I'm very confused by OP. Williams math department looks extremely applied math focused, even for a liberal arts college. The research they would get on campus would be applied mathematics research. If the goal is to go to graduate school in pure math, why you would go to a college without graduate courses is beyond me. This is not to say that lac grads don't go into graduate pure math, but it is ridiculously competitive and putting yourself in a place where pure math research happens and you can advance yourself with coursework makes a lot more sense.

You're afraid of the grind, but your kid wants to do pure math and presumably a PhD in mathematics? You sound a bit confused.

Anonymous wrote:OP: thanks for all the feedback so far. Def a lot to think about:

- DC wants to do pure math (he has a lot of experience with proofs) and loves problem solving. Also a very advanced math student

- toured both schools and liked both schools. Comes from a small high school hence liked Williams

- def aware that CMU will have better/more challenging math classes for him. But concerned about the applied math focus (and the grind at CMU)

- thought at Williams he would get more research opportunities

planning to go to both admitted student days; and looking forward to Ivy day decisions.

Hi OP,
Parent of pure math major who is currently in a top PhD program.

Re: your concern about CMU's applied math focus, I don't think that's a meaningful issue for the undergrad curriculum. CMU has LOTS of pure math and theory courses for undergrads including real analysis, complex analysis, probability theory, combinatorics, topology, graph theory, set theory, model theory, etc. Also important to know they can take graduate level classes. My son specifically chose a university with a graduate math department because he was interested in taking graduate level classes. He came in with a deep bench of mathematical knowledge and needed the additional rigor and breadth that graduate level courses would offer. He was also advised that for entry to the very top PhD programs in math, a transcript with some graduate level classes is almost expected (not true for all math PhD programs, but true for some of the top tier). To be fair, this is probably only a consideration for a small subset of math students, and knowing nothing about your son I only mention it in case he falls into that group. That would be one key difference between CMU and Williams.

I think the applied vs pure issue would be a bigger consideration if your son was applying for graduate school. CMU would not be the best place to get a phd in number theory, for example. But IMO it's not something your kid needs to worry about for undergrad. Have him take a look at the list of courses offered by the math department at both schools and compare.

The grind at CMU is real. But if your son decides to pursue a math curriculum in preparation for a PhD, some grind is to be expected. On the flip side, the kids who are truly mathematically gifted are not the same ones complaining about the grind. They are sort of in their own world of mathy paradise, lol.

I'm curious why you think he'd have more access to research at Williams. There should be opportunities at either school. Understand that access to pure math research as an undergrad is hard to get, but REUs are one way to do so. And Williams SMALL REU is excellent (not sure if they give any preference to their own?) It is true that SLAC professors are typically more accessible to undergrads than profs at research institutions, but the flip side is the research institution has more research going on, not to mention graduate level coursework.

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Anonymous wrote:OP: thanks for all the feedback so far. Def a lot to think about:

- DC wants to do pure math (he has a lot of experience with proofs) and loves problem solving. Also a very advanced math student

- toured both schools and liked both schools. Comes from a small high school hence liked Williams

- def aware that CMU will have better/more challenging math classes for him. But concerned about the applied math focus (and the grind at CMU)

- thought at Williams he would get more research opportunities

planning to go to both admitted student days; and looking forward to Ivy day decisions.

Go to CMU for sure. The math department isn’t that large there, but it’s very well staffed.

He’ll learn this in college, but the whole pure/applied split is a bit arbitrary and a lot of applied coursework relies fully on pure mathematics.

Because CMU’s math department is quite small and his options are much more widespread, there are a ton more research opportunities for a students

And now the frank part: Math isn’t easy. If he’s afraid of a challenge, good luck doing math at Williams or CMU. We know math majors at LACs who work like they’re in the navy. Those are the best students and they get into PhD programs- that is life.

Applied math is rather different from pure math, except at schools that don't have strong pure math departments. However, a high school student really has no idea whether they'd thrive in pure math or applied math. Pure math is arcane art. Applied math PhDs often come from pure math undergrad, since undergrad pure math is a foundation for rigorous applied math and physics.

I'd say the exact opposite is true. It's very easy for me to unrigorously teach you statistical linear models, but a rigorous statistics department is obsessed with pure mathematics.

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Anonymous wrote:OP: thanks for all the feedback so far. Def a lot to think about:

- DC wants to do pure math (he has a lot of experience with proofs) and loves problem solving. Also a very advanced math student

- toured both schools and liked both schools. Comes from a small high school hence liked Williams

- def aware that CMU will have better/more challenging math classes for him. But concerned about the applied math focus (and the grind at CMU)

- thought at Williams he would get more research opportunities

planning to go to both admitted student days; and looking forward to Ivy day decisions.

Go to CMU for sure. The math department isn’t that large there, but it’s very well staffed.

He’ll learn this in college, but the whole pure/applied split is a bit arbitrary and a lot of applied coursework relies fully on pure mathematics.

