# Math Geeks--Need opinions on upper level topics

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I've just cross-checked Foerster's Pre-Calculus against the Ontario math curriculum. In Ontario, one apparently does not learn about matrices, fractals, conic sections, quadric surfaces, polar coordinates or complex numbers. (Well, I think polar coordinates are mentioned briefly--but barely). These are chapters 11, 12 and 13 of Foerster's Precalculus. I'm wondering how important these topics are now for 1) anyone and 2) a kid who is very unlikely to take more than a statistics or data management course at the university level. Matrices must be less useful now that we have powerful calculators. Fractals weren't really around back when I was going to school. Polar coordinates are needed in physics or electrical engineering--but I think I learned that topic in a university calculus class. What do you think? I don't really want to put this kid through more math than necessary--or, more precisely, I'd rather use extra time, if we have it, for more work on financial calculations and statistics, which I think she'll use more often. We will do at least an intro do calculus next year--but in Ontario that just means derivatives.

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I would at least do conic sections and polar coordinates if your going to do any calculus, especially if you're using Foerster's. They were definitely in there.

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I've just cross-checked Foerster's Pre-Calculus against the Ontario math curriculum. In Ontario, one apparently does not learn about matrices, fractals, conic sections, quadric surfaces, polar coordinates or complex numbers. (Well, I think polar coordinates are mentioned briefly--but barely). These are chapters 11, 12 and 13 of Foerster's Precalculus. I'm wondering how important these topics are now for 1) anyone and 2) a kid who is very unlikely to take more than a statistics or data management course at the university level. Matrices must be less useful now that we have powerful calculators. Fractals weren't really around back when I was going to school. Polar coordinates are needed in physics or electrical engineering--but I think I learned that topic in a university calculus class. What do you think? I don't really want to put this kid through more math than necessary--or, more precisely, I'd rather use extra time, if we have it, for more work on financial calculations and statistics, which I think she'll use more often. We will do at least an intro do calculus next year--but in Ontario that just means derivatives.

If you work with quadratic equations, you learn conic sections...you just may not call them that. :) It's hard for me to believe you don't study parabolas (since that's pretty much every model for rockets, throwing a ball or a rock...) and circles. Skip hyperbolas and ellipses if you must.

We introduce matrices in Algebra 1 here. Anytime you are going to be solving systems of equations, matrices are the easier way to go. And I think we use matrices MORE not less now that we have technology to help, since it's classic computer operations to use strings and arrays (matrices!).

A basic intro to polor coordinates is a good idea prior to an intro to Calculus, but your student may not get it the first time. Complex numbers are easy, and a natural extension of working with integers, so I'd teach that. Fractals are pretty and fun to generate with software, but of all the topics you mention, are "extra" math for kids who love math and art.

Honestly, I'm just going to end with a quote I read..."Whenever you decide you have learned all the math you need, listen closely. You can hear the doors closing."

LoriM

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I'm realizing that what I'm really trying to decide is if we do these topics again at the Foerster pre-calculus level. We've already covered most of them once in either algebra I or II or in physics. I like your quote, Lori--but there's also the quote "You can lead a horse to water but you can't make him drink." It's hard to convince dd that she really should be doing these topics when she will have 2 years more math than required for an Ontario liberal arts candidate! (Three years are required by everyone--engineering/science candidates take another two math courses in grade 12.)

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