College a year early or not?

[lewelma]

We are having trouble making a plan.  DS has been thinking for about a year about going to university at 17.  He could have the required university entrance without much effort (it is objective exam based entrance here of basically 4-5 AP classes).  The problem is I have made a list of all the stuff he wants to learn that is not for 'credit' in this exam based entrance system, and the schedule is too tight from my point of view.

 

Here is the stuff that he wants to do that will not count.  He can get transcripts for this work from accredited organizations, so it is not like he just wants to do some Coursera stuff in a casual way, but NZ will not recognize any of this extra work from the point of view of high school diploma or university entrance:

 

Calc 2 (learning on his own because prof at local university said the class would be too easy for him) he must get this done by July

Calc 3 (at university for credit)

IMO training squad and 3 exams (looks like maybe 10+ hours a week)

AoPS WOOT (I've paid for this, sigh. It overlaps with the IMO squad work. But 10+ hours a week )

AoPS Programming class (he really wants to learn how to program because his best friend does, and ds just never gets around to learning on his own)

Mandarin (he does not like the NZ curriculum, and wants to continue to learn on his own. He is really disappointed that he did not make the effort this year. He has done mandarin since he was 9)

Piano (we just got one and in 2 weeks of practise having never touched a keyboard before, he is playing Rachmaninoff.  Nothing like a second instrument!! He is thinking of getting the Royal School grade 8 (12th grade) certification)

Violin (he wants to get his post secondary diploma through Royal School in the UK. This will take 2 years minimum)

 

So wow.  lots of stuff and none for NZ secondary school credit. (They won't count even the math or violin).

 

So to get his diploma he needs:

To finish Physics (has about 1/3 of the course left as he started with the correspondence school half way through the year)

Chemistry (this is a 2 year course, first year is pretty easy)

English (this is a 2 year course, he is 1/2 way through the first year)

 

It is just too much.  Something has to go.  But what?  If he graduates in 3 years he can stretch out the post-secondary diploma in Violin which I think would be very good.  He could go to the IMO again. He could get his grade 8 piano. He could also take scholarship exams in 12th grade and get some $$. (he can do these in 11th grade if he had the time)

 

To make more space to graduate in 2 years, he could skip the rest of physics (he has studied it but not in an exam sort of way which is *very* time consuming), and take a few math assessments for credit instead (right now he will be entering University without highschool math assessments.  They are *very* easy, he just doesn't want to do them because they are easy and insulting in his eyes). And he could go for he lower violin post-secondary diploma.

 

But if he decides to graduate in 12th grade, there is a chance his credits in math and physics this year could get disestablished and he would have to do them again.  Math would be easy, but physics he would definitely have to study.

 

Kids here can and do go to university early by getting good grades in 11th grade.  So it is on ds's radar that some (but certainly not all) good kids go at 17.  However, I think he will go to Auckland, and I would kind of like him to be 18 to be that far away as there is only housing for 1 year then he needs to go flatting in a very large city.

 

I'm just in a muddle about the best way forward.  There is just too much here and too many moving pieces.

 

Help!

 

Ruth in NZ

 

 

 

 

[Lawyer&Mom]

I went to university at 17. It was the best bad option. I did fine, but I think I would have done better had I been even just a year older. You mature so much each year at that age. If you have other good options I wouldn't go early.

[lewelma]

I hear you with maturity.  I just can't tell if all the classes are going to be too easy the older he gets.  We don't have any Harvards over here.  There is no differentiation between the universities, but rather a sink or swim mentality.  You get in, and the classes are of a certain level, and you either pass or fail.  There is no push to retain kids and graduate them for numbers.  So I'm having a hard time judging the difficulty of the universities here.

[Grover]

some of those year 12s going off without year 13 are only 16.  If he could go where you are - not leave home, I'd say go for it.  But if he has to go flatting or into halls of residence, I'd leave it another year. 

 

Given his current levels of achievement, he's not going to find much by way of challenge in most of the undergrad courses anyway, so he may well find he has plenty of time to work on his violin and AOPS.

 

*my perspective* - I headed off after my year 12 year as a 16.4 year old.  I took max credits (48) as opposed to the 36 required to count as full time.  I completed LTCL qualifications in two disciplines, worked almost full time and did a couple of night classes too during that year.  It really isn't onerous at all, if you enter well ahead of the curve.  I could live at home while I did that though. 

