Need help choosing Universities for a high-end math student

[daijobu]

Have you considered Indiana University?  My dd and I were just finishing up AoPS precalculus where they mentioned that an AoPS student had come up with a novel proof of Heron's formula.  After a bit of stalking, I found him at IU.  

[Kathy in Richmond]

Have you considered Indiana University?  My dd and I were just finishing up AoPS precalculus where they mentioned that an AoPS student had come up with a novel proof of Heron's formula.  After a bit of stalking, I found him at IU.  

 

 

Miles was on my dd's high school math team, and he was amazing then, too!  If I recall correctly, he was admitted to MIT and others, but chose Indiana for its strong music program.

 

[Lawyer&Mom]

I don't think that link means what you think it means. Those are the places where their phD graduates are now teaching. I picked one name from the list and googled it: http://math.sewanee.edu/facstaff/duffee.php

 

Fwiw, my ds is also doubling in math. He doesn't spend much time in the math dept, but of the people he knows one is attending UMich for math, another Vanderbilt for Econ, another UT- Austin for math. And none of those kids were superstar students, just good ones.

You must be right. Or one of their students just got a PhD at a community college! This is one time I'm thrilled to be wrong. I'm definitely in favor of good, affordable choices!

[lewelma]

The problem with Auckland is the housing situation.  It is really bad.  The university is in the middle of the city, but the housing has become so expensive that the students have to live *way* out to find something affordable.  So like 10 or more miles out.  And these are not nice places.  All of the students scatter to all these locations, so there is not really a sense of cohesion after 'work hours.' This is a huge negative for ds.  He wants more of a full immersion experience, does that make sense?

 

Butler and 8, I sure do know that many places get you where you want to be.  And Auckland was always the choice until last year when we found out that the classes would be way below level.  The head of maths at our local uni has a daughter at Auckland, and he said having seen their homework and exams, that he feels that his department is slightly harder in the classes than up there.  That is not good for ds.  He is tired of being top dog.  He is not arrogant, but I can see hints of it coming (please don't quote that). He *needs* to be a smaller fish.  He lives in NZ, he has been a big fish for his whole life, in all fields he has ever touched, not just math. Perhaps it is just different being in a country on the far side of the world with a population 1/100th the size of the USA.  Perhaps it makes your kids and mine see the world and their place in it differently.  I don't know.  But I do know that he *needs* to be a smaller fish.  And I am willing to sacrifice to pay for the experience.  

[8filltheheart]

Just be careful about how small of a fish he is. If he wants to attend a top grad school, not being a top fish will impact him and limit his options. Top grad programs will take top students.

[8filltheheart]

I also wonder if the problem is appropriate course placement? I don't know bc my ds thrives in the challenge of physics.

[lewelma]

Just be careful about how small of a fish he is. If he wants to attend a top grad school, not being a top fish will impact him and limit his options. Top grad programs will take top students.

 

Yes. exactly.  This is why I'm wondering if we are chasing the right goal. The end goal is to be the best mathematician that he can be, and being challenged in undergraduate is a huge piece this goal.  But then the end goal also includes grad school, so if being challenged when you are younger limits your options when you are older, then we need to prioritize differently.  But choosing to be NOT challenged as a way to ensure great grades that then ensures great grad school -- just seems wrong or sad or something.  But I know this is a competitive world and that I have to live in it and its realities. 

[lewelma]

I also wonder if the problem is appropriate course placement? I don't know bc my ds thrives in the challenge of physics.

 

Clearly it is.  But I'm just not clear how you place out of all the *standard* math classes.  So you simply jump over diff eq, and linear algebra, analysis and all the other 'easy' classes, because all of these classes are taught at too low a level at the university you are attending?  DS has said that he does NOT want to be self-studying all his classes.  He *wants* to be with others who love math, he is *very* gregarious. So how exactly do you jump 3 years of courses without studying all the material on your own?

