Update README.md

README.md

@@ -1,7 +1,8 @@
 # MathLibrary
 
-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:
+## Project Description
+
+MathLibrary is a Kotlin DSL project created by Eli Bradley that encompasses applications of the following mathematical computations:
 
 - [X] Vector Algebra
 - [X] Multivariable Calculus
@@ -10,7 +11,7 @@ through school and just on my own. This includes:
 - [X] Electrostatic Simulations
 - [X] Analytic Transformations
   - [X] Taylor Series
-  - [ ] Fourier Series and Transformations
+  - [X] Fourier Series and Transformations
 - [X] Complex Algebra
   - [X] Complex Numbers
   - [X] Complex Vectors
@@ -22,3 +23,80 @@ through school and just on my own. This includes:
     - [X] Parallel Gates
     - [X] Sequential Gates
   - [X] Measuring
+
+## Table of Contents
+
+1. [How to Install and Run the Project](#how-to-install-and-run-the-project)
+2. [How to Use the Project](#how-to-use-the-project)
+3. [Project Structure](#project-structure)
+4. [Testing](#testing)
+5. [How to Contribute to the Project](#how-to-contribute-to-the-project)
+6. [Credits](#credits)
+7. [License](#license)
+
+## How to Install and Run the Project
+
+1. **Clone the repository:**
+```console
+git clone https://github.com/EtherTyper/MathLibrary.git
+```
+
+2. **Build the new library:**
+- Ensure you are in the MathLibrary directory using the command
+```console
+cd MathLibrary
+```
+- Run the following command in the terminal to compile and install the new library to your local Maven repository:
+```console
+  mvn install
+```
+3. **Add dependencies:**
+- Add the following code to the **<dependencies>** section in your pom.xml file:
+```XML
+<dependency>
+  <groupId>mathLibrary</groupId>
+  <artifactId>MathLibrary</artifactId>
+  <version>1.0</version>
+</dependency>
+```
+4. **Update project dependencies:**
+- If you are coding your project using an IDE such as IntelliJ IDEA or NetBeans, update the dependencies accordingly to ensure the new library is available for use.
+
+5. **Import and use MathLibrary:**
+- Once the library is recognized, you can import classes and functions available in MathLibrary for mathematical computations in your Kotlin project.
+
+## How to Use the Project
+
+Detailed instructions and examples are provided in the src folder, categorized into subdirectories based on each mathematical topic.
+
+## Project Structure
+
+The project is structured as follows:
+
+- **applications:** Contains specific applications of the MathLibrary, such as electrostatics, mechanics, and quantum computations.
+- **core:** Core mathematical functionalities, including complex numbers, linear algebra, transformations, and vectors.
+- **tests:** Unit tests for various components, covering complex numbers, matrices, quantum computations, vectors, and more.
+
+## Testing
+
+The tests directory located under **/MathLibrary/src/tests** includes comprehensive unit tests for different mathematical components. Execute the tests by running the corresponding main functions in the test files. Feel free to write additional test cases.
+- **AllTests.kt:** Executes all unit tests in one go.
+- **ComplexTests.kt, MatrixTests.kt, QuantumTests.kt, VectorTests.kt:** Individual test files for specific components.
+
+## How to Contribute to the Project
+
+If would like to contribute to the MathLibrary functionality by implementing additional features or fixing errors, follow the steps below:
+
+1. Fork the MathLibrary repository.
+2. Implement additional changes.
+3. Initiate a pull request.
+
+Alternatively, you may [create an issue](https://github.com/EtherTyper/MathLibrary/issues).
+
+## Credits
+
+Project by Eli Joseph Bradley
+
+## License
+
+This project is licensed under the terms of the [License](LICENSE).