- Return to Math Learning Center memo...
- Visit Math Typesetting for the Internet (Math Forum)
- Re teaching linear algebra w/ Python (post to edu-sig@python.org, Dec 27, 2000)
MEMORANDUM October 30, 1997 TO: Dr. Carl C. Cowen FR: Kirby Urner, 4D Solutions RE: Teaching linear algebra and computing Greetings Carl -- Re your: http://www.maa.org/features/cowen.html I was just exploring the MAA web site again and come across your article re teaching linear algebra and the importance of computing in this connection. I thought I'd share with you my recent experiences as a curriculum writer integrating some aspects of linear algebra, the computer package MathCad, a programming language (xBase), a free rendering program (Povray), and HTML, to create some interesting (I think anyway) web pages accessible to advanced high school or college students. You can see the results at: http://www.teleport.com/~pdx4d/quadrays.html http://www.teleport.com/~pdx4d/quadxyz.html http://www.teleport.com/~pdx4d/quadcolors.html http://www.teleport.com/~pdx4d/vepacking.html What I like about MathCad is it uses standard text book typography (with a few idiosyncracies), meaning I can test some of my equations and matrices as live objects, and then capture screen fragments as GIFs for embedding in HTML. This gives me access to the large radical signs over compound expressions etc. without having to get into LaTex or PostScript or anything. My papers also share snippets of computer language and point to full source code on other pages. Although using xBase is somewhat unusual in this context, I find it congenial -- the syntax is object oriented these days, plus we have a lot of native power when it comes to tabular data. But really, the choice of language is not that central and I make a point on my web pages of referencing other languages (APL, Logo, Java). I think it's important to understand that matrix algebra does owe a lot to typography, the ability to typeset rectangular arrays and lots of subscripts and superscripts. And computers come in so naturally here because programmers use the exact same concepts of stored values indexed by row and column. A 'matrix' is what a programmer calls an 'array' after all -- at least one linear algebra books in my possession makes it clear that the generic 'matrix' is any row and column storage system, with those matrices used in eigenvalue computations etc. being a special case of a more generic concept. Finally, the links between matrix algebra and geometry are what bring the ray tracing into play. The xBase 'turtles' (concept from Logo) know how to write out data in a form which Povray can process into brightly colored spatial renderings -- suddenly students have access to all the tools they need to make web pages that compete with million dollar text books in terms of graphical sophistication! If you have the time to give my papers a more than cursory inspection, you may find some problematic aspects vis-a-vis formal linear algebra concepts. Like, I use matrix notation to define conversion between two coordinate systems, except one is not xyz, yet maps volume, yet uses 4-tuples, yet uses no negative numbers. This may take me outside the domain of formal linear algebra into more unexplored territory, but that need not distract nor detract from the points I'm making above, re the opportunities our students now have to explore, program and document their mathematical explorations by exploiting the many positive synergies offered by recombining newer and older tools. Sincerely, Kirby PS: http://www.teleport.com/~pdx4d/turtle.html http://www.teleport.com/~pdx4d/pascal.html written quite a bit earlier, bring in VRML, something I hope to get back to more. PPS: I should add that, in addition to the above resources, the professional appearance of some of these web papers owes considerably to Macmillan Publishing (although not in a legal sense as the copyright on the images in question is no longer a Macmillan property). |

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