[Grover]

another thought... could he start at your local (Victoria? Massey?) and then transfer?  Or do undergrad there and post grad in Auckland?  Or (which is what I did) do one undergrad degree at home, then move to Auckland for the "real' one, lol!

[Lawyer&Mom]

I think living at home would have been better for me at 17. Not that I would have thought so at the time!

[JennW in SoCal]

Just a few general thoughts from the "been there, done that" point of view.

 

As homeschooling parents we have wonderful, idyllic plans for everything our children are going to study and learn before heading to college. We let go of one or two plans during the early years, but more stuff gets dropped as our kids specialize in the teen years, and by high school it becomes this wanton sloughing off of so many courses, books, and activities. I had to recalibrate my thinking in high school to decide what was best for each of my boys. High school coursework had to fit them, their interests and their dreams.  It was painful to let go of some of my brilliant plans, but each year more and more had to go. Their final high school transcripts bear little resemblance to the plans I made when they were in 8th grade!

 

Some things that you let go of now are things your ds can pick up in college such as programming, or Mandarin. He could do a semester abroad in China or Taiwan or a summer language intensive. Music is a lifetime endeavor. If your ds continues playing for enjoyment, I can't see that it will matter whether he has royal school diplomas for both violin and piano. I play string quartets all the time, am a working professional musician, and nobody ever asks what kind of music education I have.  Either I can play the music or I can't.  If your ds wants to study music in college or to have a professional career either in performance or teaching, then I can understand the importance of pursing those diplomas.  

 

Teens grow and mature in breathtaking fits and starts between 15 and 17, and of course they transform during their freshman year in college. I sent my 17yo to a college 2400 miles away because he was ready for a bigger academic challenge. It was the right choice to make -- neither of us has any regrets, his maturity was never an issue. Your ds at 15 may not seem ready to live on his own in an apartment in the big city, but he will be quite a different person after a year in college, even though he is just 18.  He will likely have friends he will want to room with, and you can always be a part of the process of finding a flat that you are comfortable with.

 

Don't know if that helps! We were lucky in that the decision didn't need to be made so far ahead of time -- no worry about credits being "disestablished". I guess you and your ds will need to hammer out some pros and cons on planning for the early college.

[Dmmetler]

Will he have one more year of IMO eligibility if he waits? I could see that potentially being a benefit to taking more time before college. At the same time, it kind of stinks that all his work won't give advanced placement or credit. Is there any possibility that the department could place him ahead and let him at least do upper division/grad classes?

[lewelma]

Will he have one more year of IMO eligibility if he waits? I could see that potentially being a benefit to taking more time before college. At the same time, it kind of stinks that all his work won't give advanced placement or credit. Is there any possibility that the department could place him ahead and let him at least do upper division/grad classes?

 

Yes, one more year of IMO eligibility.  The math won't count for his *high school* diploma, but the courses he takes at the local university will definitely count for *university* credit.  He can keep IMO eligibility if he take just one university class per term. They are placing him at 2nd year right now, so he can take 5 200 level math courses if he finishes 12th grade (year 13) and still remain eligible for the IMO. 

 

Jenn, DS's violin teacher is pretty special.  *That* is the main thing ds loses if he goes after 11th grade.  Also, the list I made is my ds's list, not mine.  Clearly, he has a lot he wants to get done! The programming he is interested in because he and his friend could really do some fun stuff together if my ds got his skills up.  A bunch of the IMO kids were also doing the IOI and ds was starting to study with this other kid to get into the IOI camp. 

 

If ds does his first year here and transfers, he will have lost the opportunity for the residence hall in Auckland.  Apparently, most kids meet their future flatmates that first year in the halls.

 

Grover, he is talking about going for a top graduate school overseas. So looking to make sure he is competitive.  My understanding is that he needs to do some good research during his honors -- Mathwonk looked at the research projects at Auckland and said that they were very good.  In addition, Auckland's math program is twice the size of Vic and has twice the offerings of courses.  Given that ds will go in placing out of year 1, he will need to have enough classes to chose from.  Vic has enough, but he will need to take most of them rather than being able to choose things that interest him.