[8filltheheart]

Yes. exactly.  This is why I'm wondering if we are chasing the right goal. The end goal is to be the best mathematician that he can be, and being challenged in undergraduate is a huge piece this goal.  But then the end goal also includes grad school, so if being challenged when you are younger limits your options when you are older, then we need to prioritize differently.  But choosing to be NOT challenged as a way to ensure great grades that then ensures great grad school -- just seems wrong or sad or something.  But I know this is a competitive world and that I have to live in it and its realities. 

 

That is why I am wondering about his dept interactions.    My ds has been able to progress to his level of challenge.  For example, he is taking an upper level geophysics class next semester.  It is a geology course, not a physics course. He has never taken a geology course in his life.  He corresponded with the professor and based on his background, he told ds that if he would take on the responsibility of familiarizing himself with the necessary geology topics, that he would waive all pre-reqs.  This is not the first course that he has skipped all pre-reqs for.  He simply asks and shares his background.  That is NOT an uncommon occurrence.  

 

 

For dd, she has already been told she needs to meet with their oral proficiency tester and they will work out appropriate placement for her, even if that placement is 400 level classes.

 

I would absolutely avoid schools that don't have grad programs b/c their course options would be too limiting.  But, if they can jump into upper level coursework, it can work.  Ds's freshman yr he was taking 400 level electromagnetic wave theory.

[8filltheheart]

Clearly it is.  But I'm just not clear how you place out of all the *standard* math classes.  So you simply jump over diff eq, and linear algebra, analysis and all the other 'easy' classes, because all of these classes are taught at too low a level at the university you are attending?  DS has said that he does NOT want to be self-studying all his classes.  He *wants* to be with others who love math, he is *very* gregarious. So how exactly do you jump 3 years of courses without studying all the material on your own?

 

I was typing while you were talking.  You take higher level courses.  It depends on the dept.  My kids spent months emailing depts.  I am not exaggerating.  Depts that responded inflexibly were eliminated.  Depts that emailed with more questions and were truly interested in working with them required more interaction and more clarification.

[StephanieZ]

Have you been on collegeconfidential? If not, I *highly* advise going there and posting this query. Tons of very knowledgeable folks!!
 

If you can swing the $$$$, I'm sure that MIT or similar elite technical type or general IVY schools would have plenty of brilliant professors and peers. If I could afford *any* school, I'd look at those sorts for your son, in particular because it sounds like he may be ready for grad-level work within 2-3 years of undergrad, so having elite professors may well be beneficial to him . . .

 

I wouldn't worry for a minute about boredom/repeating classes, IF he's at an elite school. If a class is easy, he'll just have more time to do other stuff, and there'll be tons of awesome stuff to do. He'd have tons of equally brilliant peers, which makes me expect that he won't be bored, ever. 

 

There are some state schools that are exceptional . . . Maybe GA Tech? Note that many of those top state schools have zillions of out of state students. My kids going to U Alabama (not at all an elite state school, but a solid one that is advancing) has more than half it's undergrad from out of state . . . There are plenty of other great state schools that similarly have lots of out of state and international students. 

 

 

[lewelma]

I was typing while you were talking.  You take higher level courses.  It depends on the dept.  My kids spent months emailing depts.  I am not exaggerating.  Depts that responded inflexibly were eliminated.  Depts that emailed with more questions and were truly interested in working with them required more interaction and more clarification.

 

Perhaps I don't get it. But the following is the core of my problem. Mike has said that there are core classes, material that all math majors need to know. My ds doesn't know all this material; he would have to study it.  If he studies it at a high level, he should be doing this in a class with like-minded students and an interested professor.  If he studies it at a low level just to place out of a too-easy class, then it seems he will have short changed himself in the long run by only going surface deep in the basics to get into advanced material. How is that in his best interest? 

