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lewelma
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My dh's PhD advisor happens to be the head of her department, and she has recently met the new head of the math department.  They got to talking and he has offered to talk to ds and me about what the different universities in NZ and Australia have to offer in way of math.  I would like to have a clear cut list of questions to ask.

 

First of all, ds can be kept busy by AoPS until about 15 3/4, at which point he will go to the local university for maths.  He will go full time at 17.5, unless he wants one more chance at the IMO (then he would go at 18).  So there are really 2 different sets of questions I need to come up with, one about how the local university can cater to him while young, and the other about what different universities can provide.

 

So help me think this through.  Please clarify my ideas and questions and add to them!

 

Local university questions

 

1) I see a serious disconnect between the NZ exam based math that all kids will have and AoPS.  I am not clear on what will happen in the first math class taken after high school (multivariate calculus?). If it is designed for kids coming out of the NZ system it will be waaaay too easy. My ds could not just skip this class because he won't have learned the content yet, but his mathematical reasoning will far exceed the students who studied NCEA maths.  How does the university cater for these differences? 

 

2) My ds is not planning on taking the NZ exams.  Will the university be willing to take the AoPS transcript and a portfolio of his proofs?

 

3) Will the university accept his number theory and combinatorics as equivalent to a first class in those topics and let him skip up to the second class?

 

Comparison of Universities (this is where I need a lot of help because I don't know how to compare math departments)

 

1) I'm guessing that some university math departments train mathematicians and other act as support for other majors (biology, economics, etc).  Obviously, we need to know which is which.

 

2) I believe University of Auckland's focus is on applied maths - statistics and operations research.  So we need to ask some sort of question about theoretical vs applied focus of the departments.

 

3) I'd be interested in knowing if there is a chance to be involved in an undergraduate research project.  This was possible for me in Biology but Math might just be totally different, so I'd like some advice here.

 

4) I also understand that some universities in Australia have honors programs.  Not sure this guy will know much about it, but he might.

 

Any comments or guidance would be well appreciated!

 

Ruth in NZ

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Is there an honors program for math majors? or honors sections of the regular math courses? What is the difference in textbooks and teaching style?

 

The same problem exists in the US. For example, kids coming from the AoPS, math olympiad training, and the stronger math camps often enter university here with high level knowledge, but no official credit in those areas. In particular, linear algebra, multivariable calculus, and differential equations (the first classes they are likely to be placed in as a math major w/o credit) are often very mechanistic and way too simplistic. Better universities here will offer honors sections, often using textbooks such as Tom Apostol's Calculus or Spivak's Calculus, which integrate a lot of theory & proofs and introduce higher level mathematics such as the beginnings of real analysis into these subjects.

 

Kids can also sometimes "challenge" classes, which means taking an exam given by the department which demonstrates their knowledge of that subject. This might not give them official credit for the course, but will at least exempt them from having to take it. My son was able to skip several classes doing that, while my daughter went into the very theoretical honors sequences in math and CS at her university.

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Is there an honors program for math majors? or honors sections of the regular math courses? What is the difference in textbooks and teaching style?

I don't think the local university has honors anything, but will definitely ask. I'm sure I could find out which textbooks are used for the early classes. Can you tell me which multivar calc, linear alg, and diff eq textbooks are the more theoretical ones and which are the weakest.

 

The same problem exists in the US. For example, kids coming from the AoPS, math olympiad training, and the stronger math camps often enter university here with high level knowledge, but no official credit in those areas. In particular, linear algebra, multivariable calculus, and differential equations (the first classes they are likely to be placed in as a math major w/o credit) are often very mechanistic and way too simplistic. Better universities here will offer honors sections, often using textbooks such as Tom Apostol's Calculus or Spivak's Calculus, which integrate a lot of theory & proofs and introduce higher level mathematics such as the beginnings of real analysis into these subjects.

Well, I'm glad to hear it is not just me worrying about this issue, or just NZ that would struggle.