 

Auckland is much much more expensive than Vic because of housing, so scholarship would be nice. I've also just found out that NZ has the STAR program which allows highschool students to take university classes.  I need to see if the correspondence school is one of the schools with the STAR program.

 

DS just seems to be having a lot of fun as things are now.  I just can't predict the future of course.  University here is not the same as the 'college experience' in the US.  Much more specializing and getting down to business.  Much less time for exploring all the things you might be interested in.  I doubt very seriously that ds will continue to *study* music or mandarin when he gets to uni.  I'm sure he will have to do some programming.  But just saying, there is no liberal arts year here.

Edited January 12, 2016 by lewelma

[Grover]

oh yeah, you can access STAR as a homeschooler too... that's easier than the way I did it, lol!

 

I get wanting to be competitive at grad level, but honours project is a little way off.  Are you sure he's not able ot do the halls if he transfers?  Or, actually, that he's eligible for Halls if he skips first year?  I know the hall that is for first years down here won't take you if you're not taking first year papers, and I know some of the others that take transfers.  Of course it's different wherever you go. 

[lewelma]

oh yeah, you can access STAR as a homeschooler too... that's easier than the way I did it, lol!

 

I get wanting to be competitive at grad level, but honours project is a little way off.  Are you sure he's not able ot do the halls if he transfers?  Or, actually, that he's eligible for Halls if he skips first year?  I know the hall that is for first years down here won't take you if you're not taking first year papers, and I know some of the others that take transfers.  Of course it's different wherever you go. 

 

I have just learned about STAR and had *no* idea it was available to homeschoolers!

 

As for the halls, it never even crossed my mind that they would not let him.  How sad.  Will call Auckland and find out.  If he has to flat in the first year, that is a huge reason to delay. 

 

Edited January 12, 2016 by lewelma

[Mike in SA]

So, DW and I both went to the university at 16.  In hindsight, probably not the best idea, but it was - as stated earlier - the best of the bad options available.  We simply didn't have the opportunities that exist now.

 

DS13 put us in a similar quandary as yours, in that he started studying very advanced material by the 5th grade.  Even now, he's nowhere near mature enough to go off to college, but his studies were clearly accelerating along that path.  So, we decided to allow him to pursue a theoretical development, and when he (re)takes the subject later because he won't possibly get credit for what he studies now, it will still be valuable to him, and he will be more engaged in class with his back pockets stuffed with prior experience.  AP courses don't have that much theoretical rigor, so we're focusing on that this year - instead of calculus, it will be "elements of analysis."  If he stays home schooled, then we'll jump into abstract algebra, non-Euclidean and projective geometry, and other topics he may not see again.  Linear algebra, differential equations, and other traditional core sequence courses will probably be kept aside.

 

In your case, Auckland has a fine mathematics department with solid, but limited, course options.  Instead of sweating too much about the traditional calculus sequence, you could look into an intermediate analysis text (theoretical development of calculus - I'm assuming the real analysis course is a slight bit more advanced), some of those unusual geometries, calculus-based probability and statistics, finite mathematics, or computation theory (a currently re-emerging topic).  The depth garnered from those courses will go a long ways in the university setting, in a very different manner than IMO prep will.

 

[JennW in SoCal]

 

 

DS just seems to be having a lot of fun as things are now.  

 

The good news is that you seem to have a bright, motivated and happy teen! I love that he wants to fit so much in to his high school, and given that your college system doesn't include a broad liberal arts component, now is probably the time to try to do it all.  And I love that your ds has a great violin teacher!!!  

 

 

:grouphug: Hugs to you, Ruth, as you figure it all out in the next few years. It WILL work out, no matter whether he goes early or not. 

[lewelma]

In your case, Auckland has a fine mathematics department with solid, but limited, course options.  Instead of sweating too much about the traditional calculus sequence, you could look into an intermediate analysis text (theoretical development of calculus - I'm assuming the real analysis course is a slight bit more advanced), some of those unusual geometries, calculus-based probability and statistics, finite mathematics, or computation theory (a currently re-emerging topic).  The depth garnered from those courses will go a long ways in the university setting, in a very different manner than IMO prep will.

 

He can't take a course until July because the local uni won't take him underage and he won't have the English credits.

 

I was thinking that it would be prudent to do calc 3 immediately after calc 2 so you don't forget stuff.  Is that a nonevent? 

