docs: list subjects on doc home & add pre_algebra example

ladderz/src/lib.rs

@@ -2,7 +2,11 @@
 //!
 //! Implementations of mathematical and technical concepts in Rust.
 //!
-//! View [the modules section](#modules) for the various implementations based on the subject.
+//! ## Subjects
+//!
+//! The modules for currently supported subjects are:
+//!
+//! - [`pre_algebra`]
 //!
 //! # Example
 //!
@@ -89,4 +93,20 @@
 //! Great! We've successfully used the `ladderz` crate to get the factors and factor pairs of a positive integer in sorted order.
 
 /// Various pre-algebra implementations including factor pairs, factors, multiples, and more.
+/// 
+/// # Example
+/// 
+/// ```rust
+/// use ladderz::pre_algebra::get_factors;
+/// 
+/// fn main() {
+///     let x: u32 = 10;
+///     println!("The factors of {x} are {:?}.", get_factors(x));
+/// }
+/// ```
+/// 
+/// ```console
+/// The factors of 10 are {1, 5, 2, 10}.
+/// ```
+/// 
 pub mod pre_algebra;

ladderz/src/main.rs

@@ -0,0 +1,6 @@
+use ladderz::pre_algebra::get_factors;
+
+fn main() {
+         let x: u32 = 10;
+     println!("The factors of {x} are {:?}.", get_factors(x));
+     }