Are these schools good for math (pure, or applied)?

[Anonymous]

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!

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.

[Anonymous]

Anonymous wrote: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.

"Description#

The Napkin project is a personal exposition project of mine aimed at making higher math accessible to high school students."

He wrote a whole book because found himself surrounded by high schoolers who were ready (and he presumed able) to learn all the topics of advanced undergraduate mathematics!

Evan Chen, the most math-contest-obsessed person on Earth, went to college for pure math for 5 semester courses during high school.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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

UMD, for one.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Unless SLACs are particularly appealing I’d take off Swarthmore and Williams. For applied, not sure why MIT, Stanford and CalTech aren’t on the list - they are top 10. I’d swap Michigan for UCLA and Berkeley if looking for a large public school. Willing to go overseas - Cambridge in the UK. If also interested in Pure math - MIT, Stanford, UCLA, CalTech, Chicago, Berkeley and HYP. Cambridge and CMU as well.

I would put Michigan over UCLA for math. Their honors math sequence is better.

Frankly, one has Terrance Tao

He teaches the entire undergrad curriculum? Wow!

[Anonymous]

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 has the oldest Putnam training program. (Most schools, even top schools, don't have any Putnam training at all, because professors think it's silly.)

Like attracts like. Birds of a feather flock together. Math contest kids want to be together and crave the contest wins, so they prefer MIT.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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.

That's because their "Honor Analysis" class is Calculus, like Montgomery Blair's.

It's very hard to compare university math courses. There is no standard naming system, and huge variation in depth and rigor. Catalogs of MIT and Harvard are good benchmark because they offer 4 variations of the same class with different levels of depth and rigor, so you can see the difference.

OSU's Real Analysis I class (roughly equivalent to MIT or Harvard's post-calculus sophomore Real Analysis class, or highest calculus/analysis class for exceptional first-years) is this masters level class:
https://math.osu.edu/courses/math-5201

[Anonymous]

Anonymous wrote:

Anonymous wrote:

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

These will all be good. But if a truly gifted student - Rice, Harvey Mudd, and Williams. A math undergrad will get a lot more opportunities there than at Michigan, CMU, and JHU.

Completely wrong! Caltech if truly gifted and ready for research if you need a small college. Out of that group, really only Harvey Mudd has the course availability and research depth/clout to accelerate you, but you’ll be spending A LOT of time not doing math to finish their core.

Top undergrads in math at research universities get red carpet service and work with amazing professors early on. For special attention, I’d look at UCSB CCS.

can you give an example of this "red carpet service" outside of UCSB CCS?

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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.

That's because their "Honor Analysis" class is Calculus, like Montgomery Blair's.

It's very hard to compare university math courses. There is no standard naming system, and huge variation in depth and rigor. Catalogs of MIT and Harvard are good benchmark because they offer 4 variations of the same class with different levels of depth and rigor, so you can see the difference.

OSU's Real Analysis I class (roughly equivalent to MIT or Harvard's post-calculus sophomore Real Analysis class, or highest calculus/analysis class for exceptional first-years) is this masters level class:
https://math.osu.edu/courses/math-5201

I doubt MB's analysis course uses Spivak and Folland as the texts.

In any case, many universities have the "or instructor permission" prerequisite, which allows mathematically mature students to skip the line. Technically, even calculus isn't necessary if you use a book like Tao that starts from the basics.

Rice has math 302, Reed has math 112.

Also, what are the names of each of the four versions of the same class offered by Harvard and MIT?

[Anonymous]

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

These will all be good. But if a truly gifted student - Rice, Harvey Mudd, and Williams. A math undergrad will get a lot more opportunities there than at Michigan, CMU, and JHU.

Completely wrong! Caltech if truly gifted and ready for research if you need a small college. Out of that group, really only Harvey Mudd has the course availability and research depth/clout to accelerate you, but you’ll be spending A LOT of time not doing math to finish their core.

Top undergrads in math at research universities get red carpet service and work with amazing professors early on. For special attention, I’d look at UCSB CCS.

can you give an example of this "red carpet service" outside of UCSB CCS?

Berkeley. If you’re a top undergrad at Berkeley (obviously very few students), you can get top research advisors and will be passed along by research faculty. Same with Princeton. Of course, this is an extraordinarily small percent of undergrads

[Anonymous]

Anonymous wrote:Can't speak to anywhere but UChicago, but the Math 183-185 sequence, which is applied math for anyone going into exact sciences, is fantastic for students who want mastery and are willing to do 20 hours / week on problem sets minimum. The point is--you're actually going to learn this stuff if you put in the work. It's basically all of freshman year and 1/3 of sophomore year. The only issue is that it's hard to go from that to being a Math major because they really tailor it for other majors.

The Chicago 183 sequence is for STEM capable kids. It’s advanced math methods as a tool which will help you do your quantum or stat mech problem sets. But it is far from the math that a math major at UChicago or anywhere else would find interesting or research worthy. They aren’t in the same universe.