[Butler]

I would never advocate to avoid a challenge in undergrad in order to keep good grades, etc. That's not what I'm saying (nor 8 if I understand her correctly). On the contrary my son entered college very young because he absolutely needed that challenge. Many people advocate to delay college entrance in order to have a better chance at elite school admission. Never mind the fact that we could not afford an elite school so that was never on the radar, my son would not have been able to dely his math progression. He lives and breathes it. What I am trying to say in my posts is that a very advanced student can find challenge in many schools, even non-elite state schools. It takes a school with enough courses to allow for progression and a school that allows for flexibility in that progression.

 

(Edited out personal info)

 

As long as the courses are available I don't think your son will have problems being allowed to take them in the majority of US colleges. I think this may be a worry that you don't need to have.

Edited March 14, 2017 by Butler

[lewelma]

As long as the courses are available I don't think your son will have problems being allowed to take them in the majority of US colleges. I think this may be a worry that you don't need to have.

 

But I still don't get it.  How does ds learn the basic content if he skips all the classes?  If he learns it at a high level, it will take him quite a lot of time and he would rather do that in a class.  If he does it at a low level just to get through the content, then isn't he doing himself a disservice?

 

The local uni placed ds as half way through the 2nd year number theory course when he was 13, but there was no way that he was allowed to take classes at the university as you have to be 16.  I had to beg and plead to get him access at age 15.75, plus he had to get through 11th grade english which was not happening earlier than 9th grade if he had a hope of getting a good grade (we have national exams here).  This means that he didn't have the opportunity that your ds had, Butler.  He couldn't start in on classes at a young age that would be still somewhat challenging.  He has had to self study, and now he has overshot the mark and all the core classes here are too easy.  But he still needs to get through the content.  He is just not sure that he wants to self study for the next 1.5 years until getting to a higher level university.  We could ask the department to do something, but I have no idea what we would actually ask for. 3rd year classes?  Skip multivariate calc, differential equations, statistics?  When does he learn that material if he skips the classes?  On his own in his spare time?  I'm just not sure that is the right path for a gregarious young man.

[JanetC]

If he hasn't learned multi variable calculus, why can't he take that class (as a lighter class for him if it's not an honors version or something) while also taking a graduate level class in a topic he has a strong background in for the challenge he wants? No reason he can't take two math classes in the same term, right?

[Butler]

My son self teaches a lot, always has. We accelerated him very early on but it was never enough so self learning was a necessity. The classes that he has taken have never been at his level even when he was very young so he augments. For classes that he skipped over to take grad level he either learned the material beforehand on his own (Internet) or learned the pre-req material as he went along in the class. This approach works for him but may not for someone like your son if he wants a classroom situation.

 

Word of advice though - going to an elite school for undergrad would not have allowed my son to learn at his pace with peers at his level. He is at one now for grad school and has told me that the undergrad classes there would not have been sufficient either without accelerating and taking grad level. I don't know your son's ability level so obviously don't know if he would fit better, but I wouldn't automatically assume that just because it's an elite school that it would be a perfect fit.

[Lawyer&Mom]

Don't forget that at an American school he will also have breadth requirements to fufill. An easier core math class, a more challenging graduate math class plus honors physics and honors English lit? (Or honors Chemistry, or honors World Civ?) I was just browsing the Alabama catalog. As a math major he would be required to pick up a minor. Greek? Electrical Engineering? Music? I think there would be lots to keep him busy.

[8filltheheart]

I think population might be a huge influence on perceptions. AL has a larger population than NZ. NC's population is twice the size. I don't know the ratio of college bound students, etc. But I think those stats might be interesting.

Edited March 14, 2017 by 8FillTheHeart

[JanetC]

Really good point: Urban NZ might be suburban USA.

 

Anyway, I pulled up webcaspar's public U's in the undergraduate origins of PhD's in math and statistics, and put the top few below. You can definitely scratch all of California off for merit aid hunting, but midwestern and southern U's are likely to have some. Check the websites.

