Merge pull request 'main: some modification and typos' (#4) from ougur/numethods:main into main

Reviewed-on: denizdonmez/numethods#4

.gitignore

@@ -1,38 +1,3 @@
-Logo
-Issues
-Pull Requests
-Milestones
-Explore
-PhiloMath
-/
-data-fitting-models
-Private
-generated from PhiloMath/default-project-template
-Code
-Issues
-Pull Requests
-Actions
-Packages
-Projects
-Releases
-Wiki
-Activity
-Settings
-Files
-.gitignore
-LICENSE
-README.md
-data-fitting-models
-/
-.gitignore
-
-Ömür Uğur
-f9860d7f48
-Initial commit
-2 days ago
-357 lines
-6.4 KiB
-Plaintext
 # ---> JupyterNotebooks
 # gitignore template for Jupyter Notebooks
 # website: http://jupyter.org/

README.md

@@ -10,55 +10,9 @@ A lightweight, from-scratch, object-oriented Python package implementing classic
 - Lightweight, no dependencies.
 - Consistent object-oriented API (.solve() etc).
 
----
-
 ## 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.
+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. See [Tutorials](./tutorials/README.md).
-
-### 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`.
-
-- [Polynomial Regression Demo](tutorials/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.
-
----
 
 ## Features
 

tutorials/README.md

@@ -0,0 +1,47 @@
+# 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.
+
+---

tutorials/tutorial1_vectors_matrices.ipynb

@@ -142,7 +142,7 @@
     "## 5. Basic operations\n",
     "\n",
     "### 5.1 Vector addition and subtraction\n",
-    "For $ u, v \\in \\mathbb{R}^n $:\n",
+    "For $u, v \\in \\mathbb{R}^n$:\n",
     "\n",
     "$$\n",
     "u + v = \\begin{bmatrix} u_1 + v_1 \\\\ u_2 + v_2 \\\\ \\vdots \\\\ u_n + v_n \\end{bmatrix},\n",
@@ -180,7 +180,7 @@
    "metadata": {},
    "source": [
     "### 5.2 Scalar multiplication\n",
-    "For $ \\alpha \\in \\mathbb{R}, v \\in \\mathbb{R}^n $:\n",
+    "For $\\alpha \\in \\mathbb{R}, v \\in \\mathbb{R}^n$:\n",
     "\n",
     "$$\n",
     "\\alpha v = \\begin{bmatrix} \\alpha v_1 \\\\ \\alpha v_2 \\\\ \\vdots \\\\ \\alpha v_n \\end{bmatrix}.\n",
@@ -215,7 +215,7 @@
    "metadata": {},
    "source": [
     "### 5.3 Matrix addition and subtraction\n",
-    "For $ A, B \\in \\mathbb{R}^{m \\times n} $:\n",
+    "For $A, B \\in \\mathbb{R}^{m \\times n}$:\n",
     "\n",
     "$$\n",
     "A + B = [ a_{ij} + b_{ij} ], \\quad\n",
@@ -254,7 +254,7 @@
    "metadata": {},
    "source": [
     "### 5.4 Matrix-Vector multiplication\n",
-    "For $ A \\in \\mathbb{R}^{m \\times n}, v \\in \\mathbb{R}^n $:\n",
+    "For $A \\in \\mathbb{R}^{m \\times n}, v \\in \\mathbb{R}^n$:\n",
     "\n",
     "$$\n",
     "(Av)_i = \\sum_{j=1}^n a_{ij} v_j.\n",
@@ -290,7 +290,7 @@
    "metadata": {},
    "source": [
     "### 5.5 Matrix-Matrix multiplication\n",
-    "For $ A \\in \\mathbb{R}^{m \\times n}, B \\in \\mathbb{R}^{n \\times p} $:\n",
+    "For $A \\in \\mathbb{R}^{m \\times n}, B \\in \\mathbb{R}^{n \\times p}$:\n",
     "\n",
     "$$\n",
     "(AB)_{ij} = \\sum_{k=1}^n a_{ik} b_{kj}.\n",
@@ -327,7 +327,7 @@
    "metadata": {},
    "source": [
     "### 5.6 Transpose\n",
-    "For $ A \\in \\mathbb{R}^{m \\times n} $:\n",
+    "For $A \\in \\mathbb{R}^{m \\times n}$:\n",
     "\n",
     "$$\n",
     "A^T_{ij} = A_{ji}.\n",