3847 days ago by hirsthp

Using Sage in Modeling Classes

Sage can be used as a tool to investigate mathematical models at many levels.  There are pros and cons to this: 

  • Sage provides a rich set of symbolic and numerical computational tools, allowing you to focus on model formulation and interpretation of results.
  • To take full advantage of the power and flexibility of Sage requires a learning curve we often don't have time for in a modeling course (or in any course whose focus is not the software itself.

The key is to decide first what your educational goals are.  In the worksheets available for you to try in this session, I have three approaches that were decided upon based upon the "learning outcomes" -- accreditation buzzword! -- for the class.

Links to the PDFs:

The Linear Programming Worksheet

This worksheet is designed for a class with middle grades math teachers, and the goal is to have them become familiar with applications of algebra. The specific goal of this worksheet:

  • Demonstrate the graphical solution approach and why the solution occurs at a corner.
  • Provide a template for numerical solution of problems so that the teachers can focus on set up and interpretation as well as allow them to solve larger problems.

I don't want Sage to be the focus of the discussion.

The goal with this worksheet is to provide a template that the teachers can use to solve other linear programming problems through editing the existing worksheet.  I have kept the use of Sage to a minimum.


The Markov Chain Worksheet

This worksheet is designed for a class with in-service secondary teachers who have a background in linear algebra and probability, and the goal is two-fold:

  • Introduce the concept of regular and absorbing Markov chains.
  • Practice the teachers' ability to determine probabilities and manipulate matrices.

Once again, becoming highly proficient in Sage is not the point.

The Population Modeling Worksheet

This worksheet is designed for sophomore/junior level modeling, and as a "cheat sheet" for a few simple solution procedures. The main text is in the pdf handout, along with the commands. I would normally NOT provide the worksheet, but would have them copy and paste the sage commands into the worksheet from the PDF.

The goal here is to have students learn to set up ODEs, and interpret output.  We do not emphasize solution techniques in this course.