 

Kids can also sometimes "challenge" classes, which means taking an exam given by the department which demonstrates their knowledge of that subject. This might not give them official credit for the course, but will at least exempt them from having to take it. My son was able to skip several classes doing that, while my daughter went into the very theoretical honors sequences in math and CS at her university.

 

So are you just talking about taking the final exam for classes you want to skip? Does AoPS calculus do more than just standard calculus? Would it likely be just a couple months of self study to be able to take the multivariate calc exam? Obviously, hard to know, but just curious.

 

The plan is for him to do the WOOT while concurrently taking math classes at the university. So perhaps he can get all his theoretical passion focused on the WOOT and just tolerate the mechanistic university math for 1.5 years.

 

They are so desperate for mathematicians in NZ that DS has already been offered a job at a bank in their finance department after graduation. :huh:  It is all about who you know in NZ and they always make exceptions, so given that he is one of 3 students in the city working at this level, and that most kids go local for university, they are like to bend over backwards to facilitate a good experience for him.  Given this cultural difference, are there other questions you  might suggest I ask?

 

Also, I really need to know *now* if he is aiming for a NZ or Australian university as the entrance requirements differ.  The Head offered to compare the universities.  What kind of questions do I need to ask to find out where ds would be best served?  I really struggle to know what to look for or even what questions to ask. Math is a tool for me to answer scientific questions.  Math is a passion for ds.  So even though I took 9 university math/stats classes, I still can't advise him. sigh.

 

Thanks!

 

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I don't think the local university has honors anything, but will definitely ask. I'm sure I could find out which textbooks are used for the early classes. Can you tell me which multivar calc, linear alg, and diff eq textbooks are the more theoretical ones and which are the weakest.

If they don't have honors sections, ask whether they'd offer independent study (tutorial style)in such cases? Some profs might enjoy working individually with enthusiastic & capable students.

 

It would probably be easier if you could report back the list of textbooks used. There are so many! Apostol's two texts, for example, would cover all of calculus (including multivariable), linear algebra, and diff equations, all proof-based. The math prof you're meeting with should be aware of Apostol, so ask how their texts compare.

 

For an independent multivariable calc book, I really like Marsden & Tromba's Vector Calculus; for linear algebra, my faves are Strang's Intro to Linear Algebra (see MIT OCW Math 18.06) or Sheldon Axler's Linear Algebra Done Right; for diff equations I like an older book by George Simmons, Differential Equations with Applications and Historical Notes.

 

But...there are tons of other good textbooks out there, too. And my kids have had great experiences with profs who taught from their own notes w/o textbooks at all.

 

So are you just talking about taking the final exam for classes you want to skip? Does AoPS calculus do more than just standard calculus? Would it likely be just a couple months of self study to be able to take the multivariate calc exam? Obviously, hard to know, but just curious.

At MIT, ds was allowed to take "advanced standing exams" in subjects he'd self-studied at home. They were supposed to be similar to final exams. They awarded credit for those he passed, and he skipped right on to the next level. In another course, Math for Computer Science, which was a rehash of the combinatorics, set theory, logic, number theory, etc, that he was very familiar with already, simply talking about his previous experience with his department got him an exemption.

 

Yes, your boy could probably self study multivariable calc over several months at home. Or he could take an online class via CTY or Stanford to learn it. I doubt he'd have any trouble.

 

The plan is for him to do the WOOT while concurrently taking math classes at the university. So perhaps he can get all his theoretical passion focused on the WOOT and just tolerate the mechanistic university math for 1.5 years.

That's actually not a bad idea. He'd still learn the basics, and he'd get the higher stuff in later years. WOOT is plenty challenging!

 

They are so desperate for mathematicians in NZ that DS has already been offered a job at a bank in their finance department after graduation. :huh:  It is all about who you know in NZ and they always make exceptions, so given that he is one of 3 students in the city working at this level, and that most kids go local for university, they are like to bend over backwards to facilitate a good experience for him.  Given this cultural difference, are there other questions you  might suggest I ask?

A job offer already?! That's too much!

