Computing and Mathematics at 
Kenyon College
A student perspective
By David Carroll '98
Presentation to the Kenyon College Board of Trustees 4/24/98 
   
 
  
   
  Innovative Projects 

Independent Student Research
   
Introduction
Thanks to a grant from the Howard Hughes Medical Institute, the Mathematics Department of Kenyon College has purchased new computers capable of extremely rapid calculations. 
   
Professor Judy Holdener teaches a Calculus C class in the newly refurbished Roth Classroom.
 
  
 

Students hard at work in the Finkbeiner Reading room under the watchful gaze of Hilbert, Noether and Courant.
This presentation will highlight a very few of the many advances in the mathematics curriculum made possible by these number-crunchers.
  
 
  
Computers and the New Calculus
"Reform calculus" has seen an explosion of interest in the last three or four years. However, Kenyon began teaching a reform curriculum over ten years ago. 
 
   
Traditional Calculus 
Reform Calculus 
Analytical 
Theoretical 
Formulaic 
Visual 
Rote Memorization 
Conceptualization 
Pencil and Paper 
Computers 
Relies Heavily on Text 
"Hands On" 
   
Visualization is one of the key elements of reform calculus. Computers make it possible for students to understand critical theories in a visual way. The mathematical software package of choice at Kenyon is MAPLE. 

Here is an example of a computer-based exercise given to introductory Calculus students this year: 
   

THE GOBLET PROJECT

Your task is to design a goblet that meets the following specifications. 
  • It must be a solid of revolution. (Circularly symmetric.) 
  • It must hold at least 150 ml. of liquid 
  • It cannot take any more than 150 ml. of glass to manufacture. 
  • The ratio of the height of the center of mass to the radius of the base must be no more than 3:1. 
  • The radius of its stem must be at least 1/4 cm. at its thinnest point. 
  
 
  
Innovative Projects
Parametric Images

In Judy Holdener's Calculus C course, four major projects focus on the use of Maple as a mathematical tool. One such project involved learning about parametrics, a way of describing curves and lines in two dimensions. 
 
Once we students had grasped the concept, we were told to get creative--to apply our knowledge by making pictures with pure mathematics. 
The Kenyon Shield Equation
  
 
  
Computer Science

Programming is another (obvious) use of Math Department computers. This image is the result of a final project for Prof. Benjamin Shults' Introduction to Computer Science.  

An example of ray-tracing three dimensional rendering, it was created by a first-year student. 
  
  
Independent Student Research
Through the Summer Scholars Science program, students can experience intensive mathematical research.  Not surprisingly, this can often involve heavy computer use.
This fractal was a small part of the summer research of an Honors Math Major who was studying root finding methods.
Recent Independent Studies: 
  • Advanced Windows Programming
  • Discrete Mathematical Models
  • Statistical Modeling
  • Biological Populations
  
 And so much more...
  
Conclusion
With the unprecedented recent explosion of the Internet and personal computer use in general, the mathematicians of the next millenium will undoubtedly bring their computers along.  Once a marginal discipline, computing will become the central tool of a more comprehensive and stronger curriculum.
  
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