Math, Music and Identity

Homework Assignment #3

Due Friday, March 13, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to A First Course in Math and Music, the primary text for the class (available on Moodle). You are encouraged to work on these problems with other classmates, and it is ok to use internet sources for help if it's absolutely necessary; however, the solutions you turn in should be YOUR OWN WORK and written in YOUR OWN WORDS. Be sure to cite any references, websites, Internet sources, etc. that you may have used for assistance with the assignment.

Important: Please list the names of any students you worked with on the top of your assignment.

The universe is an enormous direct product of representations of symmetry groups.

- Hermann Weyl (mathematician, physicist, and philosopher)

Section 5.3 (pp. 200-201)
Problems:   1, 2, 5, 7, 9, 10

Hints: For #7, you are to construct the group multiplication table for the symmetries of an equilateral triangle. This is a 6 by 6 table, similar to the one we constructed for the symmetries of the square. First find the two triangles corresponding to the rotations R120 and R240 (assume a clockwise rotation). Use these and the triangles shown in Figure 5.27 to create the full multiplication table for the group. For #9, the goal is to determine which sets are groups on their own, with * equal to addition. The first property to check is closure.