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tutorials/README.md

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+# 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](./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](./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](./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](./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`.
+
+- [Polynomial Regression Demo](./polynomial_regression.ipynb)
+
+- Step-by-step example of polynomial regression.
+- Shows how to fit polynomials of different degrees to data.
+- Visualizes fitted curves against the original data.
+
+---