This page is www.math.columbia.edu/~bayer/F03/symmetry

Section 002 (Bayer)
Tuesdays and Thursdays, 9:10am-10:25am
304 Barnard Hall

Dave Bayer (x42643, 426 Mathematics, www.math.columbia.edu/~bayer)
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Email

My email address is  

Please include the phrase "Groups and Symmetry Fall 2003" in the subject line of any correspondence with me concerning this course.

Office Hours

Exams

There will be two exams (30 points each) and a final (40 points). The final is not cumulative.

These dates do not coincide with any religious holiday which causes suspension of New York City's alternate side parking regulations; see NYC Parking Calendar. Please discuss other conflicts with me well in advance of the exam in question.

Master University Examination Schedule ( Cached )
University Academic Calendar

Attendance and grading

Like most courses in the university, attendance is expected but not enforced. Please take note of the early meeting hour before registering for this course. I do not grade this course on a curve; if you elect to miss a substantial number of classes, you are taking a risk of failing the course. The material in this course requires a degree of practice that you are at serious risk of misjudging if you do not attend class.

Texts


Course materials

Course materials will be posted in Acrobat 4 PDF format (PDF 1.3). Your browser can be trained to automatically open these files with Acrobat Reader, a free program which you can download from (If you have trouble reading these files, check to see if you're using an outdated version of Acrobat, and upgrade to the latest version.)

Note: We do not want any student to feel time pressure. Each exam is designed to be easily taken in 2/3rds of the available time, e.g. 50 minutes for a 75 minute class, or 2 hours for a 3 hour final. However, any student who would like "time and a half" is welcome to use 75 minutes for a midterm, or 3 hours for the final. This option is not limited to students with disability certification.

Assignments

Assignments are not collected.
  1. Begin reading symmetry.pdf . Print out some pages of squarepaper.pdf, and apply the symmetries of the square to the letters of the alphabet, and various designs tha you make up. Use alphabet.pdf as a guide for what to do. How many kinds of symmetry are there? What else do you notice? Invent some more letters for the alphabet, exploiting underutilized symmetries of the square to make them distinctive.
  2. Print out some pages of triangletable.pdf and squaretable.pdf and experiment with various ways of writing out the multiplication tables for symmetries of the triangle and the square, as demonstrated in class. See what patterns you can discover. Use exampletables.pdf as a guide for what to do. You may find it useful to cut out the notched polygons in cutouts.pdf and play with them.
  3. Study triangleorbits.pdf and try to make some sense of its organization, using what you now know. Imagine for example that you found this pattern being broadcast from a distant star, and were assigned to decipher it. (If you don't regularly attend class, the whole course may feel a bit like this!)
  4. Study strip.pdf and carry out the described exercises.

Course materials from previous semesters

This course has been taught before; you can find practice materials on the web pages from previous semesters:

Class schedule