Wednesday, February 4, 2009

The First and Second Weeks

I. The First Week - Special Fractals

The first weekly session mainly consisted of going over the definition of a complex number, its significance in mathematics, and one of the most curious, new mathematical concepts - fractals. 

[Fig. 1-1 - Mandelbrot set, surrounded by different Julia sets]

Fractals are the graphed projections of figures that, when examined at any given point, seemingly expand, like the examination of an atom under a microscope. An example of a fractal is the Mandelbrot set (see Fig. 1-1). These microscopic-like projections keep seemingly expand to infinity and project all sorts of differently-shaped figures, like seen in Fig. 1-1, called Julia sets. 

II. The Second Week - Proper Introduction to Complex Geometry

Our second meeting went back to basics in terms of discussions of our course material. This week's material consisted of reviewing how to add, subtract, multiply, divide, and find nth roots of complex numbers. The review session also touched on definitions, such as amplitude (or absolute value) and modulus (or principle value). 

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