 

University of California, Berkeley 18

University of Wisconsin-Madison 10

North Carolina State University 9

Ohio State University, The, Columbus 9

University of California, San Diego 9

University of California, Los Angeles 8

Arizona State University 7

California Polytechnic State University, San Luis Obispo 7

Rutgers, The State University of New Jersey, New Brunswick 7

University of California, Santa Cruz 7

University of Illinois at Urbana-Champaign 7

University of Maryland, College Park 7

SUNY, Stony Brook University 6

Texas A&M University, College Station 6

University of California, Davis 6

University of Minnesota, Twin Cities 6

University of Pittsburgh, Pittsburgh 6

Florida State University 5

University of Central Florida 5

University of Missouri, Columbia 5

University of Tennessee, The, Knoxville 5

University of Texas at Austin, The 5

 

Note that this is a lagging indicator: 2015 PhD graduates likely entered undergrad 10 more years ago.

 

Edit: fix formatting

Edited March 15, 2017 by JanetC

[idnib]

I don't have time right now to expound, but check out Harvey Mudd in CA as well. 

Edited March 14, 2017 by idnib

[HTRMom]

I am a baby here and just graduated from an elite private school as an engineer a few years ago myself. My husband just got his PhD in Physics a couple of years ago. So I have some thoughts. :)

 

The fact is, hardly any students are as advanced in coursework as he is, because you basically have to be homeschooled to get there. He's in an extremely small group of high school students who know so much math. There is simply not a school he could attend where there would be a large group of eighteen-year-olds who know multivariate calculus! So just get rid of that idea. He will either be retaking similar courses at a higher level with same-age peers or will be studying math with senior undergrads and beginning grad students. He may still be thrilled to find at a selective school that his peers are just as smart as he is, and he will enjoy making intellectual friendships. But they won't be in his math classes unless he's redoing classes.

 

Most American universities are narrowing the number of transfer credits possible, not increasing them. They don't want students coming in with years of credits and graduating in two years. Cuts into the bottom line...

 

Grad schools also will often not allow you to finish quickly because you already took most of the classes. So at some point in his career he will have to retake classes OR branch out and take more breadth of classes. There just aren't enough math classes to fill six years of higher education starting where he is. If he's going to do that anyway eventually, might as well do it in early undergrad, where the peer interaction is so valuable.

 

Is he just as advanced in Science? One possibility since he already knows so much of the undergrad math curriculum is to study either physics or computer engineering/programming/analysis type major, and fill in the rest of the math major too. If he wants to solve practical problems using math, math academia is probably not what he's looking for. He will probably end up somewhere in big computational supercomputer math stuff, because that's where the innovative problem-solving stuff is today. And as long as he's not advanced in computational methods already, he can start off on-level with peers. Even if he ends up in math grad school after the double-major, he won't regret the computing background.

 

Look for a school with high average SAT ACT scores. That will give him a whole school full of very smart people with different specialties.

 

 

Sent from my iPhone using Tapatalk

[katilac]

We could ask the department to do something, but I have no idea what we would actually ask for.  

 

 

This is exactly what he needs to say to the department. "Here is the situation, what would you advise? Can you talk to me about working deeper versus more quickly?" 

 

I think he should get into email contact with multiple schools ASAP, outlining his situation and his desires, and just honestly asking if they think their school would be a good fit, what would they advise, and so on.  You will learn a lot from the answers! 

 

I would include the info that he is from a different country and thus not familiar with US schools. I would outline the situation, ask for help, and end the email with all of his details - classes taken, test scores, competitions. Just because the US deals with so many more students, I think they are more likely to have dealt with similar scenarios before. I would be surprised if you don't get at least several helpful responses. 

 

He needs to be reaching out to school after school after school, imo. 

[katilac]

 

He will either be retaking similar courses at a higher level with same-age peers or will be studying math with senior undergrads and beginning grad students. He may still be thrilled to find at a selective school that his peers are just as smart as he is, and he will enjoy making intellectual friendships. But they won't be in his math classes unless he's redoing classes.

