it work? What a useless comment.

I'm saying that it is very hard to differentiate between these schools at such a granular level and most people who are capable of doing so are likely doing better things with their lives than posting here. And that most people doing so might be doing it based on one or two data points, so I am pre-emptively shooting all of that down by providing a contrarian data point.

There are a handful of kids in America for whom the nuanced differences between different math departments truly matter. These kids are off the charts. You know them when you meet them (and you probably haven't met them). Skippy or Sanjay or Hong taking Calculus at TJ or Stuy as a freshman or sophomore does not qualify him in this group.

On the contrary, that elite group is the best equipped to make a random school work for them by impressing professors to get research opportunities, skipping prerequisites, taking grad courses first year even if that's against department policy, etc.

Skippy, Sanjay, and Hong need a school with a strong official math track that will challenge them without also requiring them to fight their way through red tape at the same time. Not to mention the social benefits of having a cohort of students at the same level as you whom you can bounce ideas off of and, yes, even learn from. And they stand a good chance of running out of math at a LAC, considering they could be taking analysis junior year.

Junior year? Analysis is a first or second year course for students who take MVC in high school. It is the standard honors freshman math class for the top tier of incoming math talent/preparation. Over 50 students per year take analysis as their first math course at a top school. The only prerequisite for analysis is MVC or Calculus and familiarity with proofs. (Or, the rare student who is extremely comfortable with abstract proof math but hasn’t bothered to learn calculus)

read the next comment. The only prerequisite for analysis is calculus.

At a particular university? Our DC’s requires proof-based linear algebra

OSU allows students to enroll in honors analysis without calculus credit.

Anonymous wrote:Can anyone explain why nearly all the Putnam top 100 scorers are from MIT? Why aren’t the top students more evenly distributed among Princeton, Harvard, Chicago, Caltech, etc?

MIT specifically selects students who will be able to win Putnam awards every year. They don't look at students who are not in that category.
Caltech has been playing the admissions game for some time now, which is why you'll see that they don't accept students who have the competition-capability only. (I really have serious doubts about Caltech because they played to get their yield at a higher level. Read the prof. letter published in 2023).
Princeton, on the other hand, will accept a non-competition expert in place of a competition expert. (As a counselor, I have first-hand experience with this.)
UChicago, we all know their marketing gimmick. (Do they really need that if they are known as the super elite?)
Harvard, they'll discard the math kid if the parents are not a legacy. Known fact!

Anonymous wrote:Can anyone explain why nearly all the Putnam top 100 scorers are from MIT? Why aren’t the top students more evenly distributed among Princeton, Harvard, Chicago, Caltech, etc?

I think MIT looks for math competition champs more than most when composing their class.

They also offer a Putnam prep class. They are not alone in doing so, but it’s probably more heavily attended.

Some schools that never or rarely have Putnman winners still have great math depts. In some cases their academic calendar doesn’t align with the exam administration.

I think a student doing well on the Putnman is a legit achievement, but I would put more weight on math PhD feeder rates if they are serious about going deep in the field. That broadens the field of schools significantly. (Of course MIT does great there too.)

Most schools that focus on the liberal arts should have pretty good math departments.

Also, most USAJMO qualifiers also end up qualifying for USAMO, and by "USA(J)MO" OP might have meant they qualified for USAMO or USAJMO, rather than both, or both simultaneously.

I don't believe they almost all are self studying advanced undergraduate math, as it can be hard to self teach and those classes can be inaccessible. Hence, the need for (and thus creation of) Evan Chen's Napkin book, which introduces undergraduate math to math olympiad students.

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Anonymous wrote:NYU
Johns Hopkins
Rice
Harvey Mudd
UMich - I heard their Math Honors track is good?
Williams
Swarthmore
CMU

My kid is into math - likes both pure and applied. Qualified for USAJMO & USAMO and has a few other activities/achievements in math. Objectively would be among the top 50-100 students for their grade in math.

No, the MOPers would be top 50-100. Each year around 500 qualify for USA(J)MO, and that's not counting the similarly talented students who focused on learning advanced undergrad math rather than math competitions.

There are not many in this small group at places like UMD and UVA - certainly not enough to fill a class so the professor can go at a pace and depth that challenges them. At a place like that, their best option is begging to skip into real analysis/algebra for a challenge.

500/4 =125 MO/JMO per grade. Qualifying for both is rarer, suggesting higher level. Getting honorable mention or higher would solidify further. (PP didn’t mention). MO students are all doing advanced undergrad math in addition, with few exceptions.

