Scientific Computing

Course Description

We will study a number of computational tools and techniques to model and visualize scientific processes. Each sessions we will carry out a series of computational exercises using Mathematica, matlab, Python, C, Fortran, and/or a computer language of the student’s choice (no previous programming experience is required). These exercises will be drawn from mathematics, chemistry, biology, and physics. In addition, we will have a quick introduction to the typesetting program LaTeX, allowing for the preparation of professional scientific documents incorporating high-quality images. An effort will be made to allow each student to work on problems appropriate to his or her interests.

Course Documents

Sample Student Projects
Richard Fucso, A Windy Future?
The goal of this program is to manipulate data and determine where the most suitable locations for wind farms are in the United States. The program was written in Mathematica and chooses optimal locations based on three parameters: wind speed, population density, and average value of land. The program should provide a starting point for those who want to delve further into the topic of wind farm development.
Matthew Lea, Michael Mara, and Qiao Zhang, Gamma Knife Treatment Planning
The problem of where to focus radiation during certain types of radiosurgery can be repre- sented as a sphere-packing problem. We implement a method for simulating cancerous tumors on which solutions can be tested and visualized. We then implement an algorithm to approxi- mate the optimal sphere-packing of an irregular shape and consider its performance using our visualization.
Julia sets are one of the most widely known families of fractals. First developed by Gaston Julia in the early 20th century, this family of fractals has many different and beautiful exemplars. Beyond their aesthetic appeal, Julia sets stand apart fromother fractals due to the extraordinarily simple method required to produce them. Furthermore, the Julia sets are intimately related to the highly famous Mandelbrot set. This paper demonstrates a method for producing Julia sets using Mathematica and then quickly overviews their relationship with the Mandelbrot set.

Qiao Zhang, Art Machine

This visualization project is inspired by the Double Pendulum device constructed by Professor R. H. Romer from Amherst College. The Double Pendulum, dubbed “the Art Machine”, produces intriguing Lissajous figures on paper. We will first replicate the curious patterns produced by Prof. Romer’s “the Art Machine”, and then extend to cases that are constrained by limitations of the experimental apparatus.

Useful Links for Python


Other Useful Links