https://computational-discovery-on-jupyter.github.io/Computational-Discovery-on-Jupyter/

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Computational Discovery on Jupyter

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  * Welcome to Computational Discovery on Jupyter

Preface

  * Preamble
  * Before we begin: installing Python and Jupyter

Contents

  * Computing with Fibonacci Numbers
  * Continued Fractions
  * Rootfinding, Newton's Method, and Dynamical Systems
  * Fractals and Julia Sets
  * Bounded Height Matrices of Integers (Bohemian Matrices)
  * Mandelbrot Polynomials and Matrices
  * Chaos Game Representation

Epilogue

  * Zanshin

Appendix

  * What do to when things go wrong
  * The Bare Minimum about Floating-Point
  * Binomials, Factorials, and other Combinatorial Things
  * Complex Numbers
  * Symbolic Computation: The Pitfalls

Reports on Activities

  * Reports on Fibonacci Activities
  * Reports on Continued Fractions Activities
  * Reports on Rootfinding Activities
  * Reports on Julia Set Activities
  * Reports on Bohemian activities
  * Reports on Mandelbrot Activities
  * Reports on Chaos Game Activities

Back Matter

  * Acknowledgements
  * About the authors
  * References

Powered by Jupyter Book

  * repository
  * suggest edit

  * .ipynb
  * .pdf

Contents

  * Overture
      + What's in it for you?
      + What's in it for us?
      + What's in it?

Welcome to Computational Discovery on Jupyter

Contents

  * Overture
      + What's in it for you?
      + What's in it for us?
      + What's in it?

Welcome to Computational Discovery on Jupyter#

Overture#

In this section there are no definitions, no theorems, no
computations. Well, not in this overture: just a picture, the an
infinite number of infinity symbols below, and a little discussion of
why we wrote this Open Educational Resource or book, and what you
might get out of it.

_images/SchroederIterationStrang.png

Fig. 1 Infinitely many infinity symbols#

What's in it for you?#

We'll be using Python to explore some interesting mathematics,
mathematics not in the standard curriculum. So it's an opportunity to
learn a popular programming language. Why use mathematics, instead of
some other science, like biology or physics or chemistry? Why not
some engineering, or economics, or psychology, or music?

The truth of the matter is that math is the simplest out of all of
those. You probably know that already. This is the fastest way to
learn Python. You'll wind up learning some other things too, but
let's start with that.

What's in it for us?#

Many of our students, when surveyed, say that they want to be taught
"more programming" and for it to be taught earlier. This is an
attempt to do so. Also, we feel that by offering some interesting
mathematics straight away, which we can do owing to the powerful
tools that we're going to use, we might reach a larger audience for
mathematics, and to keep people interested for longer. Math is useful
for a lot of things, although we're not going to focus on that part
of it. Instead we're going straight for the heart of mathematics.

What's in it?#

We'll use videos, images, programs, programming activities,
pencil-and-paper activities, and this Jupyter Book and the associated
Jupyter Notebooks to present material for your inspection and
interaction. We will encourage people to contribute their own
notebooks to extend this material. Indeed some of the material that
you will see was created/discovered/invented/published first by our
students.

An Introductory Video

 

next

Preamble

By Neil J. Calkin, Eunice Y.S. Chan, and Robert M. Corless
(c) Copyright 2022.