Brazil Lectures on Computer Algebra

I spent the academic year 1992–3 on sabbatical leave at the Brazilian Center for Physics Research (CBPF) in Rio de Janeiro, Brazil, as the guest of Dr Marcelo Rebouças, where I taught two computer algebra courses. The lecture notes and related material that I prepared for these courses is available via the links below as PDF files. I have briefly previewed them using Adobe Reader 6.0 on Windows NT and they look OK, but they might not render correctly on all platforms, and they may contain factual or typographical errors and omissions.

Mathematics and Algorithms for Computer Algebra

This was a fairly abstract course that I taught jointly with Dr Jim Skea and only my notes for the first part of the course are available here. This set of documents provides an outline of the whole course, lecture notes (week1–8) for the 8 weeks that I taught the course, and an examination paper that I set on my part of the course. (Sorry, exercise and exam solutions for this course are not available!) All the material for this course was prepared using LaTeX 2.09.

Mathematical Methods for Physics using Maple

This was a 10-week course in which I aimed to run through the main mathematical methods of theoretical physics and show how Maple could be applied to them. In retrospect, such a course needs much more preparation time than was available to me and the proposed syllabus was much too ambitious. This set of documents provides an outline of the course, lecture notes (week01–10), including exercises for the first 8 weeks, exercise solutions (week01–08_solns), examination papers (exam1–3) and solutions (exam1–3_solns).

The course was based on early releases of Maple V and needs some re-interpretation in the context of more recent versions of Maple (for which see my book Computing with Maple). When I began teaching this course I was using a command-line version of Maple running on MS-DOS, but later I obtained a GUI-based version running on Windows 3.1. Hence, the exercise solutions for the first two weeks consist of Maple command-line input whereas all other solutions consist of Maple worksheets. I wrote the lecture notes for weeks 1–7 in LaTeX 2.09, although they were based increasingly on Maple worksheets, whereas the lecture notes for weeks 8–10 exist only as Maple worksheets.

Maple worksheets

People occasionally ask me for copies of some of the Maple code included in these lecture notes, so here it is in a slightly more convenient form than embedded in the PDF files. However, please note that I wrote this code during 1992–3 for Maple V R3 and it is unlikely that it will run correctly (if at all) in Maple 6 or any later version (because of a Maple syntax change), although standard Maple 17 will at least open the files. Moreover, I never intended these Maple packages to be used as anything other than an indication of what might be possible (at that time). They are toy examples rather than polished professional packages. I am releasing them "as is" with no intention of supporting them in any way.

  • The Symbolic Vector Algebra Package described in section 4 of the week 6 notes is available as vecalg.ms.
  • The Symbolic Cartesian Tensor Package described in section 7 of the week 6 notes is available as tensimp.ms.
  • The Symbolic Vector Calculus Package described in section 9 of the week 7 notes is available as vecalc.ms.

The PDF files

The documents available here are all in Adobe Portable Document Format (PDF) generated using free software running on Windows NT 4.0. The page format is European A4, although the text in the LaTeX documents is formatted for US letter-size (because they were written and originally printed in Brazil). Any dates later than 1993 that appear in the notes are when I converted them to PDF, not when I wrote them. The LaTeX 2.09 files were converted to PDF with MiKTeX by running PDFLaTeX (using LaTeX2e in compatibility mode).

The Maple V worksheets were converted to PDF by using Maple 9 to print them to PostScript files and then converting to PDF using the Ghostscript ps2pdf command. (I did not attempt to re-execute any of the worksheets since I doubt that it would work in the current version of Maple without some editing.)

The two text files were converted to PDF by converting them to PostScript using the GNU a2ps command in the form

$ a2ps -R --columns=1 -P file week01_solns.txt

under Cygwin and then using the pdfwrite device from the File/Convert... dialogue in GSview to output them as PDF (because for some obscure reason my version of ps2pdf customized to output A4 actually caused the A4 PostScript files to be converted to US letter-size PDF files).