Basics

 

You find here the Basic Mathematics of DigiMat in short codes starting with the construction of the natural numbers leading up to Calculus as the  mathematics of change as the foundation of both industrial and information society:

  1. Construction/representation of natural numbers in binary form by repetition of the basic operation of +1.
  2. Construction/representation of rational numbers in binary form.
  3. Computation with natural and rational numbers in binary form.
  4. Computation with rational numbers in decimal form.
  5. Coordinate systems (line, plane, screen).
  6. Position and motion of objects (along line, in plane, on screen) according to time stepping x = x + v*dt  or dx = v*dt.
  7. Calculus as time stepping dx = f(x)*dt or dx/dt = f(x).

Go though Basic Mathematics step by step together with JavaScript Mini and use Model and Games Workshops to get perspective and inspiration.

When you have done that and understood what you have done, then you can tell your math teacher, or Mom and Dad and the World, that you now master the essence of school mathematics and introductory university mathematics. Thus get started!

1. Start: Master Plan

2. Basic Mathematics:

See code to read explanation if not given explicitly. Run code by clicking arrow.

  1. Constructing the Natural Numbers
  2. Binary Representation of Natural Numbers see Illustration
  3. Reading Binary Representation
  4. Binary Addition. Compare with 2048 Game.
  5. Binary Abacus1
  6. Binary Abacus2
  7. Abacus Adding Machine
  8. Binary Multiplication
  9. Binary Subtraction
  10. Natural Numbers: Base 3
  11. Natural Numbers: Any Base
  12. Binary Division
  13. Pocket Calculator
  14. Primes
  15. Fibonacci Numbers
  16. Screen Geometry
  17. Motion-Change: x = x + v*dt
  18. Motion on Screen
  19. Draw Line
  20. Newtonian Mechanics: Angry Birds Basic
  21. Newtonian Mechanics
  22. Polynomials
  23. Exponential Function exp(t)
  24. Natural Logarithm log(t)
  25. Harmonic Series
  26. Trigonometric Functions cos(t) and sin(t)    (Variant 1) (Variant 2) (Bessel Function)
  27. Draw Circle
  28. Solving f(x)=0 by Bisection
  29. Solving f(x)=0 by Time Stepping x = x + f(x)*dt
  30. Solving x=g(x) by Fixed Point Iteration
  31. Calculus as dx = f(t)dt as x = integral f(t)dt
  32. Time stepping: Smart, Dumb and Midpoint Euler
  33. Integral: Midpoint Euler vs Forward/Endpoint Euler
  34. Compute Area of Circular Disk. Compute Pi. (check with Archimedes)
  35. Level Curves in 2d

3. Basic Programming:

Start with

Then consult according to need and inspiration

4. Model Workshop

5. Game Workshop

Complementing material:

  • Charlie Parker Jam Session (Now’s The Time for DigiMat):

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