Mathematics 380

Bring a copy of this full syllabus (after it is complete) to class on Monday, January 28.

Here's my single favourite history of mathematics web site .  Look there for more information about the history of anything in mathematics.

Finally something worth adding:  here are some places where you can make tilings of your own.  They will probably be useful in your create symmetries project: 

Using images, but limited geometry.

Seems fascinating, worth exploring. 

Here's something more. 

Some static ones that include more than the software creates (I think).

Here is the last assignment, due 3 May
Created examples:

Find (in the book or wherever you like) three symmetry patterns.  At least one must be spherical or hyperbolic.  Try to choose diverse symmetries (e.g. all kaleidoscopic patterns would not be the best).

For each:

0.  Make 3 black & white copies of the pattern

1. Write the annotated signature and presentation for the pattern in terms presented in Chapter 10.  Indicate a fundamental region of the original pattern. 

2. Colour two of the copies in symmetric way using three colours.   For each of these colourings:

a. Write the signature of the coloured copy, and identify a fundamental region. 

b. For each colouring, include the colour signature and a justification that it preserves the relations, along with some (probably simple) reason that your two colourings are not isomorphic.  

This assignment is significant, and also is singly worth 1/6 of your course.  Please be attentive to it. 

(More will be added to this page as the semester progresses.  Please ask me if there is something you would like to see included.)

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