Best undergraduate math programs?

[Luckymama]

How does one look for a good undergraduate math program? What constitutes a good program? Is there a noticeable (to the outsider) difference in a program that turns out applied mathematicians (different kinds??) vs theorists? Particular courses to look for?

 

If it logically follows that good grad program=good undergrad program, what about colleges without grad students?

 

I know the obvious----MIT, Caltech, Princeton, Harvard, Harvey Mudd, Stanford, Berkeley.

 

Dd is curious. She is the sibling veteran of two different college searches and is now thinking ahead :)

[Kathy in Richmond]

Lol, it's hard to come up with any kind of definitive list.

 

I'd start by exposing her (IRL or even online for now since she's young) to different colleges so that she can start to articulate what's important to her: university or LAC, urban or rural, big or medium or small, close to home or far away, techy oriented school or one with a broader selection of majors, and for girls in STEM fields, whether she'd be comfortable in a school where there are a lot more males or whether she'd prefer a 50/50 balance.

 

Does she want research? Will she need access to grad classes early (that will rule out some departments right away)?

 

Some of those things were non-issues for my kids, while others mattered tremendously. Spending part of their summers at camps on different college campuses around the US also helped ds & dd figure out what they preferred. Mathcamp even runs a panel called 'the future of you" each summer, where different faculty & staff discuss life and math departments at all kinds of universities and LACs. They try to get the kids to think about the possibilities. :) And the campers also benefit by getting to know older students & hearing about their college plans.

 

The people in your student's department will make a big difference. There are terrific teachers almost everywhere who would be delighted to work with a capable and eager young math lover. How important is it to her that a good percentage of her fellow students are equally capable? Does she enjoy a collaborative atmosphere? What kind of difficulty or challenge level does she want in her coursework? Can she deal OK with stress? (the more difficult the school, the higher the stress levels if they're not careful) What kind of extracurricular activities is she looking for? (my dd wanted vibrant social dancing & Catholic communities, which narrowed it down for her)

 

In addition to your school list above, here's a sampling of some schools I like, places we've considered, & also some that have worked out happily for mathy friends of ours (and this is by no means complete!! there are plenty of places we're unfamiliar with)

 

research universities:

Carnegie Mellon - wonderful honors math program

Brown University - known for strong applied math

U Michigan

U Chicago

U Maryland Baltimore campus (UMBC) - a brilliant young lady we know is there as a full ride Meyerhoff Scholar in math. She'd completed a large chunk of the typical undergrad math major courses while homeschooling high school. They have wonderful mentorship, internships, and personalized attention.

U Rochester - good if she's interested in research. My experience there was excellent; honors math was taught out of Apostol then (but I'm not sure what they're using today).

SUNY Stony Brook - well known for math

Duke - lots of undergrad involvement; strong math; undergrads run the Duke math meet every fall

Rice

 

techy schools:

RPI

Harvey Mudd

Rose Hulman (USAMTS math competition originated there)

Georgia Tech (I'm not impartial at all!; dh & I met while I was teaching math there :-)

 

LACs:

Williams

Swarthmore

Macalester

Carleton

St Lawrence (Sam Vandervelde teaches math there. He's a pal of Richard R's; my kids adored his classes at camps & I'd go just for him :-)

 

Girls' Schools:

Smith - the 1st winner of Math Prize for Girls went to Smith

Wellesley - the woman who runs Mathcamp was on faculty there

Bryn Mawr

Mt Holyoke

[Tamarind]

St Olaf College has a strong math program. You might also look into Williams College, Hope College, and Luther College in Decorah.

[Luckymama]

Lol, it's hard to come up with any kind of definitive list.

 

I'd start by exposing her (IRL or even online for now since she's young) to different colleges so that she can start to articulate what's important to her: university or LAC, urban or rural, big or medium or small, close to home or far away, techy oriented school or one with a broader selection of majors, and for girls in STEM fields, whether she'd be comfortable in a school where there are a lot more males or whether she'd prefer a 50/50 balance.

 

She's been on campus tours with the older sibs so she does know about different school types. She used to think all colleges were like the research university down the street :D. She is used to being one of the few girls involved in the math club, Science Olympiad team, and the FLL team. She did ask if it would be like that everywhere---I couldn't answer that question.

 

Does she want research? Will she need access to grad classes early (that will rule out some departments right away)?

 

She hasn't been exposed to the idea of math research yet. She's decided to try for MathPath next year which would expose her to all kinds o' math and mathy ideas!

 

Some of those things were non-issues for my kids, while others mattered tremendously. Spending part of their summers at camps on different college campuses around the US also helped ds & dd figure out what they preferred. Mathcamp even runs a panel called 'the future of you" each summer, where different faculty & staff discuss life and math departments at all kinds of universities and LACs. They try to get the kids to think about the possibilities. :) And the campers also benefit by getting to know older students & hearing about their college plans.

