meeting with prof

[Greenmama2]

Sounds positive. Let us know how the meeting goes.

[Kathy in Richmond]

Sounds as is they are offering encouragement and flexibility, which is as positive a response as possible at this stage, Ruth. I know you've said that you're considering the AoPS precalculus and geometry courses for your son soon. How about having him take the calculus at the university afterwards? I know it is likely to be easy in terms of theoretical challenge after AoPS, but it'll still be new material, and calculus is one subject where I think you're safe taking it elsewhere. It's a requirement, but not necessarily the most critical class for a future mathematician. He'll learn more of what he needs later when he treats that subject more formally in real analysis class. So I don't think it could hurt his progress at all, & it would give him a taste of what the local university offers & a chance to make connections there. Also, I think that he would likely find the introductory discrete math or probability classes to not be worth his time after the AoPS intermediate number theory and counting & probability courses. Just my two cents!

[Laura Corin]

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 certainly went from a BA (four years but only because of a year abroad) to applying for a PhD in the UK.  That was the normal route.  The masters were for people who didn't expect to do doctorates.  I don't know if this has changed.  I applied for the PhD at Cambridge - I didn't end up doing it (for various reasons) but there wasn't a problem with my level.

 

ETA: from this page, it looks as if the M.Phil leads directly into the doctorate (in French, which I applied for), so that the total is three to four years.

 

L

[kiana]

I agree with Kathy and will also add: 

 

The calculus scope and sequence should be sufficiently similar to AOPS that it would be easy for a student to supplement more challenging problems and explanations with AOPS if he so chose.

[EmilyGF]

I have to say, I kind of wish we had that system here. 3 years of focused work in the actual area of study makes MUCH more sense to me than the 4 year BS that's two years of mostly repetition of high school.

Go to Caltech. You won't spend two years repeating high school, regardless of how amazing it was.

 

:-)

 

Emily

[1053]

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[lewelma]

Thanks for everyone's thoughts and advice.  I'm going to delete a bunch of stuff now and get out of the spotlight. :001_smile:

 

Ruth in NZ

[kiwik]

It will be fine.

[lewelma]

So I found out that they use Calculus by Anton, Bivens, and Davis for calc 1,2,and 3 (so just 1 book to buy).  Amazon reviews are quite good.  What I would like to know is how this book compares to the AoPS Calculus book.  Does Anton's Calculus have a theoretical or analysis approach?  Is it a challenging book? 

 

The two main choices for ds would be to 1) take AoPS calculus and then multivariate calc at university with Anton.  Or 2) to do calculus 1,2,and 3 at the University with Anton. 

 

Thanks for any advice.  Meeting is today.

[lewelma]

Here are the course materials for Foundations of algebra, analysis, and topology, a 200 level class.  I'm trying to get a feel for the level of mechanistic vs theoretical material in courses at this university.  What do these resources imply?

 

Recommended books:
• John R. Fraleigh ‘A first course in abstract algebra’, (any edition).
• W. Wade ‘An introduction to analysis’, (any edition).

 

The following classic texts also include the content of the analytic part of this course as well as more advanced materials:
• H. Royden, Real analysis, (any edition).
• W. Rudin, Principal of mathematical analysis, (any edition).

 

 

[Penguin]

Just a note of caution about the "faster" European 3-year undergrad degree. Because there is no general ed, you can't change your major. If you want to change your study program, you start over. All schools may not work this way, but many of them do.

[Kathy in Richmond]

Anton is a typical calculus text used here in the US in sequences for future engineering & science/math majors. It's not particularly theoretical, but an individual professor can adjust his teaching to meet his audience, so I can't say for sure how challenging that class would be for your son. I still think it would be a fine entry point for him to test the waters at your local university after taking AoPS precalculus, but he should have a copy of AoPS or another theoretical calculus like Spivak to read on the side.

 

I'm not familiar with Fraleigh or Wade, but both Rudin and Royden are excellent. They are typically used for math majors who've finished multivariable calc, linear algebra, and ODE, and are ready to move on to more advanced mathematical coursework. Rudin, for example, was used by my son in his first year analysis class at MIT; Royden in my first analysis class at Rochester.

