This 1-credit course will explore various aspects of the fourth dimension through a variety of perspectives. Just as an anthropologist studies other cultures and returns with new insights about our own society, we hope to gain a deeper understanding of our 3D world after "going outside of it" to see other alternatives. The course will involve critical reading to sort mathematical substance from fancy, much model making with a variety of materials, discussions, and presentation of a term project or paper that involves research and critical thought.

This seminar is limited to 20 students and is graded with a letter grade. Class participation is expected.  Some of the topics to be explored are:

• Geometric:  For example, what comes next in the sequence: segment, polygon, polyhedron, ...? How can we rigorously study and appreciate the mathematical properties of 4D objects?
• Computational:  How do we represent 4D structures in a computer model, to analyze, manipulate or visualize them?
• Literature and popular culture: How has the fourth dimension appeared in literature, e.g., Edwin Abbott’s Flatland, and in the popular imagination?
• Formal mathematics: What are the rigorous axiomatic (definition-theorem-proof) and coordinate (w,x,y,z) methods of exploring patterns and relationships in 4D geometry?
• Artistic: How have artists found inspiration and insight from ideas of hyperspace?
• Visualization: How can lower-dimensional shadows and cross-sections of higher-dimensional objects help us to develop intuition about structures we can not directly apprehend?
• Historical: How has study of the fourth dimension developed over time?
• Engineering: Given that geometrical insight is essential to many aspects of science and engineering, how can we, living in a 3D world, engineer good models of higher-dimensional structures, and what do we learn from them?

• Edwin A. Abbott (under the pseudonym: A. Square), Flatland: A romance of many dimensions, 1884. (many reprints are available)
• Thomas F. Banchoff, Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions, W. H. Freeman, 1990.

In this seminar we will use the web-based Blackboard system to share work with each other.  After you register for the the course with the university (using Solar), log on to Blackboard and enroll yourself in its database as a student of ITS101.

Course information can be found on Stony Brook's Blackboard site: http://blackboard.sunysb.edu    In order to log into this website, you will need your blackboard user name and password.  If you used Blackboard during the Fall 2002 semester, your login information is the same.  If you did not use Blackboard during the Fall 2002 semester, your user name is your University user name (sparky account),  (which is normally your first initial, and the first 7 letters of your last name).  Your password is your Solar (Stony Brook) ID#.  If your user name does not work, your instructor will be able to provide you with that information.  In addition, you can go to one of the following SINC Sites to look up your user name: Student Union Room 080, Computing Center Room 138, Main Library Room S1460, or HSC Library (3rd floor).   There are 11 SINC Sites (public computer labs on campus), for details (locations & schedules), go to: http://www.sinc.sunysb.edu/Sinc