Fractals, Dynamics and Chaos (2002, 2003, 2005, 2007) This was a course where students studied the geometric and analytic properties of certin fractals obtained from iterative schemes. Students used computer programs to run the iterative schemes and viewed the resulting images which showed interesting patterns coming from seemingly random processes. Students focused on the mathematical aspects of fractals and chaos.
Fourier Analysis (2002, 2003, 2004) This course introduced in an easy, intuitive form the idea of decomposing a function into frequencies and show some examples of practical applications of such decompositions. The emphasis was on hands on experience. Students played with digital images and sound in a computer classroom.
Geometry (2005) Going ‘Round in Circles: Circles provide a unifying theme for a study of Euclidean and non-Euclidean geometries. Many opportunities for student investigation were possible. Extensive use of the Geometer’s Sketchpad were expected. Time was devoted to this in four parts. 1) Euclidean geometry of the circle. 2) Studies in mutual tangency of congruent circles. 3) Circles on the sphere and a new geometry. 4) Circles and a model of non-Euclidean geometry (hyperbolic).
Graph Theory and Matrices (2003, 2004, 2006) Students covered special applications of linear algebra. Incidence matrices will be used to introduce matrix analysis of graphs; students studied how matrix operations are related to interesting properties of the graphs. Once matrices and matrix multiplication have been introduced, some ideas of computer graphics were explored. The students finished the week by using basic linear transformations to make their own “mini” movies with Mathematica or Matlab.