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Thread: Linear Algebra in High School?

  1. #1 Linear Algebra in High School? 
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    Have any of you ever heard of Linear Algebra being taught in high school? I don't mean simply solving systems of linear equations or matrix algebra but the entire subject as its defined here Linear Algebra -- from Wolfram MathWorld with vector spaces and every thing. I heard a claim that it was. I also heard a claim that engineers routinely take it too. However I can't find any evidence of such things anywhere. In fact I find that the opposite is true. Thanks.
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    Quote Originally Posted by Physicist View Post
    Have any of you ever heard of Linear Algebra being taught in high school? I don't mean simply solving systems of linear equations or matrix algebra but the entire subject as its defined here Linear Algebra -- from Wolfram MathWorld with vector spaces and every thing. I heard a claim that it was. I also heard a claim that engineers routinely take it too. However I can't find any evidence of such things anywhere. In fact I find that the opposite is true. Thanks.
    My (public) high school had an arrangement with a local university to allow some students to take math courses there. Offerings included differential and integral calculus; differential equations; linear algebra; and complex analysis. Fewer than a half-dozen students availed themselves of the opportunity, but it was a welcome way to earn college credits before starting at university.
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    Quote Originally Posted by tk421 View Post
    My (public) high school had an arrangement with a local university to allow some students to take math courses there. Offerings included differential and integral calculus; differential equations; linear algebra; and complex analysis. Fewer than a half-dozen students availed themselves of the opportunity, but it was a welcome way to earn college credits before starting at university.
    That's a given. I'm only referring to what's given normally as a high school math course.
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    Quote Originally Posted by Physicist View Post
    Have any of you ever heard of Linear Algebra being taught in high school? I don't mean simply solving systems of linear equations or matrix algebra but the entire subject as its defined here Linear Algebra -- from Wolfram MathWorld with vector spaces and every thing. I heard a claim that it was. I also heard a claim that engineers routinely take it too. However I can't find any evidence of such things anywhere. In fact I find that the opposite is true. Thanks.
    Matrix and determinant algebra, systems of linear equations ARE linear algebra. So is set theory, vector algebra and affine transformations. All of this is being taught in the better high school programs. When did you learn these subjects? College? By then, it is rather late.
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    XoX I believe he is inquiring whether the entire subject is taught not whether parts of it is. I remember in pre calc Our book had small exercises on linear algebra I believe.
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    Quote Originally Posted by ThirdReaction View Post
    XoX I believe he is inquiring whether the entire subject is taught not whether parts of it is. I remember in pre calc Our book had small exercises on linear algebra I believe.
    The entire subject is huge. I already pointed out to him the parts that are taught in HS (the better ones, at least).
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    I remember doing matrices at school. They didn't make much sense at the time probably because I didn't understand the usefulness. OK so I could calculate the determinant and multiply two matrices together, but at the time it was like "and why would I be bothered to do this?"
    I didn't really get it until much, much later. I'm not making a statement on whether teaching them pre-18 is useful just that in my case it was a bit wasted.
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    XoX I was just stating that what you started made an indirect correction to his post. He didn't say those weren't parts of it. He was asking if the subject was taught not just parts of the subject, using them as examples.
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    Quote Originally Posted by ThirdReaction View Post
    XoX I was just stating that what you started made an indirect correction to his post. He didn't say those weren't parts of it. He was asking if the subject was taught not just parts of the subject, using them as examples.
    Nah, look at his original post, "physicist" has an ax to grind.
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    XoX I did look at his original post. I believe it is you who needs . as he states "I do not mean simply solving" that means exactly what I have been correcting you about.
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    Quote Originally Posted by ThirdReaction
    XoX I believe he is inquiring whether the entire subject is taught not whether parts of it is.
    That is precisely correct. There's no reasonable way to interpret what I said in the opening post, i.e.
    I don't mean simply solving systems of linear equations or matrix algebra but the entire subject as its defined here Linear Algebra -- from Wolfram MathWorld with vector spaces and everything.
    How could anyone conclude otherwise?
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    I was introduced to matrices as part of the school curriculum when I was 8 years old. I was taught how to add and multiply them but not why they are useful. It wasn't until my senior year at high school that they were re-introduced in greater detail.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by KJW View Post
    I was introduced to matrices as part of the school curriculum when I was 8 years old. I was taught how to add and multiply them but not why they are useful. It wasn't until my senior year at high school that they were re-introduced in greater detail.
    Apparently "physicist" thinks that there aren't high schools that teach linear algebra. This is, of course, false. I have had set theory, matrix and determinant algebra, systems of linear equations (determined, over determined and undetermined), pseudo-inverse, Bezout theorem, the fundamental theorem of algebra, vector algebra, affine transformations, all in high school, "physicist" thinks that all students are like him, learning linear algebra in college. This is just false.
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    So is it only private schools that offer it? I can tell you that my school did not but as it was inner city that's not very surprising. I would find it strange for a high school to offer this course as part of a regular curriculum unless it were a school for specially placed students. Such as you proved x0x.
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    Quote Originally Posted by ThirdReaction View Post
    So is it only private schools that offer it?
    No, I went to a public school.


