BIS 329 Symmetry:  The Art of Mathematics		Hillyard/Rasmussen

SYLLABUS

The course will examine one of the key mathematical concepts of modern mathematics: groups of symmetries. 
This mathematical concept is one of the more powerful tools of 19th and 20th century mathematics, 
yet clearly it has a deep connection to the world of Art.  Most cultures, both ancient and modern use the art of patterns in varied aspects of their
culture:  whether it be in drawings, pottery, rugs, wallpaper, gardens, or architectural detail. 
 The course will begin with the students researching different cultures to see how they used patterns in their lives.  
Starting from this cultural and artistic perspective the modern mathematics will be developed building on the students’ 
research of the different cultures and the examples they have discovered.  
The students will also have first hand experience in finding different patterns in class work sessions and homework.  
Simultaneously with this work, the mathematical concepts underlying the art will be developed. 
The classification of all one-dimensional band ornaments will be done by the students in team projects and the instructor 
will outline the classification of all 17 two dimensional symmetry groups of double infinite rapport.  
The mathematics will show the beautiful interplay between geometry and algebra needed to determine all the possible "patterns".
  As a capstone to the course, there will be a team visual presentation.  Each team will pick a culture to explore and find varied visual examples of how that culture used symmetry. 

There will be homework assignments with both "pattern" exercises and mathematical exercises.  A complete listing of the course work requirements follows the weekly schedule.


REQUIRED TEXTS 

Washburn, Dorothy & Crowe, Donald Symmetries of Culture, Theory and Practice of Plane Pattern Analysis. University of Washington Press, c. 1988

Weyl, Hermann Symmetry Princeton: Princeton University Press, c. 1952


TENTATIVE SCHEDULE

Week 1	Introduction to "patterns"
		Examples from various cultures
		Student exercises in researching "patterns" in cultures
		Readings
		Homework assignments 


Week 2	Introduction to "patterns"  continued 
		Introduction to mathematical concept of symmetry
		Student research on examples from various cultures 
		Examples, and student group work on construction of examples
		Readings
		Homework assignments 

Week 3	Introduction to "patterns"  continued 
		Introduction to mathematical concept of symmetry
		Student research on examples from various cultures 
		Readings
		Homework assignments 

Week 4	Classification of all symmetries of the plane
		Student research on examples from various cultures 
		Homework assignments 
		Quiz 1

Week 5	Definition of one dimensional band ornaments
		Geometric view & algebraic view
		Student research on examples from various cultures
		Readings
		Homework assignments 

Week 6	Definition of two dimensional symmetries with infinite rapport
		Geometric view & algebraic view
		Student research on examples from various cultures
		Readings
		Homework assignments 

Week 7	Informal classification of one dimensional band ornaments
		Student teams to do informal classification
		Formal classification:  
		Readings
		Homework assignments 


Week 8	Combinations of symmetries in the two dimensional case
		Geometric view & algebraic view
		Student research on examples from various cultures
		Readings
		Homework assignments 
		Quiz 2

Week 9	Combinations of symmetries in the two dimensional case continued
		Geometric view & algebraic view
		Student research on examples from various cultures
		Readings
		Homework assignments 



Week 10	Outline of the classification of two dimensional “patterns” of 	double infinite rapport
		Readings 
		Homework assignments 

Week 11	Team Visual Presentations 

Prerequisites are an honest intellectual curiosity and the willingness to work hard.  This course does not satisfy a student's algebra deficiency.  Besides the homework problems, there will be two quizzes and the final visual team project.  Homework assignments will be due at the beginning of class.  Assignments turned in after the beginning of class are late and will be graded at 50% credit.  All late assignments will count towards class participation.  For example if a student turns in all the homework assignments late, they will receive 100% for the homework part of participation but will have the homework graded at 50% of the original possible score. The rest of the participation score will come from the student’s participation in the class work sessions.    
Grades will be based on class participation (25%), the homework assignments (37.5%), the quizzes (25.0%), and the final team project (12.5%).  For example, if a student had an 85% average on the homework, a 100% average on participation, an 82% average on quizzes, and an 81% on the final team project , their overall score would be calculated as follows:

OVERALL SCORE CALCULATION EXAMPLE

			Score		%		Times %

Homework		  85.0%		37.5%		 31.875%
Participation		100.0%		25%		 25.00%
Quizzes			  82.0%		25.0%		 20.50%
Final team project  		81.0%		12.5%		 10.125%

Overall Score					 87.50%

The students' grade for the course is determined by using their overall score and the University of Washington's grade conversion table from the faculty handbook.  The following table indicates the lowest letter grade from the chart to give the overall range.  The first column contains the overall student score which equates to the grade:

		Overall score		Letter Grade		University Grade
			90%			A-			3.5	
			80%			B-			2.5		
			70%			C-			1.5	
			60%			D-			0.7	
			below 60%		E			0.0			

For this example the student would receive a 3.2 University Grade

To request academic accommodations due to a disability, please contact Disabled Student Services (DSS) in the Counseling Center, Room LBA-102, (425) 352-5307, (425) 352-5303 (TDD).  If you have a documented disability on file with the DSS office, please have your DSS counselor contact me and we can discuss accommodations you might need in class.

Cinnamon Hillyard's office is room UW2-134 (inside QSC)				Phone is 425-352-3169
J.R. Rasmussen's office is room UW1-345  					Phone is 206-283-4698 or 425-352-5388
					  
								Class FAX    425-352-3367

Office Hours:		Cinnamon Hillyard	W  2:00-3:00 & Other times by appointment
			John Rasmussen	M & W  3:00-3:30 and 5:30-6:00  & Other times by appointment
					

e-mail: 	chillyard@uwb.edu  (Cinnamon Hillyard)  
	jrras@u.washington.edu  (John Rasmussen)

Course Web site: http://faculty.washington.edu/~jrras/bis329.htm
 
	 (Note, you will need to use Microsoft Internet Explorer to use the website.)