Other Should I Become a Mathematician?

[quasar987]

Pretty exciting news Jason! I'm happy for you.

morphism, you're in Canada too? Where?

I'm in montreal at Université de Montréal.

 

[mathwonk]

a cook book has recipes for doing things, not so good for understand why they work.

stewart is a fairly good cookbook, but a cookbook.

although the term cookbook has a sort of sneering tone, for many of us it is the place to begin.

i.e. before understanding why things work, it is useful to be able to actually perform the operations skillfully.

always choose whatever book seems enjoyable and useful at first. then try to progress upwards in level.

 

[JasonRox]

Pretty exciting news Jason! I'm happy for you.

morphism, you're in Canada too? Where?

I'm in montreal at Université de Montréal.

Nice! I'm hoping to land a summer job in Quebec City. I'd like to spend the summer there.

 

[uman]

Hi all,

I'm a junior in high school, very interested in math. I'm currently learning calculus out of Apostol's excellent book while concurrently taking AP calculus at my school (a waste of time, I must say...)

However it's clear to me that my background in geometry is deficient, having paid little attention when I learned it in 8th grade. I do not even remember what my teacher looked like, so it's obvious that I know precious little facts about geometry and have even fewer skills in geometric proof and problem solving.

I'd like to rectify this. Does anyone have any recommendations for a good, rigorous geometry textbook? Something difficult and thought-provoking but approachable to a (if I may be permitted to flatter myself) gifted high school student?

 

[mathwonk]

hartshorne, geometry: euclid and beyond.

 

[uman]

Thanks. I'll look into that.

 

[qspeechc]

You're in Junior High and reading Apostol? What, are you some sort of child genius?

 

[d_leet]

You're in Junior High and reading Apostol? What, are you some sort of child genius?

He's a junior in high school, not in junior high...

 

[qspeechc]

Ok, I'm not American, what grade is that?

 

[uman]

Normally 16 or 17 years old.

I'm 18 years old because I spent a year abroad.

So yeah, not a prodigy ;-)

 

[mathwonk]

actually it is not that odd to be able to learn math at a young age. our system of "education" in USA is so discouraging to learning that it retards all learning enormously.

my own younger son was able to easily understand and learn geometry from harold jacobs book at the age of 8, but because his peers were not doing the same, I held off teaching him until high school. then at the age of 15 his high school decided to stop using jacobs and begin using the pitiful books of john saxon. hence in high school, he actually learned less than he could have learned in 3rd grade.

my older son, read jacob's algebra when he was 11 and took first place in the state math contest for 8th graders. then he tired of learning so much more difficult material than his peers and tailed off for a while.

thus in my experience the main ingredient is interest. if a kid likes what he is doing it is very easy for a bright kid to learn at a rate 5 or 10 years ahead of the usual USA math courses.

not everyone wants to do it but it isn't that hard for someone who is smart, likes the material, and is exposed to good books or good teachers.

 

[PhysicalAnomaly]

I noticed Spivak doesn't cover vector calculus. Which vector calculus text would you recommend? I know Stewart covers it but I am looking for one similar to Spivak. The only other one I know about is Marsden and Tromba but I've had conflicting opinions on it.

Thanks.

 

[qspeechc]

That's interesting mathwonk- you're raising little mathwonk geniuses
I guess you are correct. The work in school is very much dumbed down. Also, the level of work has seemed to drop over the decades. I remember my maths teacher in high school telling me they did vector geometry/algebra in his days, now they have almost completely erased trigonometry and circle geometry. It's this silly FET education, which has not worked anywhere but they want to try and put it in place here (South Africa). He made the point- what's wrong with the old education system? His generation put people on the moon with it.

Sorry for the digression.

 

[torquerotates]

Although the current educational system dumbs things down a whole lot, it does cater to the majority of students. Just look at how it will be if we soup things up. About half the students in high school wouldn't even graduate let alone go to college. An interesting comparison would be to look a the eduation system in an asian country and compare it to ours. Look a China. The average Chinese student far exceeds the average America student in math and science. But then you have to look at it and say that the average person in China probably was never even a student. Just because they can't make the cut. So it goes to show that the more rigorous an system is, the more exclusive it is,( i.e it weeds more people out). At least in America, most people can graduate and move on in the system, hence giving them more chances.

 

[uman]

That's why they should do it like they do in Europe -- everyone gets educated; people who are able get a high-quality academic education while the rest are prepared for a career.

 

[mathwonk]

i don't see why everyone in high school should take the same courses. what would be so bad about offering higher level material to those who can handle it? they allow this in music, and they have different teams in basketball. political correctness is really kind of stupid in education.

