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Recent developments in Geometric Algebra have extended vector algebra to include the outer product (wedge product) and bivectors.

Is there a Vector Algebra text (preferably at the advanced high school level)where the more recently developed material (outer product and bi-vectors) is taught before more "traditional" material such as the cross product?

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    $\begingroup$ as of right now this question appears to be off-topic. If you intend on using this information to help teach or learn this vector algebra content, please include that additional information in your question which should help make it more relevant to this site. $\endgroup$
    – celeriko
    Commented Mar 23, 2016 at 22:58
  • $\begingroup$ Isn't this just a copy of the question you asked 2 days ago? matheducators.stackexchange.com/questions/10771/… Please carry on the conversation there rather than starting new questions because of lack of answers. $\endgroup$
    – Richard
    Commented Mar 24, 2016 at 10:05
  • $\begingroup$ OK, Ill augment the question there. $\endgroup$
    – Allyn Shell
    Commented Mar 24, 2016 at 19:54

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Though I would encourage you to stick with your previous question Geometric Algebra Resources ...

Short answer - there will not be a Vector Algebra text that addresses Geometric Algebra (GA) at High School level. Vector Algebra texts address 3D vectors. In my experience most High School students are barely equipped for basic 3D vector algebra - let alone 3D GA.

I am also not aware of any high school maths curriculum with enough "free time" to spend the months required to address 3D GA at even a basic level. Therefore I doubt someone would create a text like this designed for high school students.

I have only taught this as an extension for some advanced high-school students, and then only in 2D. For most students, attempting to teach this could be extremely counter productive as it would interfere with their later education when it is someone else's turn to teach them a traditional curriculum. I have shown you part of my methodology in my answer to Geometric Algebra Resources which attempts to augment a traditional curriculum rather than replace traditional vector algebra.

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    $\begingroup$ I doubt that learning correct mathematics could ever "interfere" with ones later education. $\endgroup$
    – Steven Gubkin
    Commented Mar 24, 2016 at 17:09
  • $\begingroup$ @StevenGubkin If there are incompatible definitions of the same concept (vectors), then students that do not have a thorough understanding of what is happening will tend to get confused. $\endgroup$
    – Richard
    Commented Mar 25, 2016 at 1:14
  • $\begingroup$ does not GA have an underlying vector space? There are just additional operations, no? I must admit I have not studied much GA, I mostly use classical tensor calculus when I do differential geometry. $\endgroup$
    – Steven Gubkin
    Commented Mar 25, 2016 at 2:50
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    $\begingroup$ Yes, but I worry that a student that does not compartmentalise GA as "something I do in this class only" will bring this "geometric product" into another class where vectors are defined classically and will simply get confused. This would especially be the case if it were taught to mathematically immature students (late high school, maybe even 1st year university), without adequate time to properly address GA and how it relates to traditional vectors. I'm not going to even start with tensor calculus!! $\endgroup$
    – Richard
    Commented Mar 25, 2016 at 3:30

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