 

All that is available in the 200 level courses in July is Calc 3 and linear algebra. )-:  He has finished the 100 level courses and doesn't have the prereqs for the 300 level courses.

 

for 2017 January, he can do Analysis/Topology, Differential eq, Discrete maths (he has done half of this class already), and Mathematical stats. 

 

He can't take the 300 level classes without the 200 level prereqs. So no logic, no abstract algebra, complex analysis, or topology until he has taken Analysis in January 2017.

 

That is why I was thinking Calc 3.  But I'm am open to other suggestions because I definitely feel out of my depth here.

 

Edited January 13, 2016 by lewelma

[lewelma]

The good news is that you seem to have a bright, motivated and happy teen! I love that he wants to fit so much in to his high school, and given that your college system doesn't include a broad liberal arts component, now is probably the time to try to do it all.  And I love that your ds has a great violin teacher!!!  

 

 

:grouphug: Hugs to you, Ruth, as you figure it all out in the next few years. It WILL work out, no matter whether he goes early or not. 

 

Oh thanks Jenn.  It all feels so important now, but maybe I just need to not worry so much.  Problem is that I have 2.5 weeks until school starts again (we are on the Southern Hemisphere school year), so I need to make a plan of some sort.

 

I'm just starting to think that my maths boy actually loves English and Music and Science and Mandarin, and maybe his 12th grade year could actually be the typical liberal arts year in America.  I'm not sure that he *really* wants to do only maths yet.  He has played the piano for 5 hours today and the violin for 1.  No math to be seen.  His violin teacher is basically the best in the country. He has 5 students who travel a round trip of 4 hours for lessons. He is kind and motivating and skilled (and expensive).  He is the associate concert master of the NZ symphony orchestra.  My ds is also in a trio with the son of two members of the NZ string quartet (and has been for 3 years).  These are national bodies based in the capital, and my ds is building connections in the music community, connections he won't get in Auckland.  When I say he is considering getting Royal School grade 8 piano, it is not about the qualification, it is about the learning. He just likes to work towards a qualification as a way to focus his studies.  His music and love for literature give him his humanity.  I think once he goes to university, he will focus.  It will be maths all the way.  Sometimes I wonder if he doesn't want permission to stay broad for just a few more years.  There is no liberal arts year here, and that might make all the difference in our decision.  I am a dual citizen, and grew up in American.  I moved to NZ 20 years ago, but I still went to Duke all those years ago.  I think in a strange cultural mix of ideas, and I get very muddled in how I perceive of things like university. So I hear you and I hear Grover and the two of you are actually talking about different things, even though you are using the same words.

Edited January 13, 2016 by lewelma

[Grover]

I htink letting him have that year of "other" is not a bad thing at all - because you're right, once he specialises, it will become all consuming, and it's that from the get go, pretty much at uni here - none  of the broad stuff I hear about from the US system.  No way would I want my under 18 year old flatting, then again, I also wouldn't want them in the Halls :-O

 

SOmething to keep in mind / give him some perspective on the whole UNi after year 12 thing is that many MANY of the kids who do that then change direction half way through their degree, or take a year off somewhere in there.  He could just do that now, as many of our private school kids do, instead of interrupting the degree process - spend the year doing all that stuff he wants to do, and see where it leads. 

 

What does he want to do?

[lewelma]

I htink letting him have that year of "other" is not a bad thing at all - because you're right, once he specialises, it will become all consuming, and it's that from the get go, pretty much at uni here - none  of the broad stuff I hear about from the US system.  No way would I want my under 18 year old flatting, then again, I also wouldn't want them in the Halls :-O

 

SOmething to keep in mind / give him some perspective on the whole UNi after year 12 thing is that many MANY of the kids who do that then change direction half way through their degree, or take a year off somewhere in there.  He could just do that now, as many of our private school kids do, instead of interrupting the degree process - spend the year doing all that stuff he wants to do, and see where it leads. 

 

What does he want to do?

 

I've not heard that about the year 12 kids. Very interesting.  We were thinking about having him get the NCEA level 3 certificate after year 12, and then have him stay at Tekura (if possible, need to call) and have him do scholarship in year 13 while doing his post secondary diploma in music (LRSM from ABRSM), and doing the IMO, and taking math classes at the local uni and continue with Mandarin for fun and continue with piano.  This would allow him to make sure his credits from this year don't expire and let him focus in the music as he wants to, before heading into a maths focus.