 

I'd ask whether they'd offer independent study classes if/when they find he's exhausted their coursework. Are the graduate level classes open to advanced undergrads? Do they have any research experiences for math majors, during the school year or during the summer?

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Also, I really need to know *now* if he is aiming for a NZ or Australian university as the entrance requirements differ.  The Head offered to compare the universities.  What kind of questions do I need to ask to find out where ds would be best served?  I really struggle to know what to look for or even what questions to ask. Math is a tool for me to answer scientific questions.  Math is a passion for ds.  So even though I took 9 university math/stats classes, I still can't advise him. sigh. 

Thanks!

I'd try to find a listing of required coursework & available electives for math majors at each university. What do their math majors do after graduation? Do they track most of their students into applied areas like actuarial science, statistics, finance, etc? Or do they have a strong theoretical track with plenty of offerings in algebra, analysis, topology, geometry, number theory, etc, & prepare several students per year for math grad school?

 

I'd want to know how often their grads are accepted to math PhD programs, and where.

 

What kind of research opportunities exist?

 

Is there any school with a cohort of students like your son? Where do the New Zealand math olympiad team kids go?

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Well, Kathy has said pretty much everything I would have, so I shan't bother repeating. 

 

Sometimes you can get extra theory while being enrolled in the standard course rather than being formally enrolled in a separate independent study. I've never had anyone ask, but I'd be more than happy to draw up a study plan for a serious calculus/analysis text such as Spivak or Apostol for a student to work alongside my class while still being formally enrolled in "calculus 1". 

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I'd try to find a listing of required coursework & available electives for math majors at each university. What do their math majors do after graduation? Do they track most of their students into applied areas like actuarial science, statistics, finance, etc? Or do they have a strong theoretical track with plenty of offerings in algebra, analysis, topology, geometry, number theory, etc, & prepare several students per year for math grad school?

 

I'd want to know how often their grads are accepted to math PhD programs, and where.

 

What kind of research opportunities exist?

 

Is there any school with a cohort of students like your son? Where do the New Zealand math olympiad team kids go?

 

excellent questions.  thanks!

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Well, Kathy has said pretty much everything I would have, so I shan't bother repeating. 

 

Sometimes you can get extra theory while being enrolled in the standard course rather than being formally enrolled in a separate independent study. I've never had anyone ask, but I'd be more than happy to draw up a study plan for a serious calculus/analysis text such as Spivak or Apostol for a student to work alongside my class while still being formally enrolled in "calculus 1". 

 

Thanks Kiana.  This is exactly the type of thing that I thought might be possible, but I hated to ask it if it were a completely unreasonable request.  Will bring it up.

 

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Kids can also sometimes "challenge" classes, which means taking an exam given by the department which demonstrates their knowledge of that subject. This might not give them official credit for the course, but will at least exempt them from having to take it. My son was able to skip several classes doing that, while my daughter went into the very theoretical honors sequences in math and CS at her university.

This is probably very individual when it comes to universities, but mine did something similar. He entered university having completed many undergrad math courses through dual enrollment, but overall he was mostly self taught. In the second week of classes as a freshman, he met with the professor teaching one of the graduate level series in which he was interested. After that conversation, the prof set it up for him to meet with the department head. After meeting with the dept head he was given authorization to enroll in graduate courses. No formal tests, no credit given for any classes, but since his first semester he has been taking nothing but graduate math courses.

 

As to the rest of your questions, I unfortunately know nothing about NZ or Australian schools. I would just make sure that there is a ceiling high enough for him. That is what ruled out LACs (undergraduate only) schools for my son. Also, as far as research, if your son is interested in applied math it should be easy enough to find opportunities. Pure math is more difficult.

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Thanks Butler.  He will have 1.5 years going part time at the local university, so I am not sure what level he will be at when he actually goes full time. Depends on if he takes 1 or 2 classes per term or takes any summer courses. 

 

Just found this at the local university:

 

In addition to the four entry levels already mentioned, advanced and gifted students
may be granted direct entry to 200-level courses. This applies to very few students.
Entry is at the discretion of the appropriate programme director.

