This course is an introduction to fractal geometry, a visually motivated mathematical technique for studying roughness. The underlying idea is that complex shapes can be produced by simple processes. We begin with studying iterated function systems, a simple geometrical language for generating intricate images. Shrinking, rotating, reflecting, and translating shapes are the main ideas used for these problems. The roughness or complexity of these shapes is quantified by an exponent, called the fractal dimension. Calculating this dimension involves logarithms, which we review. Other topics involve the Mandelbrot set and fractal analysis of the stock market. Examples of fractals in art, architecture, literature, and music will be discussed.
Students having some calculus and linear algebra background should consider taking Math 290, a course focusing on the mathematics of fractals.
Math 190 is taught at a level that should be appropriate for any incoming freshman, and does not assume that students have had any mathematical training beyond high school algebra and geometry.
Below is a list of specific topics that should be familiar to students. The list is followed by a sample problem illustrating how each topic will be used. Immediate answers are not the goal; answers after some thought are fine. Students who find these questions particularly challenging should contact the instructor for guidance as to the appropriateness of the course.
Note that these are the skills you need to enter the course. Many more quantitative skills will be developed throughout the course.
Topics
1. Properties of similar triangles
2. Deductions about areas and volumes of simple shapes
3. Finding the slope of a line
4. Solving linear equations
5. Solving quadratic equations
6. Expanding binomials
Examples
1. Suppose 
ABC is similar to DEF and segment AB is twice as long as the corresponding segment DE. If segment BC is 1 cm long, how long is the corresponding segment EF?
2. Suppose a side of square A is one-third as long as a side of square B. If the area of square B is 1 cm2, what is the area of square A?
3. Is there a line through the points (1,2), (2,4), and (3,6)? If there is, what is the slope of that line?
4. Find x if (1/2)(x/3 + 1/4) = 1.
5. Find x if 3x2 - 5x - 2 = 0.
6. Expand (x + 2)3. Note the word ”expand” means ”multiply out.”