Update README.md

README.md

@@ -12,6 +12,47 @@ A lightweight, from-scratch, object-oriented Python package implementing classic
 
 ---
 
+## Tutorial Series
+
+This package comes with a set of Jupyter notebooks designed as a structured tutorial series in **numerical methods**, both mathematically rigorous and hands-on with code.
+
+### Core Tutorials
+
+1. [Tutorial 1: Vectors and Matrices](tutorials/tutorial1_vectors.ipynb)
+
+   - Definitions of vectors and matrices.
+   - Vector operations: addition, scalar multiplication, dot product, norms.
+   - Matrix operations: addition, multiplication, transpose, inverse.
+   - Matrix and vector norms.
+   - Examples with `numethods.linalg`.
+
+2. [Tutorial 2: Linear Systems of Equations](tutorials/tutorial2_linear_systems.ipynb)
+
+   - Gaussian elimination and Gauss–Jordan.
+   - LU decomposition.
+   - Cholesky decomposition.
+   - Iterative methods: Jacobi and Gauss-Seidel.
+   - Examples with `numethods.solvers`.
+
+3. [Tutorial 3: Orthogonalization and QR Factorization](tutorials/tutorial3_orthogonalization.ipynb)
+
+   - Inner products and orthogonality.
+   - Gram–Schmidt process (classical and modified).
+   - Householder reflections.
+   - QR decomposition and applications.
+   - Examples with `numethods.orthogonal`.
+
+4. [Tutorial 4: Root-Finding Methods](tutorials/tutorial4_root_finding.ipynb)
+   - Bisection method.
+   - Fixed-point iteration.
+   - Newton’s method.
+   - Secant method.
+   - Convergence analysis and error behavior.
+   - Trace outputs for iteration history.
+   - Examples with `numethods.roots`.
+
+---
+
 ## Features
 
 ### Linear system solvers