 

so should be able to enter 200 level courses after AoPS calculus.  That means that he would be at the 300 level when he starts university full time, but a degree here is only 3 years because there is no liberal arts year.  So not sure what that means.  I guess you just do grad level work.  Will check on that too.

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Local University has PhD program.  Here are the areas "for which supervision may be available"  So I guess this is the focus of the Math section of the maths department which also contains majors in stats & operations research, and logic & computation.  Seems pretty broad and theoretical, so should be able to get some good mentorship for ds pre-undergrad.  Will ask about mentoring also.

 

 

 

DISCRETE MATHEMATICS, ALGEBRA AND NUMBER THEORY
Current staff interests encompass combinatorics, matroid theory, graph theory, universal
algebra and coalgebra, category theory, number theory and arithmetic geometry.

 

LOGIC AND THE THEORY OF COMPUTATION
This covers aspects of mathematical and philosophical logic and theoretical computer
science, including model theory, set theory, computability theory, complexity of computation,
algorithmic randomness, algebraic logic and semantics of intentional logics.

 

ANALYSIS, TOPOLOGY AND GEOMETRY
There are interests in singularity theory and algebraic invariant theory with applications to
robotics ; algebraic topology , functional and harmonic analysis; and differential geometry .

 

APPLIED MATHEMATICS AND THEORETICAL PHYSICS
Dr xx has research interests in mathematical modelling with differential equations,
with applications in biomathematics, industrial processes, geophysical processes, and two-
phase fluid flow in porous media. XX works in general relativity and quantum field
theory, as well as in differential equations and modelling.

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Looks like an excellent range of expertise at your local uni, Ruth. And the mention of exempting a few very strong students from the 100 level courses is encouraging.

 

Lots of subject choice & a PhD program should be workable if that's where your son decides to attend. You never know what subfield will intrigue him, so you want those choices. My own ds discovered your second area, "theory of computation," at Mathcamp at age 15, and that set him in a new direction and led to his career choice.

 

Good luck at your meeting!

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The main problem will be getting him in at all. There are a list of entrance qualifications - NZCEA3, Cambridge, Bacclaureate, ACE, Steiner school certificate plus a couple of others. There is a process to get qualification from other countries accepted and there is an over 20 admission. He would have no trouble with first year maths papers (statistics would be his weakest I suspect) but admission straight to 200 is generally based on the scholarship exams which can be taken in year 13.

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what is wrong with this forum today? I vaguely recall you mentioning he was going to do Cambridge? Also the maths team has to count for something. But the system isn't set up for kids like your son - it is set up for kids who have done NZCEA3.

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The main problem will be getting him in at all. There are a list of entrance qualifications - NZCEA3, Cambridge, Bacclaureate, ACE, Steiner school certificate plus a couple of others. There is a process to get qualification from other countries accepted and there is an over 20 admission. He would have no trouble with first year maths papers (statistics would be his weakest I suspect) but admission straight to 200 is generally based on the scholarship exams which can be taken in year 13.

 

 

Also the maths team has to count for something. But the system isn't set up for kids like your son - it is set up for kids who have done NZCEA3.

 

 

Thanks for your comments kiwik!  It is so important to keep my plans realistic for the NZ situation.  I so know that the NZ system was not designed for a student like my son. Certainly not a homeschooled student like my son.  In fact, he was the first homeschooler to ever make it into the IMO training camp.

 

So here is the plan; tell me if you think I have a chance in hell of making it work....

 

For full-time entrance requirements in feb 2018 (applying one year early): DS gains NCEA external credits for Physics3 and Chemistry3.  He earns internal and external credit for Music3 (from a school I hope) and for English3 (from correspondence school). This gives him enough credits for guaranteed entrance with the exception of maths.  (If they require it, he can also study for the Mandarin exam). Then, he counts the IMO  as his entrance exam for maths (this is assuming he gets there which is realistic, but see other options below).  He applies discretionary entrance which allows the university to use international qualifications.  We assume that the IMO would count as an international qualification, although an unusual one!