[Anonymous]

Anonymous wrote:

Anonymous wrote:Can't speak to anywhere but UChicago, but the Math 183-185 sequence, which is applied math for anyone going into exact sciences, is fantastic for students who want mastery and are willing to do 20 hours / week on problem sets minimum. The point is--you're actually going to learn this stuff if you put in the work. It's basically all of freshman year and 1/3 of sophomore year. The only issue is that it's hard to go from that to being a Math major because they really tailor it for other majors.

The Chicago 183 sequence is for STEM capable kids. It’s advanced math methods as a tool which will help you do your quantum or stat mech problem sets. But it is far from the math that a math major at UChicago or anywhere else would find interesting or research worthy. They aren’t in the same universe.

100%, IBL or Honors analysis is the better path for math students.

[Anonymous]

Anonymous wrote:

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

These will all be good. But if a truly gifted student - Rice, Harvey Mudd, and Williams. A math undergrad will get a lot more opportunities there than at Michigan, CMU, and JHU.

Completely wrong! Caltech if truly gifted and ready for research if you need a small college. Out of that group, really only Harvey Mudd has the course availability and research depth/clout to accelerate you, but you’ll be spending A LOT of time not doing math to finish their core.

Top undergrads in math at research universities get red carpet service and work with amazing professors early on. For special attention, I’d look at UCSB CCS.

can you give an example of this "red carpet service" outside of UCSB CCS?

Berkeley. If you’re a top undergrad at Berkeley (obviously very few students), you can get top research advisors and will be passed along by research faculty. Same with Princeton. Of course, this is an extraordinarily small percent of undergrads

How does a top undergrad a Berkeley get top research advisors? How does an undergrad know which research advisors are top and which are not in order to ask the top ones to advise research?

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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.

That's because their "Honor Analysis" class is Calculus, like Montgomery Blair's.

It's very hard to compare university math courses. There is no standard naming system, and huge variation in depth and rigor. Catalogs of MIT and Harvard are good benchmark because they offer 4 variations of the same class with different levels of depth and rigor, so you can see the difference.

OSU's Real Analysis I class (roughly equivalent to MIT or Harvard's post-calculus sophomore Real Analysis class, or highest calculus/analysis class for exceptional first-years) is this masters level class:
https://math.osu.edu/courses/math-5201

I doubt MB's analysis course uses Spivak and Folland as the texts.

In any case, many universities have the "or instructor permission" prerequisite, which allows mathematically mature students to skip the line. Technically, even calculus isn't necessary if you use a book like Tao that starts from the basics.

Rice has math 302, Reed has math 112.

Also, what are the names of each of the four versions of the same class offered by Harvard and MIT?

See here

https://www.math.harvard.edu/media/Math-for-first-year-students-2021-2022.pdf

https://math.mit.edu/academics/undergrad/subjects/181x.html

[Anonymous]

Anonymous wrote:

Anonymous wrote:

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

These will all be good. But if a truly gifted student - Rice, Harvey Mudd, and Williams. A math undergrad will get a lot more opportunities there than at Michigan, CMU, and JHU.

Completely wrong! Caltech if truly gifted and ready for research if you need a small college. Out of that group, really only Harvey Mudd has the course availability and research depth/clout to accelerate you, but you’ll be spending A LOT of time not doing math to finish their core.

Top undergrads in math at research universities get red carpet service and work with amazing professors early on. For special attention, I’d look at UCSB CCS.

can you give an example of this "red carpet service" outside of UCSB CCS?

Berkeley. If you’re a top undergrad at Berkeley (obviously very few students), you can get top research advisors and will be passed along by research faculty. Same with Princeton. Of course, this is an extraordinarily small percent of undergrads

How does a top undergrad a Berkeley get top research advisors? How does an undergrad know which research advisors are top and which are not in order to ask the top ones to advise research?

The professors invite them.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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

These will all be good. But if a truly gifted student - Rice, Harvey Mudd, and Williams. A math undergrad will get a lot more opportunities there than at Michigan, CMU, and JHU.

Completely wrong! Caltech if truly gifted and ready for research if you need a small college. Out of that group, really only Harvey Mudd has the course availability and research depth/clout to accelerate you, but you’ll be spending A LOT of time not doing math to finish their core.

Top undergrads in math at research universities get red carpet service and work with amazing professors early on. For special attention, I’d look at UCSB CCS.

can you give an example of this "red carpet service" outside of UCSB CCS?

Berkeley. If you’re a top undergrad at Berkeley (obviously very few students), you can get top research advisors and will be passed along by research faculty. Same with Princeton. Of course, this is an extraordinarily small percent of undergrads

How does a top undergrad a Berkeley get top research advisors? How does an undergrad know which research advisors are top and which are not in order to ask the top ones to advise research?

The professors invite them.

+1, office hours don’t stop existing at large schools.