OBJECTIVES. Notes from the lectures will be posted here from time to time, particularly when the class presentation differs appreciably from the presentation of the corresponding material in the text. The completeness of the presentation will vary, of course, depending on the amount of time that I can allocate to developing and maintaining this part of my website. Accordingly, students in the class should consider this material as a supplement to their own notes and not as a substitute.
COPYRIGHT AND PERMISSION. Copyright© to all materials posted here is retained by Joel Roberts. Permission to copy material for their personal use is granted to students and visitors to the class. Permission for similar use can be granted to others upon request. Other uses, such as re-publication, re-distribution, etc., are specifically NOT authorized.
ABOUT THE FIGURES. The curves (and surfaces) in the illustrations were plotted using software developed at The Geometry Center at the University of Minnesota. In particular, plane curves were plotted using the application "algcurve". The idea for this program was originally due to Professor Audun Holme of the University of Bergen. The program was written by members of the staff of the Geometry Center, and was later incorporated into the Pisces platform.
After the output from Pisces was converted to .gif format, the images were embellished to put them in the form that is posted here. This included use of the unix program xpaint. If you have access to xpaint or other software for manipulating .gif files, you can experiment with copies of the curve images - for instance, seeing how various lines or circles intersect the given curve.
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Last updated November 4, 1997.
351 Vincent Hall