 

But what we actually need is for him to be able to take classes a full year and a half before he finishes high school.  So, he will not actually be entering university as a full-time student, and will only need a professor's permission (I think, but this is one of the things I will be asking at this meeting).  DS is pretty adamant that he will not take the NCEA or Cambridge maths exam. His focus is on proof based mathematics, not speed-based algorithmic maths. He has no interest in refocusing for a period of time to do well on one of these exams.  So here are his options for entering *just* a maths class in year 11:

 

1) He should be on the squad of 12 in 2016 (maybe even in 2015), and will have been training with a maths prof from our local university (this is what the squad gives you).  He expects this prof will support his application for a 200 level class in the winter of 2016.

2) Massey allows for portfolio assessment (this is not widely known).  He can get his maths portfolio assessed, attend Massey for a couple of maths classes, and then transfer to Vic.  Once he has been taking maths classes at Vic, he expects that Vic will count them as meeting his maths requirements for full-time entrance requirements in 2018 (so he may not need the IMO as an entrance exam).

3) If all else fails, he can delay taking university courses by 6 months, studies for the scholarship exam in November 2016, and begin taking classes as a year 12 in 2017. He would rather avoid this if at all possible.

 

What do you think?

 

Man oh man, have I put more than a few brain cells into this problem.  Trying to side step an exam-based entrance system is a serious pain in the neck! 

 

We are also having to pull out the big guns to get internal assessment for music (through a school).  DS takes music from the concert master of the NZSO, who will be calling the head of the music department at Coll next week with the personal request for internal assessment. Cross your fingers. NZ works on who you know.  So I'm hoping that who I know will come in handy!

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If you can get the support of the head of maths at Massey - saying we are only going here until I can transfer to Vic may not go down that well. In fact one of the deciding factors may be that they think he will make them look good so they will ask you why you are applying to them rather than Vic. The new this year numeracy and literacy standards may be an issue - I can't work out exactly what they are but you probably need to get approval for the maths team to count or he will need a maths paper at level 3. There are high school kids who do level one papers extra-murally while in year 13 so going to lectures may be OK. From looking at the AOPS sequence I think he may be ok with first year stats but to be honest I am not hugely mathy and I went from year 12 to first year stats and calc. I didn't get As but I got a B+ in calc even though I had only done the 3 week intro to calc in year 12.

 

There is more flex in the system than you would think and there may still be a provisional registration option. Just be prepared to research and keep pushing.

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Very good points.  My plan is to send the Prof we are meeting next week some of my ds's proofs in number theory, combinatorics, and algebra.  Just to set expectations.  Give him time to skim through them before we see him. So when we come in with a million questions, including 'can ds take maths classes without NCEA3 qualifications' he will know where we are coming from. 

 

I'll go look at the numeracy and literacy standards again.  They just keep changing!  I'm sure I will need lots of approval to get anything through that is not standard.  AoPS is accredited in the USA so perhaps it can count as level 3 papers.

 

I also told ds that in between AoPS courses I expect him to start studying stats.  The stats portion of NCEA3 is not difficult, in fact as far as I could tell from the course description the 100-level stats class is not difficult.  We are about to see how much squish there is in the system.

 

Thanks so much for your comments.  They give me more things to ask this guy next week.

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The main problem will be getting him in at all. There are a list of entrance qualifications - NZCEA3, Cambridge, Bacclaureate, ACE, Steiner school certificate plus a couple of others. There is a process to get qualification from other countries accepted

 

Good news.  Talked to chief admissions officer today and there is a category called 'personal interest' that is not on the website or publicized at all (but is in the statutes), where if you can prove that your child has completed all available high school level coursework, you can take single classes at the university.  And best yet, ds does NOT have to take *any* standardized test to go into this category. All he needs is the support of the faculty.  Then, once he has taken individual classes, they can count as his maths requirement for full-time entrance.  So we are off the hook for all standardized testing in math!