Because CMU’s math department is quite small and his options are much more widespread, there are a ton more research opportunities for a students

And now the frank part: Math isn’t easy. If he’s afraid of a challenge, good luck doing math at Williams or CMU. We know math majors at LACs who work like they’re in the navy. Those are the best students and they get into PhD programs- that is life.

Applied math is rather different from pure math, except at schools that don't have strong pure math departments. However, a high school student really has no idea whether they'd thrive in pure math or applied math. Pure math is arcane art. Applied math PhDs often come from pure math undergrad, since undergrad pure math is a foundation for rigorous applied math and physics.

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Anonymous wrote:We know a math major currently transferring out of Williams due to major fit and QOL issues. He’s so far been underwhelmed by the department and wis he would’ve gone to his other choice, Uchicago. Really make sure a tiny school in the middle of nowhere with limited faculty is what you want.

Why on earth did he pick Williams over UChicago in the first place? UChicago for pure math is significantly better than Williams.

Williams is the #1 SLAC and that means a lot. A lot.

I graduated with a BS in math from Stony Brook. Yes Williams is great. But Pure Math at the UChicago is exceptionally good. Undergrads get to do independent research in Algebraic geometry and number theory from a vast number of professors. I'm just puzzled when someone says because Williams is the #1 LAC therefore it's better than Chicago for pure math. I did my junior REU at Chicago and that place is exceptional. And i.am saying this as someone who was attending another very good pure math program at Stony Brook.

Anyone who has actually looked at the opportunities would laugh if you suggested williams is better than Chicago at math, because it has a few seminar courses in math.

"More" is not "better". Your kid won't take every class Chicago offers or research with every professor. The PhD numbers don't lie.

Doing math research with a professor is not very important for a math undergrad. There is plenty to learn in class and seminar, and summer research programs. Math research, unlike other subjects, is very similar to classes, but with no teacher and less textbook support. Math homework is research, but smaller. Doing harder homework with less help is more research. You don't need access to a special lab or funding to do math research.

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Anonymous wrote:When you look at the top math reu, Duluth, very few spots across decades have gone to LAC students: https://sites.google.com/view/gallian-reu/additional-information/list-of-participants?authuser=0

SLACs are great, but the difference in talents and options between a medium elite university and Williams or Pomona (two gold standard LACs for math) is pretty vast.

Which other math REUs are considered "top"?

CMU SUAMI and SMALL are both pretty well known and important. Duluth is the best of the best, though.

How is Duluth so elite when the school itself isn't, even for undergrad mathematicians? Why wouldn't highschool wannabe mathematicians go to Duluth for undergrad to get guaranteed access to the same profs conducting these top REUs?

Many research programs for undergrads is focused on being exploratory/first time research. This is rarely publishable and often meant as an exposure program pipeline to a masters/phd program the institution offers.

Duluth is not this. Duluth is built on the idea of students generating their own research and publishing at a professional level. It’s alum have received various prizes and acknowledgments throughout the math community.

My point is why don't appropriately talented students choose to got to Duluth for undergrad where they can get access to all the same professors who manage the Duluth REU without needing to go through the competitive application process?

This is a VERY interesting question that deserves its own whole thread.

1. Duluth MINNESOTA is paradise in the summer, and frozen hell in the winter (school term)

2. An REU is just 1 or 2 professors, not a whole department. Research opportunity isn't the only valuable part of school, despite DCUM obsession. Duluth REU students (undergrads who are at the preparation of level of normal grad students) spend their semesters at schools like MIT and Harvard with larger, more challenging math departments, if they got admitted.

3. Duluth REU is the Joe Gallian REU. Joe Gallian is retiring after 50 years, and the famous Duluth REU is shutting down, and Colin Defant is moving it to wherever he goes after his postdoc, TBD:
https://sites.google.com/view/gallian-reu/additional-information/who-am-i

Anonymous wrote:Pomona is better than Williams for pure Math and UChicago is better than Pomona. But if you learn math from any of these schools you will get a similar fantastic experience.

I wouldn't go to CMU for math just my opinion. If you are interested in pure math go to a college that make it easier for undergrad to work independently with professors in their Junior years. CMU is not that school.

CMU makes this very easy. There's only about 100 math majors per class and a number of them are in applied mathematics. If you are genuinely interested (and good, is the key) at pure math, you'll have a lot of professors to work with and propel you.

Pomona is better than Williams for pure Math and UChicago is better than Pomona. But if you learn math from any of these schools you will get a similar fantastic experience.

I wouldn't go to CMU for math just my opinion. If you are interested in pure math go to a college that make it easier for undergrad to work independently with professors in their Junior years. CMU is not that school.

Anonymous wrote:

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Anonymous wrote:We know a math major currently transferring out of Williams due to major fit and QOL issues. He’s so far been underwhelmed by the department and wis he would’ve gone to his other choice, Uchicago. Really make sure a tiny school in the middle of nowhere with limited faculty is what you want.

