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:
- Construction/representation of natural numbers in binary form by repetition of the basic operation of +1.
- Construction/representation of rational numbers in binary form.
- Computation with natural and rational numbers in binary form.
- Computation with rational numbers in decimal form.
- Coordinate systems (line, plane, screen).
- Position and motion of objects (along line, in plane, on screen) according to time stepping x = x + v*dt or dx = v*dt.
- Calculus as time stepping dx = f(x)*dt or dx/dt = f(x).
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!
2. Basic Mathematics:
See code to read explanation if not given explicitly. Run code by clicking arrow.
- Constructing the Natural Numbers
- Binary Representation of Natural Numbers see Illustration
- Reading Binary Representation
- Binary Addition. Compare with 2048 Game.
- Binary Abacus1
- Binary Abacus2
- Abacus Adding Machine
- Binary Multiplication
- Binary Subtraction
- Natural Numbers: Base 3
- Natural Numbers: Any Base
- Binary Division
- Pocket Calculator
- Fibonacci Numbers
- Screen Geometry
- Motion-Change: x = x + v*dt
- Motion on Screen
- Draw Line
- Newtonian Mechanics: Angry Birds Basic
- Newtonian Mechanics
- Exponential Function exp(t)
- Natural Logarithm log(t)
- Harmonic Series
- Trigonometric Functions cos(t) and sin(t) (Variant 1) (Variant 2) (Bessel Function)
- Draw Circle
- Solving f(x)=0 by Bisection
- Solving f(x)=0 by Time Stepping x = x + f(x)*dt
- Solving x=g(x) by Fixed Point Iteration
- Calculus as dx = f(t)dt as x = integral f(t)dt
- Time stepping: Smart, Dumb and Midpoint Euler
- Integral: Midpoint Euler vs Forward/Endpoint Euler
- Compute Area of Circular Disk. Compute Pi. (check with Archimedes)
- Level Curves in 2d
3. Basic Programming:
Then consult according to need and inspiration
- Charlie Parker Jam Session (Now’s The Time for DigiMat):