 

The people in your student's department will make a big difference. There are terrific teachers almost everywhere who would be delighted to work with a capable and eager young math lover. How important is it to her that a good percentage of her fellow students are equally capable? Does she enjoy a collaborative atmosphere? What kind of difficulty or challenge level does she want in her coursework? Can she deal OK with stress? (the more difficult the school, the higher the stress levels if they're not careful) What kind of extracurricular activities is she looking for? (my dd wanted vibrant social dancing & Catholic communities, which narrowed it down for her)

 

Great questions to think about, now and in the future :)

 

In addition to your school list above, here's a sampling of some schools I like, places we've considered, & also some that have worked out happily for mathy friends of ours (and this is by no means complete!! there are plenty of places we're unfamiliar with)

 

research universities:

Carnegie Mellon - wonderful honors math program

Brown University - known for strong applied math

U Michigan

U Chicago

U Maryland Baltimore campus (UMBC) - a brilliant young lady we know is there as a full ride Meyerhoff Scholar in math. She'd completed a large chunk of the typical undergrad math major courses while homeschooling high school. They have wonderful mentorship, internships, and personalized attention.

U Rochester - good if she's interested in research. My experience there was excellent; honors math was taught out of Apostol then (but I'm not sure what they're using today).

SUNY Stony Brook - well known for math

Duke - lots of undergrad involvement; strong math; undergrads run the Duke math meet every fall

Rice

 

techy schools:

RPI

Harvey Mudd

Rose Hulman (USAMTS math competition originated there)

Georgia Tech (I'm not impartial at all!; dh & I met while I was teaching math there :-)

 

LACs:

Williams

Swarthmore

Macalester

Carleton

St Lawrence (Sam Vandervelde teaches math there. He's a pal of Richard R's; my kids adored his classes at camps & I'd go just for him :-)

 

Girls' Schools:

Smith - the 1st winner of Math Prize for Girls went to Smith

Wellesley - the woman who runs Mathcamp was on faculty there

Bryn Mawr

Mt Holyoke

 

Thank you for the list!

[Luckymama]

St Olaf College has a strong math program. You might also look into Williams College, Hope College, and Luther College in Decorah.

 

Thanks Tamarind :)

[Kathy in Richmond]

She's decided to try for MathPath next year which would expose her to all kinds o' math and mathy ideas!

 

:hurray: :hurray: :hurray:

 

Let me know if you have any questions. My two kids spent a combined total of five summers there, as campers & later as counselors. :)

[onaclairadeluna]

Can I join this discussion? DS is going to math camp this year, I am happy to hear that he will get some guidance about future plans. The older he gets the more out of my league I feel. DS's current wish list is a small school, close to nature, lots of abstract math (he's not much of an engineer practical guy...last thing I heard he mentioned an interest in theoretical physics). He has strong west coast preference and probably early access to grad classes. I think what he really needs is a cabin in the woods with Feynman, but I don't see that on the list of colleges. I am thinking Stanford if he can get in, maybe Caltech or Reed (Would it have enough math?...he'd love the laid back liberal arty atmosphere). Would Harvey Mudd be too much on the practical engineering side? Maybe he'll change his mind about the east coast, he doesn't love it. Too many people. And then there's the question of stress. Sheesh. That one is the hardest. He isn't into stress and competition at all. However he is way more stressed out when he isn't able to work at an advanced level. (Hence the dream about the campfire and the bongo drums). He has a year or so to think about this more but he's closer to needing a plan. Maybe after camp he'll have some more ideas. And then there is the getting into the school part. That's a whole other thing. Probably look at a couple of UCs just in case.

 

Lucky, your daughter will love mathpath. It is a transformational experience. My son spent two summers there and I share Kathy's jumping up and down enthusiasm. Kathy, are there really colleges with 50/50 female/male in the math department? When I graduated I think we had maybe 2 or 3 women out of I don't know 30 math majors and this was in the 1990's not the 1950's.

 

I went to a school that was supposed to have a really great math department. It was OK. I was not a stellar student so perhaps my perspective is skewed, but I do know good teaching. I had a handful of really wonderful profs. The others were all good solid mathematicians but not so much teachers. When I watched my first few MIT OCW lectures the scales fell from my eyes and I thought..."That is a good math program". I really think, especially in the undergraduate years, that this type of inspirational teaching is really important. Not all math professors who have the ability to guide students at the graduate level also have the ability to teach undergraduate courses. But then I am not sure if my son will have the same needs that I did back then with things like AOPS, math camps and other opportunities for kids to explore university math prior to college.