 

Main problem with this as I see it, is the older he gets the easier the maths classes will be at Auckland for him.  I am kind of worried about him outgrowing Auckland.  Perhaps I'm mistaken, obviously I don't know.  But Auckland is not Princeton.  A NZ kid who was on the IMO team 4 years ago, got into Harvard and just finished his degree in maths and philosophy.  He came back to talk to the kids at camp, and got ds and I really thinking about the level of courses again. 

 

As what he wants to do, well he is playing the piano for *another* hour right now.  But seriously, he does not know.  He is easily led by me.  If I suggest this or that, he follows.  He wants to major in maths, and right now he is pretty staunch that he wants it to be theoretical and not applied. He also right now wants music and mandarin and programming and science and english and great literature. It seems to me like he wants a liberal arts year. He just seems to think that all the smart kids go early, so he should or people will think he is not smart.  But I asked him how many kids at the maths camp go early, and it sounds like about 5 out of 28 have skipped a grade, so are a year young.  And 3 last year went to uni after year 12.  So that is NOT all or even a majority. 

Edited January 13, 2016 by lewelma

[Grover]

nah, it's definitely not that common.  The really smart ones stay and do scholarship.  The ones that leave are generally the ones who have had enough of school and have good enough marks to get in, but not super high... super high stay for scholarship and the equivalent of the US liberal arts year. 

 

If he wants to do his LBRSM, I'd totaly get that done before he heads off.

[lewelma]

Grover, that is very helpful.  DS has been steering away from scholarship because he thinks it just more exams rather than more learning.  I think I need to dig into the curriculum to see what it entails.  TeKura has told us that they have the capability to teach it, which is good, because I don't think I can. 

 

I agree that the LRSM needs to be done before university if he wants to do it. I really don't think he will get a conjoint degree with music.  He is more likely to get degrees in maths, physics, and philosophy.  He can do the LRSM in 2 years but only with a lot of dedication, and I think there is just too much on his plate with his current plans to make this a reality.  Something has got to go.

 

Edited January 13, 2016 by lewelma

[lewelma]

Mike, dh had a new idea about the university math classes.  He was thinking that instead of starting in July, he starts next year in Feb and takes Foundations of Algebra, Analysis, and Topology.  This would allow him all of 2016 to get through Calc 2 (and maybe with a theoretical book), rather than needing it done by July.  And gives him time to take the AoPS programming class.  Main negatives I see is that there would be a 6 month gap between calc2 and calc 3 because he only has calc 3 and linear algebra available in July 2017.  But this might pull some stress off him so he can do all the broad things he wants to do.  Does that order make sense? Is it a good idea for his first university class to be Analysis?

 

So original idea

Jan-July 2016 Calc 2 (he's 1/2 way through), squad work, (IMO team possibly), WOOT

July-Dec 2016 Calc3 at university, AoPS programming,WOOT

Jan-July 2017 Analysis at university, squad work, IMO team, WOOT

July-Dec 2017 Linear algebra at university, WOOT

 

New idea

Jan-July 2016  calc2 (at slow pace), squad work, (IMO team possibly), WOOT

July-Dec 2016 AoPS programming, calc2 (at slow pace), WOOT

Jan-July 2017 Analysis at university, squad work, IMO team, WOOT

July-Dec 2017 Calc 3 or Linear algebra at university, WOOT

 

This is on top of the normal schedule of: English, Music, Science, Mandarin

[lewelma]

7 hours of music practice yesterday.  He gave himself wrist pain. :tongue_smilie:  I think he is burned out on math, but he is starting back up on the squad work and possibly the WOOT work today because he has assignments.  That is about 20 hours per week right there.  And this is summer. sigh.  I'm nervous that if I don't teach him moderation now, he will not learn it on his own.  He has so many goals but he really needs me to help him be realistic. 

[Cosmos]

Are you saying they don't have Calc 3 available in January 2017? Normally calc is done before real analysis, but if that's when the classes are and he has the prereqs, why not? For reference, I did Calc 1 in 11th grade, then did no math for 1.5 years, and then did a couple of weeks of study at college and placed into Calc 3. It was no problem for me, so for your ds I bet it wouldn't be either.

