README.md overhaul and improvements

README.md

@@ -3,22 +3,36 @@
 This is my (Eli Bradley's) computer science project, a Kotlin DSL focusing on various topics I've learned about
 through school and just on my own. This includes:
 
-- [X] Vector Algebra
-- [X] Multivariable Calculus
-  - [X] Gradient Descent
-- [X] Basic Linear Algebra
-- [X] Electrostatic Simulations
-- [X] Analytic Transformations
-  - [X] Taylor Series
-  - [ ] Fourier Series and Transformations
-- [X] Complex Algebra
-  - [X] Complex Numbers
-  - [X] Complex Vectors
-  - [X] Complex Matrices
-- [X] Quantum Computing
-  - [X] Entangled Qubit States
-  - [X] Quantum Gates
-  - [X] Quantum Circuits
-    - [X] Parallel Gates
-    - [X] Sequential Gates
-  - [X] Measuring
+## Introduction
+MathLibrary is a comprehensive Kotlin Domain-Specific Language (DSL) designed to facilitate a wide range of mathematical operations, including vector algebra, multivariable calculus, and quantum computing simulations. Developed out of a passion for applying computer science concepts to real-world mathematical problems, this library serves as a toolkit for developers seeking to simplify complex calculations and simulations.
+
+## Features
+MathLibrary offers a robust set of features across various domains:
+- **Vector Algebra**: Perform operations on vectors with ease.
+- **Multivariable Calculus**: Simplify multivariable functions and gradient descent calculations.
+  - Gradient Descent
+- **Linear Algebra**: Manipulate matrices and solve linear equations.
+- **Electrostatic Simulations**: Simulate electrostatic forces and fields.
+- **Analytic Transformations**: Explore Taylor series and dive into Fourier series and transformations.
+- **Complex Algebra**: Work with complex numbers, vectors, and matrices effortlessly.
+- **Quantum Computing**: Design and test quantum circuits with support for entangled states and quantum gates, including parallel and sequential gates, and measuring techniques.
+
+## Installation
+To integrate MathLibrary into your Kotlin project, follow these steps:
+1. Ensure you have Kotlin set up in your IDE .
+2. Add the following dependency to your `build.gradle` file:
+    ```
+    dependencies {
+        implementation 'com.github.yourusername:MathLibrary:latest-version'
+    }
+    ```
+3. Sync your project to download the library.
+
+## Contributing
+We are an open-source project and welcome contributions from the community! Whether you're fixing a bug, adding a new feature, or improving documentation, your help is appreciated. Please refer to the guidelines for more information on making contributions.
+
+## Project Structure
+The project is organized into modules based on subject, making it easy to navigate and find specific functions.
+
+## Contact
+To contact us, please email us at [mathlibrary@gmail.com](mailto:mathlibrary@gmail.com).