[Kathy in Richmond]

Can I join this discussion? DS is going to math camp this year, I am happy to hear that he will get some guidance about future plans.

 

Great news! :001_smile: He'll love it, and Colby was one of our favorite sites. My ds had his head in the sand concerning college till he got to Mathcamp & started hearing others' plans. Make sure your ds attends the Future of You panel; it's usually towards the end of the five weeks. My ds came home wanting to discuss all the different options.

 

DS's current wish list is a small school, close to nature, lots of abstract math (he's not much of an engineer practical guy...last thing I heard he mentioned an interest in theoretical physics). He has strong west coast preference and probably early access to grad classes. I think what he really needs is a cabin in the woods with Feynman, but I don't see that on the list of colleges. I am thinking Stanford if he can get in, maybe Caltech or Reed (Would it have enough math?...he'd love the laid back liberal arty atmosphere). Would Harvey Mudd be too much on the practical engineering side?

 

Those all sound great. We have a friend who is VERY theoretical who went to Harvey Mudd happily as a math major (& works full time for AoPS now :-) Reed is urban, but the campus doesn't feel that way. My son spent the summer there at Mathcamp '05 and came home determined to apply there for college (though he never did...five app's and he was DONE mentally..haha). It's quite good at physics, too, and everyone does a senior research thesis. Their grad school placement rate is outstanding.

 

Some of my kids' west coast camp friends ended up at Santa Clara U, UCLA, and UC Santa Barbara, just to throw out a few more names for you. If he doesn't want big schools, though, I guess that rules out the UCs for him. UCSC has a gorgeous nature-filled campus (MathPath '06 was there), but I know nothing about their math/physics departments.

 

Maybe he'll change his mind about the east coast, he doesn't love it. Too many people.

 

I betcha he'd like Williams for math/physics and lots of nature. And don't leave out considering MIT for a kid like yours. :)

 

And then there's the question of stress. Sheesh. That one is the hardest. He isn't into stress and competition at all. However he is way more stressed out when he isn't able to work at an advanced level. (Hence the dream about the campfire and the bongo drums). He has a year or so to think about this more but he's closer to needing a plan. Maybe after camp he'll have some more ideas. And then there is the getting into the school part. That's a whole other thing. Probably look at a couple of UCs just in case.

 

LOL, my kids would have loved the University of Mathcamp, but, alas, it doesn't exist yet! Just learning, collaborating, and not stressing over grades. :D FWIW, you really do need to consider the stress aspect, and it is more of a personality thing. My ds seemed immune to it, but my dd has stressed out more times than I've cared to see. She's finally adjusting half-way through, but still says that her ideal would be to homeschool the academic parts of college (she misses the freedom of setting her own learning schedule), but to have all the extra academic, community, & social resources that college has provided.

 

Kathy, are there really colleges with 50/50 female/male in the math department? When I graduated I think we had maybe 2 or 3 women out of I don't know 30 math majors and this was in the 1990's not the 1950's.

 

No, I think that math departments are still very gender imbalanced. What I was thinking of was the overall m/f ratio of the university (for example, MIT strives to keep about 50/50 balance). When dd took the freshman honors math sequence at Stanford, by year's end only 4 women remained in the class. She would have loved to have had more girlfriends to study with!

 

I went to a school that was supposed to have a really great math department. It was OK. I was not a stellar student so perhaps my perspective is skewed, but I do know good teaching. I had a handful of really wonderful profs. The others were all good solid mathematicians but not so much teachers. When I watched my first few MIT OCW lectures the scales fell from my eyes and I thought..."That is a good math program". I really think, especially in the undergraduate years, that this type of inspirational teaching is really important. Not all math professors who have the ability to guide students at the graduate level also have the ability to teach undergraduate courses. But then I am not sure if my son will have the same needs that I did back then with things like AOPS, math camps and other opportunities for kids to explore university math prior to college.

 

Yes, yes! I am taking Walter Lewin's electricity & magnetism right now through MITx (and I really am procrastinating on the take-home midterm by hanging out online :rolleyes:). His teaching is incredible, and the problem sets are such a fun challenge. If I'd had a physics class like this when I was younger, I think that I would have ended up majoring in the field.

 

IMO, this is where you & your ds (and Luckymama & her dd) should visit prospective schools and sit in on some math classes. The teachers and the style of teaching used can make a huge difference.

 

good luck!

[onaclairadeluna]

Thank you so much Kathy, that's just what I needed. I love the idea of having him actually sit in on classes and I will definitely have him check out "the future of you".

[Gwen in VA]

Do look at St. Olaf. It has an AMAZING math program (and sends lots of students to grad school in math!). It is a small LAC, so it will have a very different feel from most of the schools listed.

