Update README.md

Author: B67687

README.md

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 # MathLearningNotes
-Repository for my mathematics learning notes, covering topics like trigonometry, precalculus, calculus, and discrete math.
+
+Repository for mathematics learning notes, covering topics like trigonometry, precalculus, calculus, and discrete math.
+
+## Table of Contents
+
+- [Overview](#overview)
+- [Installation](#installation)
+- [Jupyter Notebooks](#jupyter-notebooks)
+  - [Root Directory Notebooks](#root-directory-notebooks)
+  - [Algebra](#algebra)
+  - [Calculus](#calculus)
+  - [Discrete Mathematics](#discrete-mathematics)
+    - [Combinatorics](#combinatorics)
+  - [Fractals](#fractals)
+  - [Trigonometry](#trigonometry)
+  - [Translated Notebooks](#translated-notebooks)
+- [Usage](#usage)
+- [Contributing](#contributing)
+- [License](#license)
+
+## Overview
+
+This repository contains a collection of Jupyter notebooks documenting various mathematical concepts, proofs, and explorations. The notebooks are organized by mathematical discipline and include both theoretical explanations and practical examples.
+
+## Installation
+
+To use these notebooks, you'll need to have Jupyter installed. You can set up the environment using either the provided `environment.yml` file (for conda) or `requirements.txt` (for pip).
+
+### Using Conda
+
+```bash
+conda env create -f environment.yml
+conda activate math-learning
+```
+
+### Using Pip
+
+```bash
+pip install -r requirements.txt
+```
+
+## Jupyter Notebooks
+
+### Root Directory Notebooks
+
+| Notebook | Description |
+|----------|-------------|
+| [Math-Lessons.ipynb](Math-Lessons.ipynb) | Main notebook with comprehensive math lessons compiled from previous Google Docs |
+| [Template_Notebook.ipynb](Template_Notebook.ipynb) | Template for creating new detailed notes |
+| [Template_QUICKNOTE.ipynb](Template_QUICKNOTE.ipynb) | Template for creating quick notes |
+
+### Algebra
+
+| Notebook | Description |
+|----------|-------------|
+| [general-properties.ipynb](algebra/general-properties.ipynb) | General properties of algebraic operations |
+
+### Calculus
+
+The calculus section contains a series of advancement reports documenting progress in learning calculus concepts, as well as specific topic notebooks.
+
+| Notebook | Description |
+|----------|-------------|
+| [derivative-proofs.ipynb](calculus/derivative-proofs.ipynb) | Proofs related to derivatives |
+| [advancements-report-*.ipynb](calculus/) | Daily/weekly progress reports from March-April 2025 |
+
+### Discrete Mathematics
+
+#### Combinatorics
+
+| Notebook | Description |
+|----------|-------------|
+| [binomial-expansion.ipynb](discrete-mathematics/combinatorics/binomial-expansion.ipynb) | Binomial expansion formulas and applications |
+| [pascals-triangle.ipynb](discrete-mathematics/combinatorics/pascals-triangle.ipynb) | Pascal's triangle properties and applications |
+| [permutation-and-combination.ipynb](discrete-mathematics/combinatorics/permutation-and-combination.ipynb) | Permutation and combination concepts |
+
+### Fractals
+
+| Notebook | Description |
+|----------|-------------|
+| [mandelbrot.ipynb](fractals/mandelbrot.ipynb) | Mandelbrot fractal exploration and visualization |
+
+### Trigonometry
+
+| Notebook | Description |
+|----------|-------------|
+| [fun-simulations.ipynb](trigonometry/fun-simulations.ipynb) | Trigonometric function simulations |
+| [getting-definitions-right.ipynb](trigonometry/getting-definitions-right.ipynb) | Precise definitions of trigonometric concepts |
+| [r-formula.ipynb](trigonometry/r-formula.ipynb) | R-formula in trigonometry |
+| [the-way-is-to-simplify-case-study.ipynb](trigonometry/the-way-is-to-simplify-case-study.ipynb) | Case study on simplification techniques |
+| [advancements-report-*.ipynb](trigonometry/) | Progress reports from March 2025 |
+
+### Translated Notebooks
+
+The `translated-notebooks` directory contains translated versions of various notebooks, primarily in Chinese. These translations are generated using the `translate_notebooks.py` script.
+
+## Usage
+
+To use these notebooks:
+
+1. Clone the repository:
+   ```bash
+   git clone https://github.com/B67687/MathLearningNotes.git
+   ```
+
+2. Set up the environment as described in the [Installation](#installation) section.
+
+3. Launch Jupyter Notebook or Jupyter Lab:
+   ```bash
+   jupyter notebook
+   # or
+   jupyter lab
+   ```
+
+4. Navigate to the notebook of interest and open it.
+
+## Contributing
+
+Contributions are welcome! If you'd like to contribute:
+
+1. Fork the repository
+2. Create a new branch for your feature
+3. Add your changes
+4. Submit a pull request
+
+## License
+
+This project is licensed under the MIT License - see the [LICENSE](LICENSE) file for details.
+