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Numbers & Functions

The Mathematics Foundation

Where the numbers come from and what a function really is, built from scratch — why negatives, fractions and the irrationals had to be invented; functions as machines with inputs and outputs; polynomials and the quadratic formula, exponentials and logarithms, sine and cosine; how to bend and combine functions; and the imaginary numbers that should not exist and make everything fit together.

Start reading → PDF EPUB

8chapters
43pages
29kwords

Contents

  1. 1 Counting Isn't Enough
  2. 2 The Hole in the Number Line
  3. 3 Functions as Machines
  4. 4 Polynomials, Factoring, and the Quadratic Formula
  5. 5 Exponentials and Logarithms
  6. 6 Trigonometric Functions
  7. 7 Functions as Objects
  8. 8 Numbers That Shouldn't Exist

Interactive notebooks

5 notebooks to work through alongside the chapters. Each one downloads from this site; "open in Colab" runs it in your browser with a free Google sign-in, nothing to install.

  1. Notebook 2.1 · Finite Precision download .ipynb · open in Colab
  2. Notebook 5.1 · Growth Decay Sigmoid download .ipynb · open in Colab
  3. Notebook 7.1 · Iteration Sqrt2 download .ipynb · open in Colab
  4. Notebook 7.2 · Logistic Map Chaos download .ipynb · open in Colab
  5. Notebook 8.1 · Complex Rotation Roots download .ipynb · open in Colab

Solutions (PDF)