MOP is “top” 15 per grade. 60 students across 4 grades.

Top math students at state schools will find themselves in classes with older students, but that’s not terrible. They can also take more courses per term, or attempt the harder problems in their textbooks, to increase pace and depth. They will also have plenty of research opportunities because their classmates aren’t interested. They will also find an extra $300k in their pocket, which isn’t bad.

Thank you for writing this. Even though DC made USAJMO and USAMO, it is not their primary focus; they are much more into research.

Very strong math students are much more widely distributed than I initially expected. Math departments are usually small and strong math students find their peers anywhere in the T100 and they have all the advantages you mentioned above.

That took the pressure off college admissions.

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Anonymous wrote:Take NyU off and add some ivies and uchicago

Really? Ever hear of Courant? NYU is very good at math.

That's at the graduate level, though. I don't see any evidence of their undergraduate program being particularly rigorous.

Who said this is just about undergrad? Why do you make the rules?

And how do you determine if an undergrad program is rigorous? One of the smartest mathematicians I have ever met went to a completely random school for undergrad, mainly for financial reasons. They were highly motivated and did the work to get into an elite PhD program and went from there.

So we should just conclude that every college has a good math program since there’s always going to be an incredibly intelligent student who can make it work? What a useless comment.

I'm saying that it is very hard to differentiate between these schools at such a granular level and most people who are capable of doing so are likely doing better things with their lives than posting here. And that most people doing so might be doing it based on one or two data points, so I am pre-emptively shooting all of that down by providing a contrarian data point.

There are a handful of kids in America for whom the nuanced differences between different math departments truly matter. These kids are off the charts. You know them when you meet them (and you probably haven't met them). Skippy or Sanjay or Hong taking Calculus at TJ or Stuy as a freshman or sophomore does not qualify him in this group.

On the contrary, that elite group is the best equipped to make a random school work for them by impressing professors to get research opportunities, skipping prerequisites, taking grad courses first year even if that's against department policy, etc.

Skippy, Sanjay, and Hong need a school with a strong official math track that will challenge them without also requiring them to fight their way through red tape at the same time. Not to mention the social benefits of having a cohort of students at the same level as you whom you can bounce ideas off of and, yes, even learn from. And they stand a good chance of running out of math at a LAC, considering they could be taking analysis junior year.

Junior year? Analysis is a first or second year course for students who take MVC in high school. It is the standard honors freshman math class for the top tier of incoming math talent/preparation. Over 50 students per year take analysis as their first math course at a top school. The only prerequisite for analysis is MVC or Calculus and familiarity with proofs. (Or, the rare student who is extremely comfortable with abstract proof math but hasn’t bothered to learn calculus)

read the next comment. The only prerequisite for analysis is calculus.

At a particular university? Our DC’s requires proof-based linear algebra

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:NYU
Johns Hopkins
Rice
Harvey Mudd
UMich - I heard their Math Honors track is good?
Williams
Swarthmore
CMU

My kid is into math - likes both pure and applied. Qualified for USAJMO & USAMO and has a few other activities/achievements in math. Objectively would be among the top 50-100 students for their grade in math.

No, the MOPers would be top 50-100. Each year around 500 qualify for USA(J)MO, and that's not counting the similarly talented students who focused on learning advanced undergrad math rather than math competitions.

There are not many in this small group at places like UMD and UVA - certainly not enough to fill a class so the professor can go at a pace and depth that challenges them. At a place like that, their best option is begging to skip into real analysis/algebra for a challenge.

500/4 =125 MO/JMO per grade. Qualifying for both is rarer, suggesting higher level. Getting honorable mention or higher would solidify further. (PP didn’t mention). MO students are all doing advanced undergrad math in addition, with few exceptions.

MOP is “top” 15 per grade. 60 students across 4 grades.

Top math students at state schools will find themselves in classes with older students, but that’s not terrible. They can also take more courses per term, or attempt the harder problems in their textbooks, to increase pace and depth. They will also have plenty of research opportunities because their classmates aren’t interested. They will also find an extra $300k in their pocket, which isn’t bad.

State schools can be bureaucratic. There is no guarantee a student can skip prerequisites or overload their first semester, or even afterwards. Usually the textbooks used have a lower ceiling than the ones used at top colleges (e.g. Bartle and Sherbet vs Rudin/Zorich) and the prerequisite chains are longer (e.g. the intro to proofs course requires calculus 2, and real analysis requires intro to proofs, so no freshman analysis)