Outline your Course Day by Day

Careful planning in advance is essential. Without it sometimes you don't have enough material to fill the hour (this is mostly a problem when you teach the course the first time) and sometimes you have way too much material for the time (this is definitely a problem when you have taught the course many times). It takes a lot of careful planning to outline the course day by day, but it is definitely worth the effort. My suggestion is that you start with a rough outline and then fill in more and more details.

Here is an example for just one day. You will note that it is somewhat cryptic; I wrote it for myself and typed it here without much elaboration. Note that nothing is said in the outline about what will be said about these materials. Those things will be filled in when more detailed class notes are prepared.

This is prepared for a class of prospective secondary teachers.

Day xx.     Descartes on Analytic Geometry.

Biographical information worth mentioning:

• Attended a good school. Recent work of Galileo and his telescope was discussed.
• A sickly lad. Laid in bed.
  • Fly and analytic geometry. True?
• Importance of contact with the Dutch. Latin.
• Queen Christina of Sweden. Death.

His work:

• Philosophia mathematica.  Newton used this title.
• Method. Cogito ergo sum. Tell Ari Katz joke.
• Geometry is an appendix. You can read it. Translations.
• Optics: Snel's law, rainbow.
• Started analytic geometry. Oblique axes. xyz for variables. Exponent notation
• Curves: geometric vs. mechanical. Examples.
• He went from geometry to algebra, no v.v.
• Had a method to solve any problem (and Newton believed him!).
• Folium of Descartes. Fermat has a better method for tangents.
• Says you can't do arc length. Set up for van Heurat and Newton.

Overheads to have:

• Portraits of Descartes: seated, Schooten, stamps.
• Vic Norton's cartoon on aliasing.
• Title pages:
  • Geometrie: 1637, 1649, 1659. Newton read the second Latin edition.
  • Translations: Smith-Latham, Olscamp.
• Quotations:
  • Rules of problem solving. For prospective teachers especially.
  • Newton on reading Descartes.
  • This method will solve all problems.
• Selected Pages:
  • Solution of quadratic equations.
  • Conchoid is geometric.
  • Finding tangents by the two circle method.
  • Heurat on arc length from second Latin edition (1659).
  • Folium of Descartes. 1638 definition. Graphs of Newton and L'Hospital.

Things to take to class to pass around:

• Smith-Latham translation of Geometry.
• Olscamp translation of the whole Method.
• Polya's How to Solve It.

Things to read before class:

• Sections of the text the students are to read.
• The DSB article on Descartes.
• Look at J. F. Scott's, The scientific work of René Descartes, 1952

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If you have comments, send email to V. Frederick Rickey at fred-rickey@usma.edu .
Posted 11 January 2003.