Mathematical Foundations for AI/ML

Python implementations of core mathematical algorithms used in machine learning and optimization.

What's Here

This repo contains implementations of fundamental mathematical techniques - gradient descent, matrix operations, optimization methods, and more. Each folder has working code with comments explaining the math behind it.

Projects

HW1 - Gradient Descent

Basic gradient descent implementation with sigmoid activation function. Includes 1D optimization with configurable learning rate and iteration count.

Key files: pweek1.py

HW2 - Matrix Operations

Row operations for Gaussian elimination: swap rows, scale rows, add multiples. Also includes RREF computation and max/average pooling for CNN applications.

Key files: pweek2.py

HW3 - PageRank Algorithm

Implementation of Google's PageRank using power iteration on column-stochastic matrices. Includes matrix normalization and result ranking.

Key files: pweek3.py

HW4 - Least Squares Fitting

Linear and polynomial regression using NumPy's lstsq. Fits lines and cubic polynomials to data with residual analysis.

Key files: wh4.py

HW5 - Projected Gradient Descent

Constrained optimization on convex sets (unit ball and square box). Uses SymPy for symbolic differentiation and projects gradient steps back onto feasible regions.

Key files: pweek5.py

HW6 - Probability & Statistics

Statistical analysis including chi-square testing and distribution fitting.

HW7 - Linear Regression

Multi-variable regression analysis with golf score prediction dataset.

HW8 - K-Means Clustering

Centroid-based clustering algorithm for unsupervised learning. Implements iterative centroid assignment and update steps with projection onto feasible regions.

Key files: pweek8.py

HW9 - Integration

Numerical integration using Simpson's rule and Gaussian quadrature.

Setup

pip install numpy scipy matplotlib sympy

Usage

Each homework folder contains standalone Python files. Import and call the functions directly:

from HW5.pweek5 import PGD, Proj, BoxProj
import numpy as np
from sympy import symbols

x, y = symbols('x y')
result = PGD(x**2 + y**2, np.array([3, 4]), 10, 0.1)

Interactive Portfolio

Open index.html in a browser to see an interactive visualization of all the mathematical concepts covered in this project.

Tech Stack

• Python 3.8+
• NumPy for numerical computing
• SymPy for symbolic math
• Matplotlib for visualization