 

Most American universities are narrowing the number of transfer credits possible, not increasing them. They don't want students coming in with years of credits and graduating in two years. Cuts into the bottom line...

 

 

Look for a school with high average SAT ACT scores. That will give him a whole school full of very smart people with different specialties.

 

 

 

Retaking similar courses at a higher level can be very worthwhile, definitely not something to necessarily dismiss.

 

Remember that some universities will have opportunities for even freshmen to work on research or projects (individual or collaborative). Working on ways to apply the knowledge definitely adds another layer. 

 

Agreed on transferring in credits; you have to check with each and every school. 

 

Regarding ACT scores, one helpful trick it to google "XYZ University common data set." The CDS will give you more information than just the average and the range - it will tell you how many students scored over 30, and it also breaks down it down into math and other subscores. 

[8filltheheart]

Remember that some universities will have opportunities for even freshmen to work on research or projects (individual or collaborative). Working on ways to apply the knowledge definitely adds another layer.

Research is my ds's way of finding what it is he wants. He loves research. For him, finding the opportunity to work directly on a project with a professor vs being an assistant to a grad student was a big part of what he wanted. At one top school he was told by the dean of the physics dept that as a high school sr he had more direct research experience than their UGs bc their focus was on their grad students and UGs worked for the grad students. That was not the answer he wanted to hear.

[Butler]

I disagree about there not being enough advanced math courses at the grad level to fill the time or that any student would have to repeat at that level. My son started grad school having taken about 15 grad classes already. He will not run out of classes. There is always more math to learn. Also, most math PhD programs in the US on average only entail about 2 years of coursework. The rest of the time is research and dissertation.

[quark]

Ruth, I think you should visit the campuses and have your DS speak to the profs regarding higher math classes. In the SF Bay Area, 2 math genius kids, Evan Chen and Evan O'Dorney, attended MIT and Harvard respectively and found enough to challenge them. Both were IMO gold medalists if I am not mistaken. I suspect it was from dealing directly with profs, asking relevant questions (and I'm sure they didn't know all the questions in the beginning either and somehow figured it out as they went along) and chasing down the research paths themselves. I know Evan Chen took lots of math classes at Cal before entering MIT as a freshman (I think he switched from Harvard to MIT?). If I am not mistaken Evan O'Dorney also started taking classes at Cal very young (prior to high school I believe).

 

List down all your doubts, worries, questions and then ask at the campuses when you visit. Ask your DS to ask the questions. I think it will be a lot clearer once he has.

 

 

Edited March 15, 2017 by quark

[plansrme]

I was thinking about a couple more elites, and I am struggling with knowing what to do with flagship state schools and the preponderance of students that will be from a single state.  I'm seriously not sure how ds would feel if 85% of the students were from Georgia, for example.  

 

 

Have you seen the QS Rankings of the top mathematical universities in the world?  Georgia Tech is #25 on this list for 2016.  I guess I can see why your son might be intimidated by classes full of Georgia residents, but I can assure you that the math department at Tech is warm and welcoming and always willing to help a hard worker catch up. :leaving:

[idnib]

If I am not mistaken Evan O'Dorney also started taking classes at Cal very young (prior to high school I believe).

 

He did, and he was integral to the math circle too. He still comes back once in a while. Unless my recollection is faulty, when he went to Harvard he started with graduate-level math.

[Arcadia]

Your son can arrange to meet with head of dept for math for U of Waterloo if you decide to make a trip there in the future. We are interested in engineering and wasn't going to apply anytime soon so we didn't make an appointment.

 

Unless my recollection is faulty, when he went to Harvard he started with graduate-level math.

He was a IMO silver and gold medalist, won Intel Science Talent Search and went to Harvard.

 

"At Harvard, O’Dorney has taken the math department by storm. He is one of the few freshmen ever to place out of Math 55—the most advanced undergraduate math course offered—directly into graduate mathematics classes in his first semester.

...

He attended math classes at the University of California, Berkeley and literature classes with other homeschooled students.