[1053]

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[Luckymama]

(The Boy used the Anton Bivens Davis book for AP. I have his copy here on my math shelf. I'm glad to know it's a decent book. I'm keeping it in case AoPS calc is too much for dd next year. Thanks Kathy)

[kiana]

Fraleigh and Wade are standard undergraduate modern algebra and analysis texts. Wade is generally used at less selective schools -- the more selective schools frequently go straight to Rudin's Principles. Fraleigh is just a great book and I teach out of it. I like it better than any other undergraduate abstract algebra text I've ever seen (and I spent a fair amount of time investigating texts for my students). It is not mechanistic and does an excellent job of motivating a difficult subject.

 

If he takes the AOPS Group Theory class there will be some overlap but Fraleigh goes further -- I'm not sure how much of the textbook they'll cover.

[EndOfOrdinary]

Would it be possible (and not demoralizing) to do the AoPS at home and then do calc 1 as well? I found that one of the best parts of my initial experiences at CalTech was the overlap in what I had self taught and then watching someone else teach it. It was like seeing into someone else's world. Though the fundamental material was not anything brand new, the theory behind it was. I got to see their theory, the way their brain put the reasoning together. It was amazing. Completely changed how I looked at math as a young student and greatly fortified the way I later focused on mathematics communication.

[lewelma]

Thanks for all the comments, and right before the meeting no less!  They helped a lot. The professor was really nice and welcoming and we stayed for an hour. I brought the AoPS books and he helped us map those courses to the university's.  The plan we came up with was to self study Calc 1 (as it is a repeat of high school calculus for kids that did not do so well) and take Calc 2 in June, and then take the Stats/probability course over NZ summer as half of it ds will already know.  This will finish the five prerequisites required for 200 level classes that he would start in 10th grade.  He will take the WOOT from AoPS to give him something to stretch his mind, and I do like the idea of AoPS calc come October, for another viewpoint. As for entrance, the professor said he had seen enough with the proof portfolio to support ds for part time admission.  So that is done.

 

As for the full-time program.  Prof said that our university had a department half the size of Auckland, so definitely fewer options in classes to take; however, his daughter goes to Auckland, and he has seen her coursework.  He said that our university has more challenging classes.  He did say that the 100 level classes here are mostly mechanistic and there is no honors sections or ability for faculty to lead an independent study. However, the 200 level classes become much more proof based, and undergrads can take grad level classes.  In the past few years they have had students accepted with scholarships to PhD programs at Cambridge, Oxford, Berkley, Standford, Chicago, and Penn.  So they seem to know what they are doing.  He did say, however, that we should look at Australia and evaluate what they can offer.

 

Overall, a very positive experience leading to a plan that we can implement.  DS was feeling pretty good and handled himself well at the meeting.

 

Thanks for everyone's help during this process!

 

Ruth in NZ

[kiwik]

Sounds like you have a plan. I think the first year.courses arent much more than 13 as I skipped year 13 and went straight to.first year. In fact until recently it was normal to do UE in year 12 then.straight to Uni. For some reason extra years have been added to school for all.

[lewelma]

Sounds like you have a plan. I think the first year.courses arent much more than 13 as I skipped year 13 and went straight to.first year. In fact until recently it was normal to do UE in year 12 then.straight to Uni. For some reason extra years have been added to school for all.

 

The professor definitely said that the calc 1A class was a repeat of ncea 3, but the other 4 required first-year courses are new material.

 

Calculus 1B - covered by AoPS calculus

Algebra (matrices, vectors, complex numbers etc, including more proof based work) is covered by AoPS precalc

Discrete maths and logic: is covered by AoPS intermediate counting and number theory but he will have to self study some logic

Probability and decision modelling: The probability section is covered by AoPS counting/probability, but the rest is calculus based stats

 

NCEA year 13 does not cover any material in any of those classes because the university is dovetailing directly with NCEA for a seamless transition. So if you wanted to go from year 12 to university, you would just start with calc 1A, which is still very mechanistic and only just getting you into proofs.

 

So strangely, starting in January, ds will do AoPS precalculus while concurrently self-studying NCEA year 13 calculus (which is pretty basic). He will enter Calc 1B in July.

 

He will not be required to take any tests to skip classes, but rather be expected to fill in holes where he needs to.