 

[mathwonk]

lets start a list of good free books. i have listed good books, but free books are a special category worth knowing about.

i have found a good linear algebra book today, at least i think so. there are lots of free books out there but most of them are not that great. this is probably for a second course in linear algebra.http://www.math.brown.edu/~treil/papers/LADW/LADW.pdf

 

[morphism]

There's the algebra book by Robert Ash:
http://www.math.uiuc.edu/~r-ash/Algebra.html

 

[torquerotates]

i don't see why everyone in high school should take the same courses. what would be so bad about offering higher level material to those who can handle it? they allow this in music, and they have different teams in basketball. political correctness is really kind of stupid in education.

I agree. But sometimes there really isn't enough students for the schools to make a course for. For example, there was only about 10 people in my high school that was ready for calc BC. As a result, the class wasn't offered. So what ended up happening was that one teachers actually had to teach the class for free at 6:00 in the morning. And this was off the record. But how many teachers are there that are willing to teach for free? Almost none. Most likely the best choice for the students that are really advanced would be to move to a better public or private school. Education is important enough that its worth the cost. Private schools or top publics usually has the more advance classes or special program to cater to gifted students. If worst comes to worse, there's always self study, homeschooling or private tutoring.

 

[mathwonk]

well, i recommend paying teachers who teach better courses, but i have also taught many courses for free. and i have encountered schools who declined to let me teach them for free because they did not like that their students could not all take them successfully. i have not only taught them for free, i have also brought in grants that paid the students to take the course while i have taught it for free. many of us are ready to teach if students are available. the pay on this site is rather low for example.

 

[qspeechc]

It becomes tricky deciding which teachers teach better, but it does provide incentive. Also, at least here in South Africa, teaching attracts very few people- we have a serious shortage. No wonder, the wages are pathetic. Many not-so-good teachers get through.
Also, not everyone has the money to afford better education, or to buy books toteach yourself from, or, for that matter, have access to the internet (again, this is in my country)
I do believe in free edution, up until the end of high school, if the free education can be of quality. Somehow, I don't see this happening in the majority of capitalist nations.
Maybe there should be specialised schools for gifted kids, and those that cannot afford it, the government subsidises their study. But this is my dream world.

A tougher education for all is realisable, in my opinion. Kids today are just lazy, or society has become dumber. I believe (I stand corrected), that in 18th or 19th century Germany high school children were taught real analysis and some pretty hard-core calculus.

The topic of good free e-books seems worthy of a thread of its own, but until then:
Another good linear algebra e-book I found:
http://linear.ups.edu/download.html
I suppose it can be used for both 1st and 2nd courses.

 

[Gib Z]

Well, I've been learning Linear Algebra for about 2 weeks now (after Finishing Calc, I heard that would be beneficial for this) and been using the free textbook, "Linear Algebra" by Jim Hefferon. It is available, complete with exercises (and answers in a different file) in pdf form at http://joshua.smcvt.edu/linearalgebra/. In fact, when looking at that sight again, I found a link to a review at http://www.theassayer.org/cgi-bin/asbook.cgi?book=29. It rates the book very highly, so I guess its a good thing I found it =]

That review sight may have links to other good books, all free. Check it out.

 

[mathwonk]

i didn't say teach courses better, i said teach better courses. that is easier to determine.

 

[RufusDawes]

i don't see why everyone in high school should take the same courses. what would be so bad about offering higher level material to those who can handle it? they allow this in music, and they have different teams in basketball. political correctness is really kind of stupid in education.

Teachers really aren't smart enoguh to make that distinction.

They told me I wasn't cut out for mathematics back in year 9, by the end of high school I scored reasonably well in the highest band of mathematics classes.

In short, teachers are stupid it really needs to be up to the kid to decide what level of course work he or she would like to undertake.

 

[torquerotates]

lol same thing happened to me. They thought I as stupid so they put me in remedial arithmetic classes for years on end. By the time I was 16, my comprehension level was still below 6th grade math. But when I was 17 I was acing pre-calc/trig without even trying. Oh the irony! And now I'm a math major with mostly A's in math and science classes.

 

[mathwonk]

I am a teacher. Are you calling me stupid? That may be true, but it is undiplomatic.

get smart, kids. the game is not against your teachers, but to gain ground against the unsolved problems of the world.

 

[Gib Z]

I think they have generalized the initial statement to the point where it is not true anymore. The more specific statement holds though: Some teachers are not capable of recognising talent in a student and may wrongly label them as failures.

 

[RufusDawes]

I am a teacher. Are you calling me stupid? That may be true, but it is undiplomatic.

get smart, kids. the game is not against your teachers, but to gain ground against the unsolved problems of the world.

teachers... where to start with teachers... they make it hard for good teachers to want to be teachers.

 

[Gib Z]

Well I don't know about that? I want to be just like mathwonk in the future, I am not too sure if I am a good teacher but I can't see any restrictions put in my way? I mean, it's not like they have a tax on good teachers salarys or anything...

 

[RufusDawes]

Well I don't know about that? I want to be just like mathwonk in the future, I am not too sure if I am a good teacher but I can't see any restrictions put in my way? I mean, it's not like they have a tax on good teachers salarys or anything...

wait until you have to meet all the other teachers.