...

O’Dorney contemplates one day working on number theory—the “most concentrated†form of math, he says. He is uninterested in the potential applications of his work, preferring instead to puzzle over pure math and number theory’s simple equations.

 

O’Dorney says that he hopes to be a math professor one day.

...

O’Dorney says he has found a community in the math department. He says that he appreciates the department’s intimate feel and the individual guidance that he receives.

 

The feeling is mutual. Harris says that admissions recruiters actively seek out talented math students, and that the department is lucky to have O’Dorney as a student.

 

“He’s content and he’s challenged,†says his mother, adding that O’Dorney has told her that he feels at home among his professors."

http://www.thecrimson.com/article/2012/1/27/Freshman-Math-Profile/?page=single

 

"He will now have the opportunity to explore his love of mathematics across the pond at the University of Cambridge. O’Dorney was recently named a Churchill Scholar and will complete Part III of Cambridge’s Mathematical Tripos next year.

 

O’Dorney was inspired to apply for the scholarship after hearing from past Harvard classmates who had also won the Churchill.

 

“Since the coursework is extremely flexible, I’m looking forward to conducting my own research and working with Cambridge professors outside of class,†O’Dorney said.

 

O’Dorney plans to pursue an academic career. Following his year at Cambridge, he will attend Princeton University, likely studying under recent Fields Medal recipient Manjul Bhargava.

 

At Harvard, O’Dorney concentrates in mathematics with a secondary field in music. A versatile composer and performer, he plays the organ and piano, and sings. He also composes for and leads Harvard’s Renaissance vocal chamber ensemble, the Lambda Singers, and lately has been exploring jazz piano."

http://news.harvard.edu/gazette/story/2015/03/senior-named-churchill-scholar/

Edited March 15, 2017 by Arcadia

[Joules]

Perhaps I don't get it. But the following is the core of my problem. Mike has said that there are core classes, material that all math majors need to know. My ds doesn't know all this material; he would have to study it.  If he studies it at a high level, he should be doing this in a class with like-minded students and an interested professor.  If he studies it at a low level just to place out of a too-easy class, then it seems he will have short changed himself in the long run by only going surface deep in the basics to get into advanced material. How is that in his best interest? 

 

Many U.S. universities have "Honors" sections of the same core classes to take care of this.  The Honors section is usually small with a professor heavily involved in research. The basic concepts are covered, but since the students are more advanced, the professor can spend more time on advanced topics and applications.  Sometimes they barely resemble the regular level core class.  It's been a long time, but I took honors intro calc and physics classes at Georgia Tech, and they were a whole different ballgame than the core.  If your ds is just looking at course descriptions, he may not be seeing opportunities like honors classes.

 

As to the small-big fish, I would encourage him to be careful.  It sounds like he is an enormous fish where he is, but having the pendulum swing ALL the way to the other side may create an enormous amount of stress.  There are downsides to the other side that he hasn't experienced and may not be able to factor in meaningfully.  A middle fish might be good for undergrad, being so far away from home, and then he can get into an elite grad school to be a small fish.  

Edited March 15, 2017 by Joules

[Shelly in VA]

I would definitely suggest visiting campuses and talking with math profs, and I would encourage you to look at schools that have an honors college. I have two students currently in college, and both have feel that their honors classes and programs have greatly enhanced their college experience. Both would say that their honors classes have been their favorite classes, in part because they expose them to so many people and ideas outside of their major.

 

As for math, ds20 is currently a math major at George Mason University (in VA). He loves the school, which is very diverse (students from all 50 U.S. states and students representing over 130 countries). It is also a Tier 1 research university with a big emphasis on undergrad research. The math department, while they couldn't give him credit for his high school courses in number theory or combinatorics, was eager to work with him on exempting some of the entry level math classes that he would have taken. He met with his math/honors advisor, and between his transcript and sitting for a test in the advisor's office, they took care of it before he registered for his first semester of classes.

