MathFromScratch

Description

Implementation and visualization of various math theorems, formulae, operations and examples only using built-in modules and NumPy. Implementing math operations from scratch and playing with them changing various parameters give us deeper and more conceptual understanding of math. In addition, building something from scrach is fun! In each tutorial, details explanation of each implementation is shown and also you know how to use it.

Features

Demo

Requirments

• NumPy
• Matplotlib

Usage

Tutorials

1. Geometry

• Triangle
• Circle
• Ellipsoid, Hypobolic

2. Descrete Math

• Combination
• Factorial

3. Linear Algebra

• Elementary Operation
• Rank
• Inverse Matrix
• Determinant
• Eigen-decomposition
• QR Factorization
• LU Factorization
• Cholesky Factorization
• LDL Factorization

4. Differentiation

• Differentiation
• Taylor Series
• Gradient
• Hessian Matrix
• Jacobian Matrix

5. Integration

• Integration
• Numerical Integration Algorithms
• Convolution
• Fourier Transform
• Continuous Fourier Transform

6. Probability & Statistics

• Descrete Distributions
  • Bernoulli Distribution
  • Binomial Distribution
  • Poisson Distribution
  • Geometric Distribution
• Continuous Distributions
  • Uniform Distribution
  • Gaussian Distribution
  • Exponential Distribution
• Cumulative Distribution Function (CDF)

7. Rootfinding and Optimization

• 1D Rootfinding Algorithms
  • Bisection Method
  • Newton Method
  • Secant Method
• Solving System of Equation
  • Newton-Raphson Method
• Optimization using Gradient
  • Gradient Descent
  • Newton Method
  • Quasi-Newton Method

8. Differential Equation

• Numerical Differential Equation
  • Euler Method
  • Runge-Kutta Method

Author

References

Licence