 

Happy dance over here! :hurray:

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Definitely not late to the party.  My ds just finished making up his proof portfolio yesterday, and I have drafted the letter.  We hope to send it tomorrow.

 

So thanks for the extra ideas.

 

I don't think we are going to try for any credit, just access to 200-level courses when he is 15.5 There are 5 required courses: Calc 1, calc 2, discrete maths, statistics, and mathematical reasoning (which I think is the learn how to write proofs class).   The main problem we will have is the Statistics.  So I am going to ask for the book they use for the 100 level class, and get ds to do it in the next 1.5 years.  The 100-level stats class looks really easy, so I'm going to ask if he can test out.

 

I think the plan is definitely to go to a cheaper and/or local undergrad and then get into an elite maths department for grad school, which actually might be in china.

 

Although the IMO stuff is driving my son right now, he is really not too caught up in it.  I think he has a very good shot at representing NZ as there is just not a focus in maths in this country and not enough competition to keep him off the team.  However, he very definitely may *not* get a medal.  He just loves maths, and this competition stream is a good way for him to meet others with his passion through both AoPS and the NZ summer program.  My guess is that once he gets into university part time, he is not likely to need the competition for that human element and the desire to be involved might fade.  Only time will tell.

 

Thanks so much for taking the time to respond.

 

Ruth in NZ

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If your DS has a good shot at making the team then he should definitely be going for it

Can you tell me why? Obviously, it would help with university entrance, but if he goes local that won't matter. Is it something that you would put on your resume even after finishing undergrad?

 

As for making it onto the team, well he was 13 when he made it into the camp of 24, and he felt he was about middle of the pack for the juniors - so maybe around #19. The ten most senior kids leave every year to be replaced with 5 additional new senior kids and then the rest kind of moving up from the juniors. He has until he is 18, so 4 more chances (3 if he goes to university a year early). The numbers are in his favour, and he could possibly go twice.

 

I went on the local uni for BSc, elite uni for PhD path. I had some regrets. The local uni was solid, but I found I was out of touch (this was pre-internet) and un/under educated in some parts of math. The local expertise may not cover all the mainstream topics.

This is definitely my concern, which is why I am getting serious about the research. If he needs to go to Australia, I will need to do some changes in his high school program to get him in. And those changes might need to be happening now.

 

Thanks for your insight.

 

Ruth in NZ

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A big difference between UK and USA for PhD (not sure about other countries) is that in the UK there's no coursework, you jump straight into research and try to finish in 3 years, whereas in the USA there is coursework and it takes longer.

Unless I'm mistaken, the time from bachelors to PHD in the US and UK is essentially the same. In the US, a Bachelors degree holder can apply directly to a PhD program which generally takes about five years including about two years of coursework, no need to obtain a Master's degree first. In the UK, a Bachelor's holder applies to a Masters program first which takes about two years, then applies to a PhD program for an additional three years.

 

End result is the same amount of time invested. (This is obviously very generalized.)

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Good news. Talked to chief admissions officer today and there is a category called 'personal interest' that is not on the website or publicized at all (but is in the statutes), where if you can prove that your child has completed all available high school level coursework, you can take single classes at the university. And best yet, ds does NOT have to take *any* standardized test to go into this category. All he needs is the support of the faculty. Then, once he has taken individual classes, they can count as his maths requirement for full-time entrance. So we are off the hook for all standardized testing in math!

 

Happy dance over here! :hurray:

Yay. Good to know. That must be how high school kids do extramural papers some times.

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The main reason to do it would be for the community of learners.  He just has no peers in the homeschooling community and I have had no luck with getting local schools to allow him to join the physics club (which is competitive internationally).  And there are no math clubs.  Right now AoPS is filling that void, but I am concerned about his focus on internet relationships over real ones. 

 

I am working on other outlets for friendships by focusing on other things he likes to do like violin and badminton and tramping.  But the bonds he formed after 1 week of math camp would take him 1 to 2 years to form through other activities.  It is just that different to him.  Math is his passion, and he needs a community of learners.  AoPS classes end for him in 1.5 years and I am hoping that university part time will be good enough.