 

When it came to looking at schools, I found it harder to search for ds than I did for dd22 (she graduates in May with a BS in Nursing). EVERYONE has a math program, which was not the case with nursing. So while we had to get much more specific in what features we were looking for at a university even to narrow our search initially, ultimately it helped us to have criteria in mind when we visited campuses and met with faculty. 

 

 

[lewelma]

Thanks guys for giving me so much to think about. 

 

So how do I track down honors programs in math?

[quark]

Thanks guys for giving me so much to think about. 

 

So how do I track down honors programs in math?

 

I googled math honors programs. :coolgleamA: :drool:

[mathnerd]

I am not very sure about the details, but I thought that I would throw this in anyway as I know that you are excellent at research :) State universities require a minimum number of months of residency after the out of sate student enrolls for them to become eligible for in-state tuition. For UCs, I think that this might be in the 12-24 months range. So, you are not looking at full price for the tuition for Berkeley or UCLA. 

 

The tech industry in california has many "Math Gods" who went to CalTech, MIT or Stanford. Those three are bound to have plenty of peers for your son :) Good luck to both of you!

[8filltheheart]

I am not very sure about the details, but I thought that I would throw this in anyway as I know that you are excellent at research :) State universities require a minimum number of months of residency after the out of sate student enrolls for them to become eligible for in-state tuition. For UCs, I think that this might be in the 12-24 months range. So, you are not looking at full price for the tuition for Berkeley or UCLA.

 

This is inaccurate information. Students under 24 will have a very difficult time establishing residency. http://www.ucop.edu/residency/establishing-residency.html

Edited March 15, 2017 by 8FillTheHeart

[mathnerd]

This is inaccurate information. Students under 24 will have a very difficult time establishing residency. http://www.ucop.edu/residency/establishing-residency.html

Thank you for that link. I was previously told by someone IRL that after 1-2 years of residency, most state U's will accept the student as an instate resident. But, your link states that a person can establish residency in California only by being physically present for a year before the first day of classes. This information is new to me and I stand corrected. 

 

"you must be continuously physically present in California for more than one year (366 days) immediately prior to the residence determination date (generally the first day of classes)"

[8filltheheart]

Thank you for that link. I was previously told by someone IRL that after 1-2 years of residency, most state U's will accept the student as an instate resident. But, your link states that a person can establish residency in California only by being physically present for a year before the first day of classes. This information is new to me and I stand corrected.

 

"you must be continuously physically present in California for more than one year (366 days) immediately prior to the residence determination date (generally the first day of classes)"

It is actually quite difficult to establish residencies in most states. In CA if you are under 24:

 

If you’re an unmarried undergraduate under the age of 24 and your parent(s) are not California residents, you must be able to document (for example, using tax returns, W-2 forms, bank statements) that you have been totally self-sufficient for two full years prior to the residence determination date, supporting yourself, for example, through jobs, financial aid, commercial/institutional loans in your name only, and documentable savings from your earnings. This also means you can't have been claimed as an income tax dependent by any individual or have accepted gifts (cash or other support) that contributed to your subsistence for two tax years immediately preceding the term.

[Pegs]

I'm an undergrad in math at a top 10 Australian university, about to transfer into their "advanced" math degree. It comes with a compressed first year calc subject, and personalised subjects (projects and special topics), including research for credit points.

 

I'd be happy to PM with you about my experiences as a student if you'd find that helpful at all.

 

I'm sorry that I have nothing to offer in regard to your search for a suitable institution in the US.

[Shelly in VA]

Thanks guys for giving me so much to think about. 

 

So how do I track down honors programs in math?

 

When we were looking at schools, we didn't look specifically for honors programs in math, but rather at honors colleges within the university. Once we were on campus, we talked with math professors about honors math offerings, but we found that while there are many standard honors courses, often professors will work with students to create an honors section for classes that don't already have them or even create an individual honors-level course where a student works closely with a professor.