    I can tell you that my school did not but as it was inner city that's not very surprising. I would find it strange for a high school to offer this course as part of a regular curriculum unless it were a school for specially placed students. Such as you proved x0x.
    The point is that the better schools, be they private or public (as in my case) teach it.
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    Quote Originally Posted by ThirdReaction
    So is it only private schools that offer it?
    Who made that claim? Did they offer evidence that it's true?
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    It was x0x and it wasn't a claim but the link he gave was a private school so I was just questioning about it
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    Quote Originally Posted by x0x
    I have had set theory, matrix and determinant algebra, systems of linear equations (determined, over determined and undetermined), pseudo-inverse, Bezout theorem, the fundamental theorem of algebra, vector algebra, affine transformations
    I think we had most of these in my school, but the part underlined does'nt ring any bells.

    To be precise, in Belgium we have an "a la carte" programs, which mean students had already sub-specialized in some way. You can choose between 2 hour and 8 hour of math per week. I was preparing for engineering, so I got the heavy dose.
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    Quote Originally Posted by ThirdReaction View Post
    It was x0x and it wasn't a claim but the link he gave was a private school so I was just questioning about it
    He's in my ignore list so I can't see it. Please post the link for me.
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    Quote Originally Posted by ThirdReaction View Post
    If it was a private school then I'm not all that surprised since private schools are harder than public schools and better all around. After all, the parents expect more for their money.
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    Quote Originally Posted by Physicist View Post
    If it was a private school then I'm not all that surprised since private schools are harder than public schools and better all around. After all, the parents expect more for their money.
    Peter,

    I had almost the same curriculum in a public school. You would have benefited as well, if you went to a better school, so rather than denying the fact that some of us had a better education than you, learn to accept it.
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    Quote Originally Posted by Boing3000 View Post
    I think we had most of these in my school, but the part underlined does'nt ring any bells.
    .
    Rotations, translations.
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    Quote Originally Posted by x0x View Post
    Rotations, translations.
    Oh we did them.
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    Quote Originally Posted by Jilan View Post
    Oh we did them.
    Good. What else did you do from the curriculum I posted?
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    I guess it was probably all of it, but the names were different.
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    Quote Originally Posted by Jilan View Post
    I guess it was probably all of it, but the names were different.
    So, you did all this in high school, contrary to Peter's claims?
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    x0x do you not find the way you address physicist ignorant? He created a thread to ask about this which implies he does not in fact know.
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    Quote Originally Posted by ThirdReaction View Post
    x0x do you not find the way you address physicist ignorant? He created a thread to ask about this which implies he does not in fact know.
    Yes, I think "physicist" is ignorant on the subject, I correct quite a few of his elementary errors . I also think that he has an ax to grind on this particular subject since he did not study these subjects in high school. I also think that you are stalking, it is quite transparent. Not the sharpest tool in the shed.
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    I am obviously not the sharpest tool in the shed, assuming the shed is this forum. I have more responsibilities that stop me from gaining an education at the moment. However I am not stupid. I do not find physicist ignorant, I do however find the way you address him ignorant. He is asking a question because he does not know and you consider that ignorance. And before you try insulting me about not getting an education I'll tell you about my responsibilities. I'm 20 years old with a 4 year old daughter. I'm fighting for sole custody because I do not believe her mom is clean. Might not seem like much but it's the most responsibility I've had. I can't go to college yet because I need to work Tu pay
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    Sorry I'm on my phone so it's kinda screwed up. Anyway I have hospital bills to pay. That was the rest.
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    Quote Originally Posted by ThirdReaction View Post
    I have more responsibilities that stop me from gaining an education at the moment.
    The lack of education is quite obvious. Goes hand in hand with the stalking.