 

I should also add that I can keep teaching/facilitating him in Science for 2 more years, and then he needs university classes in that subject also.  I am already paying for tutors in mandarin and violin that cost more than the cost of full time enrolment each year.  At some point it is a bit of a burden to keep him *out* of full time enrolment.

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I could also be mistaken, but my understanding is that in the UK one could do a BA or BSc in 3 years, followed immediately by a PhD in 3 years.

 

 

I've been told that ds should expect to do an honors year, which is like a one year masters.  So if he enters at 17.5 after completing all 200 level courses, he would do a 3 year BSc and a 1 year honors all at 300 and grad level classes.  There is no liberal arts requirements so these 4 years would be all maths and physics. 

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This is a sensible timeline. I thought you might have been talking about your DS14 starting university right now.

Sorry, I'm talking about two different possibilities. The post I wrote about his lack of relationships is why I would consider early university - at age 15. The post about a 4 year program starting at age 17 is the alternative (which we are strongly leaning to). I'm just not sure that he can last 3.5 more years before being surrounded by mathematicians, but clearly there are benefits of waiting which is what we were kicking around on the other thread.

 

 

Another thing you might consider, though it would cost several thousand dollars, would be Canada/USA Mathcamp (which some students from other countries go to). 

http://www.mathcamp.org/

Yes, we have considered these camps. He does not want to do it because it is too far away.
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Very academic students: 3 year BA/MSc, 1 year honours school (by invitation), 2 years PhD. For a course like Engineering the honours year is automatic as it is the fourth year of your degree.

 

Less academic: 3year BA/MSc, 2 years masters, 2 years Phd.

 

The first year of masters is course work plus reasearch and honours is course work plus a smaller research project.

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When one is at/near the top in math ability in one's age cohort in an area, being socially isolated from math peers is inevitible by definition. You look to other interests for social outlets. For math, find interactions with older kids and adults. This is why taking some uni math courses is an obvious choice, and even then, the social aspect is secondary; you want the educational level to be right.

 

But there is a big potential downside to formal full-time uni enrolment too soon, and that is that one may be much less competitive than they would be if they had waited for a more optimal time. For mathy kids, math is fun, but it is also highly competitve in terms of getting elite uni places, jobs, grants etc.

 

Based on poulation, getting into the NZ IMO would take being in the top 0.01% of age cohort. While such kids are extremely able, being in the top 0.01% of age cohort would put one in the top 400 in the USA or the top 10,000 in the world, so there are still a lot of kids at/above that level. So while it may seem I'm setting an absurdly high standard, I would say your DS shouldn't even consider starting uni full time before he can make the NZ IMO team. Also, making the team, or even better, doing so more than once and/or getting a medal (or at least honorable mention) would be a definite help for undergraduate and graduate college applications, and even throughout his career.

 

Wow, you talk sense!  I'm very aware of the fact that my son is a big fish in a small pond, and wouldn't have a chance of making it onto the USA team.  All of them are gold medal winners, and the NZ team gets honourable mentions and bronzes with a smattering of silver every few years (only 1 gold ever, however the last silver medal winner was only 14).  All the kids on AoPS think my boy is some genius kid because he told one kid that he had made the camp, and it got spread around.  Somehow their mathematical skill doesn't seem to translate to thinking about population size feeding into the camp. :001_rolleyes:

 

(edited for privacy) He loves mathematics, exam prep... not so much. :001_smile:

 

Thanks so much for your thoughts.

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Unless I'm mistaken, the time from bachelors to PHD in the US and UK is essentially the same. In the US, a Bachelors degree holder can apply directly to a PhD program which generally takes about five years including about two years of coursework, no need to obtain a Master's degree first. In the UK, a Bachelor's holder applies to a Masters program first which takes about two years, then applies to a PhD program for an additional three years.

 

End result is the same amount of time invested. (This is obviously very generalized.)