[lewelma]

Are you saying they don't have Calc 3 available in January 2017? Normally calc is done before real analysis, but if that's when the classes are and he has the prereqs, why not? For reference, I did Calc 1 in 11th grade, then did no math for 1.5 years, and then did a couple of weeks of study at college and placed into Calc 3. It was no problem for me, so for your ds I bet it wouldn't be either.

 

You are right.  No Calc 3 in Jan 2017.  The head of department told ds to self study calc 2, which he is doing using the AoPS calc book and then we will go through the tests that the prof gave us.  They use Anton at the university for all three calc classes which is a pretty applied book, so ds should buzz through some of it I think.

 

DS would really like to do a university class this year to be with people, I think. I'm just trying to find *something* to drop because he has too much on.  DS wants to make room for programming and mandarin, which he wanted to do last year but simply ran out of time. If he graduates standard time, he would not have to take a music exam this year, so that is *one* thing less.

 

here is the availability for 200 level classes (there are only 6):

Jan term: Analysis, differential equations, mathematical stats, discrete maths (he has done half of this class through AoPS),

July term: multivariate calc, linear algebra

 

[Cosmos]

Could he do programming and/or mandarin at the university instead of math? That might get the social part in plus ensuring it happens without crowding the math. Sorry if you've already explained all this.

 

It's too bad linear algebra and Calc 3 are both in July. It would be great to do one in January and one in July.

Edited January 13, 2016 by Cosmos

[lewelma]

Could he do programming and/or mandarin at the university instead of math? That might get the social part in plus ensuring it happens without crowding the math. Sorry if you've already explained all this.

 

If he takes too many university classes, he will be ineligible for the IMO, so we are being very careful about that.  One kid last year who made the team had taken 5 uni classes, which was too many.  I need to find out the exact details.  But I agree that the math crowding is what I'm concerned about.  The lack of classes at the local uni is why we are talking about sending him to Auckland.  As Gover said, most kids who go a year early, stay at home and go locally.  In fact, in NZ most kids stay local if the university has their speciality because the universities are not differentiated in student ability like they are in the USA.

[Mike in SA]

Mike, dh had a new idea about the university math classes.  He was thinking that instead of starting in July, he starts next year in Feb and takes Foundations of Algebra, Analysis, and Topology.  This would allow him all of 2016 to get through Calc 2 (and maybe with a theoretical book), rather than needing it done by July.  And gives him time to take the AoPS programming class.  Main negatives I see is that there would be a 6 month gap between calc2 and calc 3 because he only has calc 3 and linear algebra available in July 2017.  But this might pull some stress off him so he can do all the broad things he wants to do.  Does that order make sense? Is it a good idea for his first university class to be Analysis?

 

So original idea

Jan-July 2016 Calc 2 (he's 1/2 way through), squad work, (IMO team possibly), WOOT

July-Dec 2016 Calc3 at university, AoPS programming,WOOT

Jan-July 2017 Analysis at university, squad work, IMO team, WOOT

July-Dec 2017 Linear algebra at university, WOOT

 

New idea

Jan-July 2016  calc2 (at slow pace), squad work, (IMO team possibly), WOOT

July-Dec 2016 AoPS programming, calc2 (at slow pace), WOOT

Jan-July 2017 Analysis at university, squad work, IMO team, WOOT

July-Dec 2017 Calc 3 or Linear algebra at university, WOOT

 

This is on top of the normal schedule of: English, Music, Science, Mandarin

 

The difference between ca;c 2 and 3 depends on the school, but the most common sequence has a very significant shift in content style.  While calc 2 was more about integration techniques, Calc 3 launches into multivariate analysis and vector analysis.  I would argue that a break would actually be healthy, to allow the principles to seep in a little deeper.  It would certainly be wise to refresh for 2-3 weeks before taking calc 3 if the break will be for a full year.  However, depending on the quality of that Analysis course, the depth and prep for Calc 3 could be extraordinarily strong, and the calc 2 review may need to be in late 2016.

 

There are also options for math that do not extend official credit, also, such as MOOCs or OCW.  I guess we're a bit fortunate to have DW, who is qualified to teach at a pretty high level.  :)  I know Stanford and CTY have some advanced online offerings for high school students, as well.

