Dr. Moretti’s Mathematica Notebooks – Standard Algebra
Mathematica Notebooks for Standard Algebra
Important Note: The links for the notebooks open a new window or tab with a Google Drive page – the current settings for our homepages won’t allow me to host mathematica notebooks locally.
Slope and Slope Intercept
This notebook contains two simple manipulations to illustrate the idea of the slope between two points and the slope-intercept form of a line.
Roots of Polynomials
This notebook has a manipulation which displays the complex roots of a polynomial graphically in the complex plane. By changing the degree and selecting “Random Polynomial”, you can see the Fundamental Theorem of Algebra (a polynomial of degree n has n roots) and the Conjugate Theorem (if p(x) is a polynomial with real coefficients and a+bi is a root, so is a-bi). Real roots are blue, nonreal roots in green.
This notebook demonstrates how to multiply two polynomials step by step.
Solving Cubic Equations by Trisections
This notebook demonstrates the steps to solving a cubic equation geometrically by trisecting a particular angle. You can find a version of this on the Wolfram Demonstrations Project.
Solving Cubic Equations by Common tangents
This notebook lets you (approximately) solve a cubic equation by trying to find a common tangent to two particular parabolas. It’s based on an idea from David A. Cox’s excellent textbook Galois Theory.