This repository contains a collection of Python and Jupyter Notebook projects focused on applied mathematics, numerical methods, probability simulation, routing optimization, and machine learning fundamentals.
The Mission: As a mathematics graduate transitioning into applied data analytics, the goal of this portfolio is to bridge theoretical math with functional code. It demonstrates my ability to tackle practical mathematical problem-solving, data visualization, and algorithmic engineering using Python.
Implemented classical root-finding methods to solve nonlinear equations.
- Methods covered: Bisection Method, Newton-Raphson Method, Secant Method
- Skills demonstrated: Numerical approximation, error analysis, convergence comparison, Python function implementation
Implemented numerical methods to approximate definite integrals.
- Methods covered: Trapezoidal Rule, Simpson's Rule
- Skills demonstrated: Approximation of integrals, comparison with exact values, error calculation, visualization of convergence behavior
Solved ordinary differential equations numerically and compared results with the exact solution.
- Methods covered: Euler Method, Fourth-Order Runge-Kutta Method
- Skills demonstrated: Initial value problems, numerical solution of ODEs, convergence study, error analysis
Simulated basic probability experiments using Python to visualize theoretical limits.
- Topics covered: Coin toss and dice roll simulations, Experimental vs. theoretical probability, Law of Large Numbers
- Skills demonstrated: Random number generation, probability simulation, convergence visualization, statistical thinking
Built a small-scale routing optimization project using real-world German city locations.
- Topics covered: Route optimization, Traveling Salesman Problem (TSP) example, Distance matrices, OR-Tools routing solver
- Skills demonstrated: Optimization modeling, applied logistics problem-solving, route analysis, use of Google OR-Tools
Analyzed a network using graph-based mathematics and centrality metrics.
- Topics covered: Graph creation, network visualization, Degree centrality, Eigenvector centrality, PageRank
- Skills demonstrated: Network analysis, graph algorithms, node ranking, NetworkX visualization
Engineered a framework-free machine learning optimization algorithm to fit a linear regression model.
- Topics covered: Mean Squared Error (MSE) minimization, partial derivatives and vector calculus, learning rate tuning, algorithmic optimization
- Skills demonstrated: Translating foundational multi-variable calculus into functional Python code, NumPy matrix operations, demonstrating ML logic without relying on black-box libraries like
scikit-learn.
- Languages: Python
- Environment: Jupyter Notebook
- Libraries: NumPy, pandas, Matplotlib, NetworkX, Google OR-Tools
- Translating pure mathematics into applied algorithms
- Numerical methods & error analysis
- Algorithmic optimization & machine learning fundamentals
- Data visualization & scientific computing
- Clone this repository:
git clone [https://github.com/Inf1n1ty-8/Applied-Math-Python-Portfolio.git](https://github.com/Inf1n1ty-8/Applied-Math-Python-Portfolio.git)