At what level should a high school graduate be at in terms of mathematics?

[TheAbsoluTurk]

I graduated from high school this year and took the three main sciences (biology, chemistry and physics) as well as math up to Calculus.

I've decided to take a year away from school for a couple reasons. But that doesn't mean that I must stop learning.

Recently I bought a book which gives very simple descriptions of many facets of mathematics. It's not a textbook by any means but I've found out about things like complex numbers, matrices, polar coordinates and other subjects which I never learned in high school. I have, by no means, learned them but this new knowledge has made me feel interested in math.

I heard about some of these concepts from friends in summer school who knew people learning them in advanced IB courses but I had no idea about them. They have IB courses at private evangelical schools here in British Columbia, but I do know of one public school which supports such programs.

I plan to graduate from university in some discipline of engineering.

Anyway my question is in regards to your educations. Did you learn these kinds of concepts in high school?

Will one learn such things in mathematics and physics curricula throughout university?

Does anyone have a suggestion of any particular textbook from which I can learn any material I'm expected to know?

Thank you.

 

[MarneMath]

Did you learn these kinds of concepts in high school?Yes, but I know plently of people who did not.Will one learn such things in mathematics and physics curricula throughout university? Yes, you'll learn all about polar coordinates, complex numbers, linear algebra, and even more neat stuff you haven't had the honor to meet you. However, there's no reason why you can't learn a lot of the basics for those topics on your own. Properties of complex numbers, how form polar coordinates, and using matrix for gaussian elimination are all pretty simple, but useful things to know.

Does anyone have a suggestion of any particular textbook from which I can learn any material I'm expected to know?
I think most standard calculus books mention these topics in some regard, if not many an 'advance' algebra book of some sort.

 

[Best Pokemon]

Students who did mathematics at A-level or equivalent (CAPE, IB, HK A-Levels) would learn these concepts in high school.

Here are some of the books I used in high school:

Core Maths for Advanced Level (http://books.google.com.jm/books?id...YGE8ASq04H4Dw&redir_esc=y#v=onepage&q&f=false)

Pure Mathematics 1 (http://books.google.com.jm/books?id=aTtlRgAACAAJ&dq=y)
Pure Mathematics 2 (http://books.google.com.jm/books?id=-MZ2SwAACAAJ&dq)

Mathematics - The Core Course for A-Level (http://books.google.com.jm/books?id=yGmS4_cG7aMC&printsec=frontcover&dq#v=onepage&q&f=false)

 

[TheAbsoluTurk]

It seems that Canada's closest equivalent to A-Levels and GSCEs is the Advanced Placement (AP) and International Baccalaureate (IB) systems. At my school there was AP Calculus but no AP Mathematics. I took Chemistry AP and English AP. There were those three AP classes but no IB classes.

It's a shame that so many people have missed out on an education easily attainable in other countries. Especially the United Kingdom; we inherit their head of state but not the educational system? Even Pakistan follows the British system.

I can see why Canada would want to be integrated with the US system but we don't take SATs here unless you pay for it and do it outside of school. No one here wants to go to the US for 'college.'

I can't believe teachers teach the students knowing they're teaching a shell of a curriculum.

Anyway thank you both for the responses. I can learn a lot over the course of this year.

 

[Mépris]

It's funny how everyone has something to complain about their educational system.

I went through the English system (an international variant, at least), and I thought it was pretty crappy. It was an extremely exam-oriented experience. Not learning-oriented. Throughout my schooling, everything we did had something to do with the exams.

In primary/elementary school, there's the big exam at the end of year 6, which determines where one goes to secondary school. Then, during years 10 and 11, one studies for the IGCSEs/O-Levels, and takes the whole set of exams in year 11. That's a little different to the current English system, which includes coursework and what not. Now, those exams also determine where one does sixth form. So, there's a lot of pressure for that as well. Same for A-Levels, except that instead of sixth form, it's university. At least, that's the way it works if one isn't applying to uni/college in the USA - only grades matter.

I think the American system is better, in that it's more flexible. At the average American high school, one can get a broad education, can take more or less advanced variants of certain courses (say, regular chemistry instead of honors, accelerated or AP), and one can even graduate a year early without too much trouble.

One can also cross-register for courses at the local U or community college. That's completely unheard of at the typical A-Level school. In the US, one can count the college credit towards their high school GPA. In the A-Level system, anything one does outside of A-Levels has no bearing towards their grades, which entirely based on the exam. (note: some examining boards have a compulsory coursework component, and some have an optional one)

However, that's just my opinion. I went through the English system, and I hated it. At the end of the day, I still had a very specific syllabus to complete, and ignoring that would (most probably) result in worse grades.

My advice: if one does not think their high school can provide them with an adequate education, and going elsewhere is not an option, then one should learn the material on their own.

Just my two cents.

Edit:

If I could go back and do it again, I would learn high school math from the following:

- anything Art of Problem Solving (algebra, geometry, trig, pre-calc)
- supplemented Euler's Elements of Algebra
- Calculus Made Easy

And then college level math. (i.e, calculus I course using a book like Apostol's)

 

[TheAbsoluTurk]

It's funny how everyone has something to complain about their educational system.

Of course there are advantages and disadvantages to all educational systems.

Chances are I would've failed badly in the British system. But at least I wouldn't have this illusion in front of me that I am ready for university.

 

[bcrowell]

If you had a year of calculus in high school, and really understood that course thoroughly, then you are well prepared mathematically to be an engineering major at any of the world's best universities. If you want to learn more math that's not just for fun but that will also help you in your engineering coursework, then what would really probably help would be vector calculus, because that will help a lot when you take freshman electricity and magnetism.

 

[TheAbsoluTurk]

If you had a year of calculus in high school, and really understood that course thoroughly, then you are well prepared mathematically to be an engineering major at any of the world's best universities. If you want to learn more math that's not just for fun but that will also help you in your engineering coursework, then what would really probably help would be vector calculus, because that will help a lot when you take freshman electricity and magnetism.

Thanks for the information.