 

Linear algebra is a "relaxer" course that many students take between Calc 2 & 3, or simultaneously with 3.  Unless it's taught like MIT-OCW's advanced version, it's one of the easiest courses for math majors.  Differential equations, as well (partial differential equations, well, not so much).

[lewelma]

For the analysis class they are using either Judson, Abstract Algebra: theory and applications or Fraleigh, A first course in abstract algebra.  Sounds like you could buy either.

 

"An introduction to some fundamental structures and spaces, and their study by the axiomatic method.  One half of the course will discuss groups, including permutation groups, groups of matrices and symmetry group.  The other half will study concepts of continuity and analysis in euclidean spaces and metric space. "

 

The prereqs are calc 2 and either discrete maths or intro to linear algebra.  All of which the university has placed him out of.

 

All three of their calc classes use Anton.  So I'm guessing not so much of a jump.

 

++++

 

So he could take linear algebra this July.  It would be easier than Calc 3 (I think this is what you are saying).  He would not have to finish calc 2 by July while doing all this squad work.  And then he can take the AoPS programming class at the same time (summer class apparently is running). 

 

Analysis and Calc 3 in that order next year (2017) (opposite order not available). 

 

Is this reasonable? preferable?

Edited January 14, 2016 by lewelma

[Cosmos]

So the class is actually half algebra and half analysis? Interesting. I bet he'll really like the algebra. It was the class that turned me into a math major!

 

Linear algebra will probably be easy for him, especially with the groundwork laid by AOPS precalc.

[Mike in SA]

Interesting.  I wouldn't have mixed those topics (algebra and analysis).  Our local university has a similar intro broken into two semesters, and we're considering them for DS. I also couldn't imagine trying to get through Fraleigh (a great text) in half a semester.  I'm guessing they won't go very deep into the material.

 

I don't think that will help Calc 3 per se, so I'd plan for a few weeks review of calculus, maybe 3-6, or peek back on a regular basis through the year to make sure the formulae, definitions, and theorems still stick.

 

 

 

[Mike in SA]

So the class is actually half algebra and half analysis? Interesting. I bet he'll really like the algebra. It was the class that turned me into a math major!

 

Linear algebra will probably be easy for him, especially with the groundwork laid by AOPS precalc.

 

Ha! I was typing the exact same thing while you were! 

 

ETA: That was my favorite in college, as well...  I taught my kids some of the content from Fraleigh at a fairly young age, because it was so much fun.

Edited January 14, 2016 by Mike in SA

[lewelma]

So are you guys saying:

July 2016 Linear Algebra

Feb 2016 Foundations of Algebra, Analysis and Topology

July 2016 Multivariate Calc

 

With regular review for 2016-7 of Calc 2?

 

The Linear Algebra class uses Elementary Linear Algebra by Anton. "Fields, vector spaces, linear transformations, eigenvectors, spectral decomposition, quadratic forms"  Is that the class you are imagining?

 

I think you are saying that this order will give him more time to master Calc 2, and give him an easier math class this year which would allow him to squeeze in AoPS programming. Yes?

 

 

[Cosmos]

Sounds like a good plan to me!

 

And then in 12th (if he stays home) he could do diff eq and one more class without losing IMO eligibility. Is that right? 

[lewelma]

I think that is right.  I think he can take 4, but 5 is a no go.  The IMO is in July, so he would not have started the 5th class yet. But I'm going to contact the head dude and check!  I'll also run this by the head of the maths department at local uni who has been helping us.

 

I'm still muddled about early entrance.  I think the big deciders are music and housing in Auckland his first year.  So will make calls to his music tutor and to Auckland. 

[Mike in SA]

So are you guys saying:

July 2016 Linear Algebra

Feb 2016 Foundations of Algebra, Analysis and Topology

July 2016 Multivariate Calc

 

With regular review for 2016-7 of Calc 2?

 

The Linear Algebra class uses Elementary Linear Algebra by Anton. "Fields, vector spaces, linear transformations, eigenvectors, spectral decomposition, quadratic forms"  Is that the class you are imagining?

 

I think you are saying that this order will give him more time to master Calc 2, and give him an easier math class this year which would allow him to squeeze in AoPS programming. Yes?

 

Yep, looks good.  I wish this were an available sequence around here!