    However I am not stupid. I do not find physicist ignorant, I do however find the way you address him ignorant.
    By your own admission (see above) you lack education. As such, you disqualify yourself from passing judgement.

    He is asking a question because he does not know and you consider that ignorance.
    Wrong on both statements. He isn't really asking, he's grinding an ax. He has been told off on the same subject in another forum, so he is posting here, hoping in an audience that would be more sympathetic.
    I do not consider his asking ignorance, I consider it ax grinding.


    And before you try insulting me about not getting an education I'll tell you about my responsibilities. I'm 20 years old with a 4 year old daughter. I'm fighting for sole custody because I do not believe her mom is clean. Might not seem like much but it's the most responsibility I've had. I can't go to college yet because I need to work Tu pay
    Then mind your own business, you already have a lot on your hands. No point in getting involved in areas you know very little about.
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    A lack of education does not mean one is stupid.
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    Moderator Action: xOx, personal remarks of the kind you are making - rude and provocative - are wholly unacceptable here. Has the message failed to get through to you that such posts are to be a thing of the past? Apparently so. Reflect on how you will return with an attitude more suited to the forum. One week suspension.
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    That's no fun but I applaud you anyway Ophiolite.
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    Moderator Comment: The convention (and implicit rule) is that we do not respond to moderator comments within the thread. If one wishes to make such a comment, be it positive or negative, you can use the Report function (the small button at the lower left of the post), or send a pm to the moderator, or any other member of staff. In my own case you can recognise when I am wearing my moderator hat because I shall use green or red font, as appropriate, and identify it as a Moderator Comment or Action. So, you don't want to respond to this note by, for example, saying "Ah, I get it. Sorry about that."
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    Crap. It is now going to be another week before I can prove xOx wrong again. I am still working on the last proof but I am pretty sure the two hands of a clock do not meet 23 times in 24 hours. Science is not about knowing everying or thinking you do, it is about continually learning. I really need to learn more about geometry, btw. Is this correct?
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    22 times in 24 hours. Just played with my pocket watch.
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    Quote Originally Posted by ThirdReaction View Post
    22 times in 24 hours. Just played with my pocket watch.
    I did the same thing with my alarm clock, and I also have only high school math, and had never even heard of linear algebra until now. What I found there is that 12/11 ratio but it took me a while to figure it out how to arrive at that ratio mathematically based on the minutes and the degrees on the clock face. I will see if I can post the spreadsheet I created tomorrow.

    I also agree it takes some of the fun of it out of it for me since oXo won't be able to see me prove him wrong again.
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    I honestly have no idea how to arrive at it mathematically, I might be able to do it given time but I don't really have time on my hands.
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    Quote Originally Posted by ThirdReaction View Post
    I honestly have no idea how to arrive at it mathematically, I might be able to do it given time but I don't really have time on my hands.

    Time takes time. Ok, now to be more philosophical. I can do that. You have current responsibilities. The need for food and shelter and to be right by your child and whoever you had that child with. If I read you correctly, that is of first priority. There can be time a little to improve the mind and the heart and this will help to achieve the more immediate goals as well. So in short improving the the long term mental and psychological aspects of yourself also helps to facilitate the more immediate goals, and the more you facilitate the one, the more you facilitate the other. "Win, win" ya know?
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    First priority is getting custody while paying hospital bills. Second priority is a better job. Then education and everything else falls in line. But you are correct.
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    One of the things I consider to myself in anything including physics is "why"? I do not want an anwer from you on the next question, but why do you want custody? If you are to understand yourself, it makes sense to understand why you want certain things, and also why you decided to create certain things. Be honest with yourself. Are you wishing to possess people or things, or just to want the best for them - this I think should include not only possession of something, but also why would you wish to deprive another of the possession of something? This is straying far from the topic, but my take on possessiveness is that it is not possible, nor would I think it would be desirable.

    I give you roughly 80 thousand million billion points^12 for wanting to be honorable and to pay the bills.
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    Moderator Request: Please limit discussions to the thread topic. There are PMs for important personal matters.
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    Quote Originally Posted by ThirdReaction View Post
    x0x do you not find the way you address physicist ignorant? He created a thread to ask about this which implies he does not in fact know.
    Actually I'm quite certain that in the majority of the cases the answer is no. I posted this to find exceptions.
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