Ecosyste.ms: Awesome
An open API service indexing awesome lists of open source software.
https://github.com/saadsalmanakram/matrix-singularity-and-cipher
My love triangle. Your complete guide to Maths, Physics And Computer...
https://github.com/saadsalmanakram/matrix-singularity-and-cipher
computing mathematical-programming mathematics physics
Last synced: about 15 hours ago
JSON representation
My love triangle. Your complete guide to Maths, Physics And Computer...
- Host: GitHub
- URL: https://github.com/saadsalmanakram/matrix-singularity-and-cipher
- Owner: saadsalmanakram
- Created: 2024-08-22T21:10:59.000Z (6 months ago)
- Default Branch: main
- Last Pushed: 2025-01-28T19:36:47.000Z (17 days ago)
- Last Synced: 2025-01-28T20:31:36.928Z (17 days ago)
- Topics: computing, mathematical-programming, mathematics, physics
- Homepage:
- Size: 0 Bytes
- Stars: 2
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
README
---
# 📊 Matrix, Singularity, and Cipher – The Ultimate Guide to Mathematics, Physics, and Computing
## 📌 Introduction
Mathematics, Physics, and Computing are the **fundamental pillars** of modern science and technology. This repository serves as a **comprehensive guide** to understanding advanced topics in **Linear Algebra, Calculus, Quantum Mechanics, Cryptography, and Computational Mathematics**.
📌 **Learn the foundations of Pure and Applied Mathematics**
📌 **Understand key concepts in Physics, including Quantum Mechanics and Relativity**
📌 **Explore the relationship between Mathematics, Algorithms, and Computing**
📌 **Delve into Cryptography and Secure Communication Techniques**
---
## 🚀 Features
- 📖 **Linear Algebra, Calculus, and Differential Equations**
- 🔥 **Physics Topics: Quantum Mechanics, Relativity, and Thermodynamics**
- 🤖 **Computational Mathematics with Python, NumPy, SymPy, and SciPy**
- 🔑 **Cryptography: RSA, Elliptic Curves, and Quantum Cryptography**
- 🎯 **Real-world Applications in Engineering, AI, and Cybersecurity**
---
## 📂 Repository Structure
```
Matrix-Singularity-and-Cipher/
│── mathematics/ # Pure and Applied Mathematics
│── physics/ # Classical and Quantum Physics
│── computing/ # Computational Mathematics and Algorithms
│── README.md # Documentation
```
---
## 🏁 Getting Started
### 1️⃣ Clone the Repository
```bash
git clone https://github.com/saadsalmanakram/Matrix-Singularity-and-Cipher.git
cd Matrix-Singularity-and-Cipher
```
### 2️⃣ Install Dependencies
```bash
pip install -r requirements.txt
```
### 3️⃣ Run Example Scripts
```bash
python mathematics/linear_algebra.py
python physics/quantum_mechanics.py
python cryptography/rsa_encryption.py
```
---
## 🔍 Topics Covered
### 📖 **Mathematics**
- **Linear Algebra**: Vectors, Matrices, Eigenvalues, Singular Value Decomposition (SVD)
- **Calculus**: Differentiation, Integration, Partial Derivatives
- **Complex Numbers & Fourier Transforms**
- **Differential Equations & Chaos Theory**
- **Mathematical Optimization & Numerical Methods**
### 🔥 **Physics**
- **Classical Mechanics**: Newtonian Laws, Lagrangian & Hamiltonian Mechanics
- **Quantum Mechanics**: Schrödinger Equation, Quantum States, Superposition
- **Relativity**: Special & General Relativity, Time Dilation, Lorentz Transformation
- **Thermodynamics & Statistical Physics**
### 🤖 **Computational Mathematics**
- **Symbolic Mathematics with SymPy**
- **Numerical Computation with NumPy & SciPy**
- **Matrix Computations & Eigenvalue Problems**
- **Optimization & Scientific Computing**
### 🔑 **Cryptography & Secure Computing**
- **Classical Cryptography: Caesar Cipher, Vigenère Cipher**
- **Modern Cryptography: RSA, AES, Elliptic Curve Cryptography (ECC)**
- **Quantum Cryptography & Post-Quantum Cryptography**
---
## 🔥 Example Code
### 🔨 **Solving a System of Linear Equations with NumPy**
```python
import numpy as np
A = np.array([[2, -1], [4, 3]])
b = np.array([3, 7])
x = np.linalg.solve(A, b)
print("Solution:", x)
```
### 🔥 **Quantum Mechanics: Solving Schrödinger’s Equation**
```python
import numpy as np
import scipy.linalg
# Define a simple Hamiltonian matrix
H = np.array([[0, 1], [1, 0]])
# Compute eigenvalues and eigenvectors
eigenvalues, eigenvectors = scipy.linalg.eig(H)
print("Energy Levels:", eigenvalues)
```
### 🔑 **RSA Encryption Implementation**
```python
from Crypto.PublicKey import RSA
key = RSA.generate(2048)
private_key = key.export_key()
public_key = key.publickey().export_key()
print("Public Key:", public_key.decode())
print("Private Key:", private_key.decode())
```
---
## 🏆 Real-World Applications
✅ **Quantum Computing & Quantum Cryptography**
✅ **Secure Communication & Cybersecurity**
✅ **Machine Learning & AI Applications**
✅ **Physics Simulations & Chaos Theory**
✅ **Mathematical Modeling for Science & Engineering**
---
## 🤝 Contributing
Contributions are welcome! 🚀
🔹 **Fork** the repository
🔹 Create a new branch (`git checkout -b feature-name`)
🔹 Commit changes (`git commit -m "Added Fourier Transform explanation"`)
🔹 Push to your branch (`git push origin feature-name`)
🔹 Open a pull request
---
## 📜 License
This project is licensed under the **MIT License** – feel free to use, modify, and share the code.
---
## 📬 Contact
📧 **Email:** [email protected]
🌐 **GitHub:** [SaadSalmanAkram](https://github.com/saadsalmanakram)
💼 **LinkedIn:** [Saad Salman Akram](https://www.linkedin.com/in/saadsalmanakram/)
---
⚡ **Master Mathematics, Physics, and Computing Today!** ⚡
---