[daijobu]

 

Let me know if you have any questions. My two kids spent a combined total of five summers there, as campers & later as counselors. :)

 

Thank you for your offer. :)

 

We've looked at the MathCamp quizzes and sadly there are solutions posted for only 2 years. Those sorts of thought problems are very different from what we find in AoPS. Is there a source for more problems like the MathCamp quizzes? What would you recommend as preparation for someone who may want to apply in the future?

 

PS. I took honors math/calculus with Brad Osgood way back when! (It was 43H/44H/45H.) I saw Osgood is still there, but maybe in the school of engineering now. Unlike your dd, I barely scraped by, and dinged my GPA for it!

[Kathy in Richmond]

Thank you for your offer. :)

 

We've looked at the MathCamp quizzes and sadly there are solutions posted for only 2 years. Those sorts of thought problems are very different from what we find in AoPS. Is there a source for more problems like the MathCamp quizzes? What would you recommend as preparation for someone who may want to apply in the future?

 

Hi daijobu!

 

You're talking about MathPath, right? If I remember correctly, you have a daughter of that age, not Mathcamp age. Correct me if I'm wrong, but it really shouldn't make a huge difference; Mathcamp's quiz is the same sort of beast as MathPath's, just more challenging.

 

Yes, it sure is very different learning how to answer the kinds of in depth questions posed on these admissions quizzes. We lucked out with ds; it was the first year of MP & he got in based on his AMC 8 score alone - no need to do the quiz. So he learned proof techniques that summer at camp. Dd participated in Summer Solve It (sort of a junior USAMTS run by a prof at U Delaware for 4th to 7th graders) during the years leading up to her MP summer, but sadly, it doesn't run any longer.

 

Other things I did to help her prepare were to have her try any old MathPath quizzes that were posted online, similar to what you found. She did AoPS number theory and Mathcounts classes online during middle school & worked through the first classic AoPS problem solving volume. AoPS taught her a lot --the graders for the online classes are sticklers for proper mathematical writing. Also, we used Gelfand's Algebra and Trigonometry volumes in middle school, and they stretched her, too. I like how Gelfand treats math carefully in a technical sense and with great insight, making connections between algebraic and geometric thinking.

 

Ruth (lewelma) and I have recently been talking about how to prepare her son for the junior test of the New Zealand math olympiad program, which requires writing a take-home math paper similar in difficulty to the MP entrance quiz: (2012 junior prob set & solutions)

 

How much overlap is there between AoPS contest prep books and their standard curriculum?

 

Need help setting out a study plan for the Math Olympiad

 

How do Mandelbrot team problems compare to USAMTS problems?

 

I'd especially recommend using the Mandelbrot resources mentioned in the third thread. You can buy the books on the AoPS website, and I think they're very appropriate for your goals. Each volume includes several proof based contests with full solutions, in addition to short answer contests. Let her attempt one of the proof based team contests. If she struggles (and almost every kid does at first!), then read through the solution together with her until she understands it. Put it aside for a while, and later on pull out the same problem and try again. It's a process, and sometimes a lengthy one, but eventually it'll all come together if she's interested & willing to invest the time.

 

I also like MIT OCW 6.042 for getting into this deeper kind of math/proofs, and The Art & Craft of Problem Solving by Paul Zeitz & old USAMTS proof based contest problems for further work. The various high school math meets (HMMT, PUMaC, SMT, ARML, Duke) all have proof-based rounds, too, with old exams & solutions posted online (usually called the Power Round).

 

Finally, there are some good notes about proofs on the MP website itself, so definitely take a look at those. And get her started early! The problems are usually posted sometime during the fall, so keep checking the website. What I did was to print them out right away, and give my dd a LOT of time to think them over. Then more time to write them up! I usually tried to carve out regular weekly time for her to work on summer camp applications.

 

PS. I took honors math/calculus with Brad Osgood way back when! (It was 43H/44H/45H.) I saw Osgood is still there, but maybe in the school of engineering now. Unlike your dd, I barely scraped by, and dinged my GPA for it!

 

 

Cool! Dd took the sequence with Leon Simon (51H) and Eliashberg (52H & 53H)...very, very tough & demanding classes (_{and it did ding her gpa a bithaha}). I was proud of her for sticking it out. Currently, about 75% of the kids who start 51H drop out before the quarter is over. :ohmy:

[daijobu]

You know how some profs will often stop their explanation of a solution to say "The rest is trivial." (with a bunch of us students thinking it isn't trivial at all!) Osgood's version was to say "The rest you can do with your spine."

 

Thank you for your links and resources! That will keep us busy for some time!

 

If anyone has tips on obtaining a copy of the solutions manual to Zeitz's book, I'd love to hear them!