Computer work

I have used several different computer packages, including Sage, Magma, Macaulay 2, and Excel in my research and in my teaching. Here I have gathered several materials I created in different contexts.

Sage and calculus

• Computer assignment 1: Graphing a parametrized curve in Sage. Example.
• Computer assignment 2: Graphing surfaces in Sage. Example.
• Saddle and cross sections.
• Two cylinders intersecting.
• Multiple integrals in Sage.
• Computer assignment 3: Graphing vector fields in Sage. Example.
• Surface areas via frusta. Hurricane candleholder, Horn and egg.

Option Pricing

• Using Sage to plot graphs of the density function for normal and log normal random variables with varying mu and sigma.
• MSFT prices resembling Brownian motion
• Examples of Brownian motion
  
• Increments of the scaled random walk approach a normal random variable as n goes to infinity
• Delta hedging spreadsheet for Homework 12
• Computer Lab 3: Historical volatility & testing the Black-Scholes assumptions Prototype
• My Monte Carlo spreadsheet
• My Monte Carlo with VBA spreadsheet
• My VBA code for Monte Carlo
• How many times do you have to flip a coin to get two heads in a row?

Algebraic Geometry

• How to dualize polytopes in Sage, polymake and 4ti2
• The Nephroid of Freeth:
  • Sage animation (Warning: this was created in Sage 4.1.1; the code breaks in newer versions of Sage)
  • Macaulay 2 commands for finding equations in rectangular coordinates (elimination)
    
• An old Magma tutorial on curves with automorphisms. See my IVRG page for more recent work on this project.
• A Macaulay 2 tutorial
• Creating the Chow ring of \overline{M}_{0,n} in Macaulay 2 Code, Example
• Computing Nef(\overline{M}_{0,6}) in Macaulay 2
• The package ConformalBlocks for computing conformal blocks in Macaulay 2.

Excel

Here is an introduction to Excel that I used with my MATH 5003 class ("Algebra and Problem Solving for Future Elementary Teachers") during our unit on statistics.