Why on earth did he pick Williams over UChicago in the first place? UChicago for pure math is significantly better than Williams.

Williams is the #1 SLAC and that means a lot. A lot.

I graduated with a BS in math from Stony Brook. Yes Williams is great. But Pure Math at the UChicago is exceptionally good. Undergrads get to do independent research in Algebraic geometry and number theory from a vast number of professors. I'm just puzzled when someone says because Williams is the #1 LAC therefore it's better than Chicago for pure math. I did my junior REU at Chicago and that place is exceptional. And i.am saying this as someone who was attending another very good pure math program at Stony Brook.

Anyone who has actually looked at the opportunities would laugh if you suggested williams is better than Chicago at math, because it has a few seminar courses in math.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:We know a math major currently transferring out of Williams due to major fit and QOL issues. He’s so far been underwhelmed by the department and wis he would’ve gone to his other choice, Uchicago. Really make sure a tiny school in the middle of nowhere with limited faculty is what you want.

Why on earth did he pick Williams over UChicago in the first place? UChicago for pure math is significantly better than Williams.

Williams is the #1 SLAC and that means a lot. A lot.

I graduated with a BS in math from Stony Brook. Yes Williams is great. But Pure Math at the UChicago is exceptionally good. Undergrads get to do independent research in Algebraic geometry and number theory from a vast number of professors. I'm just puzzled when someone says because Williams is the #1 LAC therefore its better than Chicago for pure math. I did my junior REU at Chicago and that place is exceptional. And i.am saying this as someone who was attending another very good pure math program at Stony Brook.

Anonymous wrote:OP: thanks for all the feedback so far. Def a lot to think about:

- DC wants to do pure math (he has a lot of experience with proofs) and loves problem solving. Also a very advanced math student

- toured both schools and liked both schools. Comes from a small high school hence liked Williams

- def aware that CMU will have better/more challenging math classes for him. But concerned about the applied math focus (and the grind at CMU)

- thought at Williams he would get more research opportunities

planning to go to both admitted student days; and looking forward to Ivy day decisions.

Go to CMU for sure. The math department isn’t that large there, but it’s very well staffed.

He’ll learn this in college, but the whole pure/applied split is a bit arbitrary and a lot of applied coursework relies fully on pure mathematics.

Because CMU’s math department is quite small and his options are much more widespread, there are a ton more research opportunities for a students

And now the frank part: Math isn’t easy. If he’s afraid of a challenge, good luck doing math at Williams or CMU. We know math majors at LACs who work like they’re in the navy. Those are the best students and they get into PhD programs- that is life.

Anonymous wrote:OP: thanks for all the feedback so far. Def a lot to think about:

- DC wants to do pure math (he has a lot of experience with proofs) and loves problem solving. Also a very advanced math student

- toured both schools and liked both schools. Comes from a small high school hence liked Williams

- def aware that CMU will have better/more challenging math classes for him. But concerned about the applied math focus (and the grind at CMU)

- thought at Williams he would get more research opportunities

planning to go to both admitted student days; and looking forward to Ivy day decisions.

https://math.williams.edu/courses/placement/

https://www.cmu.edu/math/undergrad/exams/mathematics-maturity-survey.html

See how the math department determines placement at both Williams and CMU, and familiarize yourself with the math major progression at both schools to see how placement affects the courses you can take.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:When you look at the top math reu, Duluth, very few spots across decades have gone to LAC students: https://sites.google.com/view/gallian-reu/additional-information/list-of-participants?authuser=0

SLACs are great, but the difference in talents and options between a medium elite university and Williams or Pomona (two gold standard LACs for math) is pretty vast.

Which other math REUs are considered "top"?

CMU SUAMI and SMALL are both pretty well known and important. Duluth is the best of the best, though.

How is Duluth so elite when the school itself isn't, even for undergrad mathematicians? Why wouldn't highschool wannabe mathematicians go to Duluth for undergrad to get guaranteed access to the same profs conducting these top REUs?

Many research programs for undergrads is focused on being exploratory/first time research. This is rarely publishable and often meant as an exposure program pipeline to a masters/phd program the institution offers.

Duluth is not this. Duluth is built on the idea of students generating their own research and publishing at a professional level. It’s alum have received various prizes and acknowledgments throughout the math community.

My point is why don't appropriately talented students choose to got to Duluth for undergrad where they can get access to all the same professors who manage the Duluth REU without needing to go through the competitive application process?

OP: thanks for all the feedback so far. Def a lot to think about:

- DC wants to do pure math (he has a lot of experience with proofs) and loves problem solving. Also a very advanced math student

- toured both schools and liked both schools. Comes from a small high school hence liked Williams

- def aware that CMU will have better/more challenging math classes for him. But concerned about the applied math focus (and the grind at CMU)

- thought at Williams he would get more research opportunities

planning to go to both admitted student days; and looking forward to Ivy day decisions.