In the UK (England & Wales at least, Scotland is slightly different) a BSc is 3 years and typically the honours is a standard part of that.  It's common now to do a combined masters & BSc for funding reasons, taking 4 years in total; separately a BSc(hons) + MSc would be 3+1. PhDs here are typically minimum 3 years.

 

Just to clarify, I was replying to Butler about (my understanding of) the British system. I believe you are correct that in NZ one would do a 1 year "honours" after a 3 year Bachelors, before going on to Masters and/or Doctorate. But I believe in almost any country, in math at least, a Masters is optional. One can go straight to Doctorate if ready.

I checked the websites for Cambridge, Manchester & York - all require a Masters.

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The main reason to do it would be for the community of learners.  He just has no peers in the homeschooling community and I have had no luck with getting local schools to allow him to join the physics club (which is competitive internationally).  And there are no math clubs.  Right now AoPS is filling that void, but I am concerned about his focus on internet relationships over real ones. 

 

Can I ask what it is about internet friendships that you feel is not 'real'? In what ways do you feel non internet relationships are better? Where is the boundary between 'real' and 'not real' - does is have to involve physical proximity to be real, and if so how frequently must they be in the same space? Where do pen & paper or telephone based friendships rank in this hierarchy?

 

Are there opportunities for short residential courses for maths/science in NZ? In the UK there are a number of companies/charities/universities that organise such things for interested teens & they can be a good place to meet like minded friends.

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I wonder also if there is some sort of mathematics club at the university for highly talented students that part-time enrollment would let him join. Our clubs at grad school were open to anyone who was enrolled in at least one class and maybe that would be an outlet for him.

 

ETA: I should have said highly interested rather than highly talented.

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Can I ask what it is about internet friendships that you feel is not 'real'? In what ways do you feel non internet relationships are better? Where is the boundary between 'real' and 'not real' - does is have to involve physical proximity to be real, and if so how frequently must they be in the same space? Where do pen & paper or telephone based friendships rank in this hierarchy?

 

 

(edited for privacy)

 

Thanks for your concern. 

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I wonder also if there is some sort of mathematics club at the university for highly talented students that part-time enrollment would let him join. Our clubs at grad school were open to anyone who was enrolled in at least one class and maybe that would be an outlet for him.

 

This is an *excellent* question for the head of school. Perhaps he can join now.

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Well at least if he stays involved in the music world he should find plenty of people to interact with. And there should be some at Victoria especially if there is someone who it also involved in competitive maths.

 

Are you going to be here long term Ruth? I remember you said your husband had completed his study. Might interacting with Americans be in his future anyway?

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Well at least if he stays involved in the music world he should find plenty of people to interact with. And there should be some at Victoria especially if there is someone who it also involved in competitive maths.

 

If he gets onto the squad, he will get tutoring/mentoring/training from a professor at a university. Last year of the 12 kids who made the squad,  11 were in Auckland and only one in my city, so clearly the Auckland crowd has a group dynamic that does not exist here.

 

Are you going to be here long term Ruth? I remember you said your husband had completed his study. Might interacting with Americans be in his future anyway?

Been here almost 20 years with no plans to leave. :001_smile:   Believe it or not my dh did a part time PhD while concurrently holding down a full time job and even doing all the history read-alouds for the kids every night. :huh:   He's amazing! :hurray:  and his new job is awesome!

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Been here almost 20 years with no plans to leave. :001_smile:   Believe it or not my dh did a part time PhD while concurrently holding down a full time job and even doing all the history read-alouds for the kids every night. :huh:   He's amazing! :hurray:  and his new job is awesome!

 

:lol:   This struck me as funny, given your recent concerns in the thread.... ;)

 

 

ETA: I'm glad things are going well! :coolgleamA:

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We sent a brief description of what ds is studying with AoPS and let his proofs portfolio stand on its own merits.  Below is the response we got -- I am very pleased with the nuanced understanding.  Sounds like he is suggesting a 100 level course at age 14 as a warm up, before focusing on 200 level courses the following year. And he does mention research. :001_smile:  Would welcome some comments on the ideas kicked around here.

 

(edited for privacy)

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